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The given time series has a cycle component and a trend component. Is it an additive or multiplicative model?
[ "Multiplicative", "Additive" ]
Multiplicative
multiple_choice
11
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Sine Wave", "Additive Composition", "Multiplicative Composition" ]
For a multiplicative composition, the amplitude of the cyclic component will increase or decrease depending on the trend component.
Pattern Recognition
Trend Recognition
601
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null
Which of the following time series is more likely to be an AR(1) process?
[ "Time Series 2", "Time Series 1" ]
Time Series 2
multiple_choice
49
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "AutoRegressive Process", "Stationarity" ]
AR(1) process is a stationary process with a constant mean and variance. You should check if the time series has a constant mean and variance over time. The other option is likely not stationary.
Pattern Recognition
AR/MA recognition
602
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Two time series are given, one with an upward trend and the other with a downward trend. Do they exhibit similar patterns aside from the trend?
[ "No, they have different cyclic components", "Yes, they share a similar pattern" ]
Yes, they share a similar pattern
binary
89
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Sine Wave", "Square Wave" ]
You should focus on the cyclic components of the time series. Do they have similar patterns aside from the trend?
Similarity Analysis
Shape
603
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Is the given time series likely to have an anomaly?
[ "Yes, it's pattern is distorted by random spikes", "No", "Yes, it's pattern is flipped at certain point in time" ]
Yes, it's pattern is flipped at certain point in time
binary
63
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Flip Anomaly", "Spike Anomaly" ]
Anomaly is an observation that deviates from the general pattern in the time series. You should check if the time series has any sudden changes or unexpected patterns. If so, check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
604
[ 0, 0.5063155188370082, 0.9319827400408571, 1.2109503549260734, 1.3037190415807105, 1.204490669279966, 0.9422177347742504, 0.5753630870759894, 0.18131840762685036, -0.157603345370517, -0.36906622217854845, -0.4038037718788978, -0.2445360543944174, 0.09090276597539115, 0.5527923262487417, 1.0685252328806645, 1.5557486822584254, 1.9372699577724413, 2.155027973720629, 2.1806020777401534, 2.0203560645138703, 1.7142863567812472, 1.3287828278503182, 0.944612525056746, 0.6423011876396497, 0.4875584403269069, 0.5193846388103984, 0.7430119760347088, 1.1289574781706815, 1.618359293858454, 2.133630431719054, 2.592501666266616, 2.9229119077040826, 3.0760509438309267, 3.035193874853739, 2.818728247059232, 2.476825987401832, 2.0823625042816145, 1.7177265575329748, 1.4599082534349255, 1.3665641723899493, 1.4655817801813331, 1.7500319187043396, 2.179422953260579, 2.687029581243525, 3.191969819914612, 3.6138442913323603, 3.8872881579251866, 3.9738018720496626, 3.868719425636651, 3.602052877232941, 3.2330603007396688, 2.839520333354631, 5.1650476223161625, 5.497782452512199, 5.8907318947809815, 6.261781224056652, 6.532779539888327, 6.643684737426592, 6.563430865651849, 6.29555092856155, 5.877537426907397, 5.374056379629698, 4.865243057413283, 4.432197849372375, 4.142307447523246, 4.037048150419253, 4.124478834616536, 4.377782333283721, 4.740119226044119, 5.134915525329737, 5.479722233036673, 5.701138248378006, 5.748095645916647, 5.601102746591831, 5.275772026331829, 4.819994326232466, 4.305270819893247, 3.813771613891157, 3.423463318073698, 3.193997430365113, 3.155913676682215, 3.3051124541879107, 3.6035968414645057, 3.986349875012483, 4.373102335124093, 4.682861123385388, 4.84856865905639, 4.829240007735228, 4.61738097513128, 4.240344523436535, 3.7553800048677703, 3.2392712794434106, 2.7744391723330057, 2.4340236651822, 2.2686458795017206, 2.297245875196363, 2.503654582605545, 4.9637435479779075, 4.941297981624537, 5.112766068138186, 5.458105429814939, 5.925803749022075, 6.442202272267243, 6.924827722243511, 7.297319600111713, 7.503251101630241, 7.516342121794177, 7.3452158388371895, 7.031837956707, 6.643921096296394, 6.262669107377924, 5.9680795271501, 5.824464376080616, 5.868809963636647, 6.104082528126577, 6.498691360546689, 6.992206584667176, 7.506296700183376, 7.9589062414855, 8.279107457852207, 8.419937925945206, 8.366900542921847, 8.140587438609103, 7.792952890117788, 7.397909825041928, 7.037951905013582, 6.789222533946849 ]
null
Given that following time series exhibit piecewise linear trend, how many pieces are there?
[ "1", "2", "4" ]
2
multiple_choice
5
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Piecewise Linear Trend" ]
Check if the time series values increase or decrease linearly over time with different slopes. The slope change could be both positive and negative.
Pattern Recognition
Trend Recognition
605
[ -0.09777782109588512, -0.00577510215628306, -0.05868197779243041, 0.03672717951612506, 0.05481285056645957, 0.11682044039573895, 0.20295458746995113, 0.028840537745921248, 0.19609653558839296, 0.09046079509584469, -0.05954630346061596, 0.28083123584886216, 0.33907635852736373, 0.18305092167066597, 0.13943832983554028, 0.11263788690529365, 0.10270215550141873, 0.2794856372927274, 0.1660067477012747, 0.3444466107586851, 0.18985743209524097, 0.1544550807480999, 0.14487826316738361, 0.1399552606172233, 0.2750600113153939, 0.10351465271710439, 0.16044879939739642, 0.384049369843245, 0.1654647357048064, 0.3565087185143721, 0.07325560469340509, 0.43388404958917803, 0.17117072099696443, 0.21987309008035943, 0.38486528175458407, 0.35319039690487264, 0.4249668866216647, 0.21696043961454267, 0.3254247211350625, 0.3017160006754889, 0.2617235013094065, 0.44165068650480166, 0.4856846448415608, 0.36701143920494417, 0.5622877491667307, 0.3407651566773957, 0.5785004707070504, 0.494196203797289, 0.32493413880207755, 0.6547618435859618, 0.42148022308670835, 0.5957583098953724, 0.49913000765500676, 0.5313277774353429, 0.5933228925675068, 0.5971058924932926, 0.48762467726216235, 0.5843244526964841, 0.5861364375005911, 0.5711511321277816, 0.5387819183040004, 0.5895886145345143, 0.7745047653627917, 0.5575665150599062, 0.7077279922517429, 0.5095713971538852, 0.467869362587467, 0.868106552605251, 0.5789348270670851, 0.5661495427713319, 0.5533867631000005, 0.6190597458442487, 0.503576565926775, 0.5288835409949285, 0.32587031518776677, 0.514585286012074, 0.37698266575808437, 0.4522987590552354, 0.19807830464078824, 0.4170740486209789, 0.11433224318119428, 0.29539612088926925, 0.1368982981171361, 0.35522291910635895, 0.2833120238731036, 0.18377208472569811, 0.3887574188074183, 0.14011575414480698, -0.08887119039665398, 0.25007748551307984, 0.0065198994593793635, 0.08114459637389979, 0.10037669265526591, -0.005822245746197774, 0.07167016989179104, -0.035019470953666115, 0.10621282555933724, -0.04843422925497659, 0.06192072547265344, 0.15957264529578274, 0.10607494117208771, 0.004132384202923242, -0.10210448915069109, -0.0028472564422414616, -0.10387109120699833, -0.029721043615927478, -0.23689612195717033, -0.00017570530409645457, -0.09311436536213623, 0.10888143561167604, 0.003101703069241013, -0.08641996019871617, -0.170972161937369, -0.24706751166256902, -0.09540035651477925, -0.22812247587595424, -0.10387324417494337, -0.19616160182203513, -0.21097841619637753, -0.20785972695034804, -0.3748092442166902, -0.40059438548608706, -0.41958591666083755, -0.22469949106270637, -0.439555552027943, -0.4426335748214196, -0.32230010203036197, -0.41679093791695215 ]
null
Both time series have a cyclic components. Which time series has a higher amplitude of the cyclic component?
[ "Time series 1 has higher amplitude", "Time series 2 has higher amplitude" ]
Time series 1 has higher amplitude
binary
84
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave", "Amplitude" ]
Amplitude refers to the height of the peak and the depth of the trough in the cyclic component. You should check the height of the peak and the depth of the trough for both time series.
Similarity Analysis
Shape
606
[ 0.2054092441435975, 1.3057765271770714, 2.561863353686122, 3.820889327229425, 4.955303175862743, 6.046667807803028, 6.933547642963661, 7.80043349748639, 8.36091324089049, 8.988152838995038, 9.534022264024294, 9.634105172470342, 9.637281281415158, 9.696653889292032, 9.073070219771584, 8.64188277247148, 8.31951131706945, 7.413020171361012, 6.524765134018568, 5.468068049127753, 4.589999618952239, 3.496681210786696, 2.1922039702457274, 1.132831276868699, -0.0320516081665578, -1.0853590139686264, -2.279604546032479, -3.021717029323701, -3.9368092954179605, -4.830060632520089, -5.448471867235103, -5.927710080695547, -6.322516446654751, -6.455276270621611, -6.435259017016746, -6.073974689642829, -5.7993246606841495, -5.296152573326621, -4.693520913488814, -4.039747681440117, -3.0003799806372213, -1.8547145650473602, -0.9392150290320828, 0.4619615204311677, 1.8935799808598095, 3.058839904631104, 4.390188465449545, 5.547904311542105, 6.858039007400077, 7.860071582316773, 9.09628077970011, 10.06164239686524, 10.881852677749134, 11.703116009517375, 12.085795303625103, 12.52904354813415, 12.798788238071246, 12.75790455400419, 12.785303833367477, 12.325851453862654, 12.17744414958135, 11.501857404378988, 10.731464878196366, 9.863531287210508, 8.98148931980554, 8.04585986850648, 6.9392034567745915, 5.67902920805933, 4.51115392253098, 3.5122738533366227, 2.2533665806796446, 1.2617971045149758, 0.27158266519220803, -0.6123924219043642, -1.3479968126012987, -2.22114894303219, -2.8036773754263105, -3.0323360770234338, -2.9954144415103015, -3.0050421082609664, -2.885566861673593, -2.780441613519908, -2.467408162609376, -1.8948798859288865, -0.947439410368222, 0.001048138794310649, 1.1740377788320102, 2.2517400034239863, 3.3862966715385685, 4.529031717482135, 5.809434811435674, 7.227994582537337, 8.555279708404843, 9.77030209489119, 10.813085391751857, 12.085439834090572, 13.065267672347899, 13.79842645269882, 14.574732859511595, 15.3214910761455, 15.670279952392521, 16.12821075313032, 16.12550674832913, 15.96268645070196, 15.778750271039344, 15.392835297096633, 14.767647418750604, 14.06238532396119, 13.410730552113561, 12.502912194641814, 11.466563971140413, 10.476424003100245, 9.14255725842523, 8.212274694819722, 6.802731565673779, 5.66298922126696, 4.5062965351775, 3.624591649905282, 2.695437360341984, 1.9839854415857068, 1.2673891290947608, 0.5759886326866648, 0.26091459239508175, 0.029551274952584992, -0.17690525621927025, 0.006724393455487948, 0.30135791207379475, 0.9610100099695397 ]
[ 0.01914507159573526, 0.38234762332969713, 0.46735996720675443, 1.0085628182995106, 1.2496056720610427, 1.0985528732430896, 1.3484704751070276, 1.5275932553696552, 1.54023771420969, 1.3485359409276216, 1.2766901749063067, 1.0990684924757714, 0.9949243214517259, 0.9165706544829998, 0.5357235046263966, 0.546819560607389, 0.23427058534180162, 0.13711664913073307, 0.26625163047902933, 0.2983198410185836, 0.3748240799081927, 0.302380402514449, 0.5876213856650404, 0.9646559216378088, 1.1715719038431138, 1.3688528421263875, 1.8400030762069515, 2.034637526676529, 2.5767282260586795, 2.8085862572305493, 2.9255225109607927, 3.157668964926157, 3.1244772267525813, 3.2290719191204396, 3.27476545970735, 3.0713775925092053, 2.895219551126749, 2.589721730501469, 2.5703752688769885, 2.473373330672404, 2.3069223313878258, 2.1077185511284666, 1.8848660000910815, 1.670809733619562, 1.8043767870627787, 1.8695589237040782, 1.976626286503251, 2.236968446226501, 2.5940279332600418, 2.67201568793591, 2.93412050510948, 3.2440912258070584, 3.5998369390663765, 3.810006339563003, 4.18394777393087, 4.456937591047058, 4.623117532578052, 4.781061780515594, 4.850632399349144, 4.640402192878657, 4.8332819343256315, 4.6029450619575645, 4.419231410954576, 4.247822202697784, 4.215879599349286, 3.964365100823939, 3.6474047212750698, 3.7214172995175123, 3.4291090097429135, 3.5378808695730886, 3.556800231447265, 3.6921438613393383, 3.913646182358068, 3.7881585786431433, 4.158354802355062, 4.414357066366894, 4.790389861013715, 5.085869449413968, 5.343491711588501, 5.631319065555929, 5.828774820414096, 6.2605893830740245, 6.3761187338724605, 6.531196008775327, 6.455785827922074, 6.40779691694654, 6.29625621698194, 6.322600703615394, 6.028301746172484, 6.138827239620874, 5.635572688970394, 5.611920998973837, 5.580096357646661, 5.356372882607864, 5.232791662794382, 5.091615239194683, 5.08351223203334, 5.393819009904163, 5.622657071448494, 5.638092129038357, 5.824037235731701, 5.982691121923958, 6.442088561795165, 6.8467787249173195, 7.3272097342609515, 7.520317530419542, 7.732558161436682, 7.86340344448199, 7.990623438479086, 8.274372538486817, 8.176911350609776, 7.910293072104354, 7.96367869221671, 7.811722173976623, 7.67736232200357, 7.604482114802627, 7.35032287788648, 7.1780470324266945, 7.167946460656307, 6.85685763866687, 7.052367871208011, 6.795333134587916, 6.929084114345155, 7.0113753500440446, 7.229553847675044, 7.491027677394308, 7.761110201125072, 7.943031474300348 ]
Is the given time series likely to have a non-stationary anomaly?
[ "Yes, due to trend reversal", "Yes, due to cutoff", "No, the anomaly is stationary" ]
Yes, due to trend reversal
binary
69
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Stationarity", "Linear Trend", "Sine Wave", "Cutoff Anomaly", "Spike Anomaly" ]
Non-stationary anomaly refers to the anomaly that changes over time. You should check if the time series has a constant mean and variance over time. If not, you should check the type of anomaly based on the given definitions. For example, spikes anomaly are stationary.
Anolmaly Detection
General Anomaly Detection
607
[ 0.029307247329868127, 0.05888483011437019, 0.4472173949484896, 0.4383432078421997, 0.40214953794776304, 0.7172552204484178, 0.6844516644793097, 0.990948263793294, 1.1584193332367962, 1.0908115154178917, 1.399537332094502, 1.4747977837807265, 1.646045679003533, 1.8838389331864855, 1.7999407952378106, 1.8794259623193557, 1.9961681077095592, 2.133858494092575, 2.3380493235647153, 2.5101946639047967, 2.6340685182731414, 2.819437735160749, 2.868339571361944, 3.1427127618068917, 3.101213642684372, 3.5300162145841365, 3.450886004618682, 3.43292348611756, 3.5418699638700843, 3.827526427117521, 3.887252878977624, 4.111319178836425, 4.217562863801578, 4.293276181995544, 4.346199673371396, 4.409714294626658, 4.646867493805549, 4.907478840361605, 4.973568307259286, 4.957905026892074, 5.2301169692653975, 5.38165058657017, 5.385053076894179, 5.619131303025853, 5.739899636192907, 5.750101706482252, 6.030497444217149, 6.181117132736151, 6.363663776333863, 6.491058829136832, 6.37823165905464, 6.552536063775843, 6.8281420664052295, 6.95833710669259, 7.088783252148982, 7.552871604500855, 7.355007478421707, 7.541794963287457, 7.6539585475357255, 7.754017468233991, 7.787671390556384, 8.025415208986752, 8.002555737400675, 8.186476370097438, 8.161621875988528, 8.079648810978734, 8.164230419976114, 7.607341210318252, 7.72399691488354, 7.355402474995786, 7.33078404180447, 7.348175454348813, 7.107011562830285, 6.85411224939647, 6.751659522532067, 6.752452834620193, 6.472759562823674, 6.428745251222248, 6.272959742523094, 6.064545690040794, 6.205403300002571, 5.915703959570502, 5.511100964941602, 5.5935638213529675, 5.370042909667848, 5.3827680558929725, 5.0795758148387415, 5.008657410803984, 4.931932949117383, 4.829312906905011, 4.484010913051084, 4.4318935964412285, 4.2791523551778905, 4.122617129305278, 4.225798642859421, 3.9510545561960693, 3.645771155935132, 3.724948912342776, 3.706681503607224, 3.4590155762297377, 3.065135219847884, 3.029951975425323, 3.0663696638992732, 2.730214768687395, 2.7066668243325585, 2.6010514531295317, 2.292198166897452, 2.2402418447177426, 1.7833708125856775, 1.8663619487278182, 1.8048470639905936, 1.566628727202087, 1.7159513420603978, 1.2709992401398342, 1.2313120955348613, 1.1496937682018311, 1.142050205648496, 0.7156398278926028, 0.836845584494705, 0.58285568164983, 0.3449846767117386, 0.3506490555115231, 0.18564784391120623, -0.032976647093357916, -0.10467158460981424, -0.2888799865263298, -0.3776937260463667, -0.4615292268507245 ]
null
The following time series has an anomaly with random large fluctuations. What is the likely pattern of the time series without the anomaly?
[ "Sine wave with linear trend", "Sawtooth wave with linear trend", "Square wave with log trend" ]
Sine wave with linear trend
multiple_choice
66
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Sawtooth Wave", "Square Wave", "Linear Trend", "Log Trend", "Spike Anomaly" ]
Spikes anomaly bring constant large random fluctuations. Can you check the place where the spikes disappear and try to recover the original pattern?
Anolmaly Detection
General Anomaly Detection
608
[ -12.452104230873235, 2.1267073022323357, -0.9228894009692994, 1.2109503549260734, 1.3037190415807105, 1.204490669279966, 1.9502264948931458, -8.908782553252887, -4.241379546975837, -0.157603345370517, -0.45606480427161616, -8.252117258659943, -0.2445360543944174, 0.09090276597539115, 0.5527923262487417, 1.0685252328806645, -1.5356496243127384, 1.9372699577724413, 2.155027973720629, 0.9658232362278008, 2.0203560645138703, 1.7142863567812472, 1.3287828278503182, 0.944612525056746, 4.240729329667878, 0.4875584403269069, -3.1167456336793613, 4.368847080834606, 1.1289574781706815, 8.109043030302752, 2.133630431719054, 2.592501666266616, -1.207070837642327, 3.436668807750488, 0.7211203109058282, 2.818728247059232, 2.476825987401832, 6.1792759531889425, 1.7177265575329748, 1.4599082534349255, 1.3665641723899493, 1.4655817801813331, 4.265312283681658, 2.179422953260579, 5.597243791909061, 3.191969819914612, 1.7929824431582118, -0.2655409498709993, 3.9738018720496626, 6.476790030506812, 8.497495174398146, 5.701969050917183, 9.235803237725497, 14.411685626779512, 0.7754653391866557, 2.2686458795017206, 2.4340236651822, 2.7744391723330057, 3.2392712794434106, 3.7553800048677703, 4.240344523436535, 10.32513524410166, 4.829240007735228, 4.84856865905639, 5.50278373842746, 4.373102335124093, 8.907523789474778, 3.6035968414645057, 6.749736710258103, -1.3204371117837645, 3.193997430365113, 3.423463318073698, 7.424770722620368, 10.25369693379045, 6.810727468169816, 9.686646080253603, 5.601102746591831, 5.748095645916647, 5.701138248378006, 1.8602656832947315, 9.255672270263693, 4.740119226044119, 4.377782333283721, 4.124478834616536, 4.037048150419253, 4.582043603841821, -2.1634872065636914, 4.70330770207467, 5.374056379629698, 5.877537426907397, 6.492426815145115, 5.919660756309406, 6.061535223762465, 10.00479076110842, 6.261781224056652, 9.534898935078562, 5.497782452512199, 5.1650476223161625, 4.9637435479779075, 4.941297981624537, 8.442998835352391, 5.458105429814939, 8.880695879779463, 14.709933211530789, 6.924827722243511, 7.297319600111713, 12.462299960410391, 7.516342121794177, 7.3452158388371895, 7.031837956707, 6.643921096296394, 12.74392122415847, 10.212872635077506, 2.992305582482698, 7.296599347737308, 7.310320619037616, 6.498691360546689, 11.081262705451131, 14.247134406119518, 7.99317128202752, 14.52060433714162, 8.419937925945206, 8.366900542921847, 8.140587438609103, 7.792952890117788, 0.3596855702831059, 7.811867097723121, 6.789222533946849 ]
null
What is the most likely variance of the given time series?
[ "1", "0.84", "varies across time" ]
0.84
multiple_choice
42
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Variance" ]
Check the degree of variation of the time series over time.
Pattern Recognition
First Two Moment Recognition
609
[ 0.7348008179743784, -0.4497263243608542, 0.013366021901534617, 0.6252858619263374, -1.3871590238655804, 0.5155608077256916, 0.9692974955932279, -0.04248459678531283, 0.5677795903300855, -0.4742894084034421, -0.017315930818076662, -0.2421765104881608, 0.4266543480216287, -0.12986919179622, -1.489708944265407, -0.6703602131034607, 1.7385647128182509, 0.6056890002893836, -1.8186527553265392, 1.0019405467518132, -1.1415072282073622, 0.7343311370383915, 0.9433447834457027, 0.03682381410679211, -0.7319853595466108, -0.7526009323366277, 0.4398481270185911, -1.0461734405932632, -0.6570371280185727, 0.5183015845655141, -0.5207866173733801, 1.3776661899512963, -0.9739475127677877, -2.9469605662151777, -0.5613944785006248, 0.2251455250282046, 0.6805547760565815, -0.19619934922835292, -0.21654578141752917, 0.06440274546681006, 1.4050173528641408, 0.24652929234992188, -0.45161978738831593, 1.7953201541350308, 0.014531154654385339, -1.701325906812374, -1.428502689880328, 0.28202821736762634, -1.712397226899418, 0.3815988876306759, -0.7967640783169563, 1.1610026995988887, 0.13896426528890765, -1.3572603559646577, 0.6611072865665832, 1.0365137404052924, -0.9204037075645116, -0.497979660188386, 0.4647604154144892, 0.3710608346978994, 1.93968475177863, 0.7817745206348015, 1.9994794411444108, -0.19566597229945445, 0.5080955851050292, -0.5621069212238173, -0.5743241788450467, 0.12082084995906844, -0.3722411223744163, -2.1085302671729353, -0.6932368474432958, 0.7588830010450787, -0.15782793428770872, 0.036886968788679794, -0.6903891759749304, 0.33184440199598086, 1.3286029266543924, 1.2772415392755612, 0.3736543796282938, -0.7920139428022898, 1.5276988006998535, 1.025139532743379, -1.3434445220933966, -1.5011505420698212, -1.2239765246422991, -0.451608000819464, 0.8397972312567696, 0.827641760185384, 0.32766922045017466, -0.08241655644667362, 1.9412264063453066, 0.06168227437535715, -0.20178817698574067, -0.1796994548466081, 1.9982767379753774, 0.7028963890616607, -0.830556725908655, -0.9302685890388647, -1.584174537428931, -0.20737406466907, -1.375623969292187, -0.9776832858503163, 0.8717543992370945, 0.8316545308312491, 1.1597125419581389, -1.1358480103804909, -0.9263322135841615, -0.5712613819339685, 1.4710533835256148, 0.10343357255239566, 1.4096190420916346, 0.6349273226168268, -0.08579836393532857, 0.2691459047486774, -1.5409947181731602, -1.7713287388094463, 0.10144925689293234, 0.1464026795933604, 1.5912872081209097, -1.1155260006645111, 0.33439030678101217, 0.6562353773895919, 0.456069925601177, 0.9932560616964234, -0.35841091989480467, 0.7712470610597815, 0.48614816880518413, 1.014191104379877 ]
null
The given time series is a sine wave. What is the most likely amplitude of the sine wave?
[ "1.0", "7.47", "7.24" ]
7.47
multiple-choice
22
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Amplitude" ]
Check the distance between the peak and the baseline.
Pattern Recognition
Cycle Recognition
610
[ -0.01815589215952325, 1.387244482436273, 2.791324033183596, 3.988450836970891, 4.97561299760635, 5.987615061415588, 6.930850240877099, 7.398164190317643, 7.375276975553273, 7.472700390291321, 6.963456941736418, 6.643665214802623, 5.716439160124942, 4.7714221201476565, 3.32177065277246, 2.2525798162876387, 0.7972267565357171, -0.532254799504861, -1.919258138223102, -3.3253486325910506, -4.593693244441745, -5.494726671904322, -6.417933935462643, -7.108456799343326, -7.470639967862862, -7.6191544929182875, -7.347318606043249, -6.749191530167643, -6.158835595142879, -5.325229800782839, -4.098313424192281, -3.0187207447909086, -1.577331871920579, -0.1993110391914834, 1.3085879736307355, 2.440837038489523, 3.7882281530821045, 4.84519802903549, 5.939189838028929, 6.828480092985265, 7.158422929566134, 7.40098115358322, 7.5150373843498715, 7.244136166766391, 6.5818629842322585, 5.876255389996159, 4.708857072233095, 3.790373736032393, 2.572471674229582, 1.0301924016186068, -0.644970907345362, -1.8913129864279696, -3.1073301046111226, -4.430241854354494, -5.322976380543209, -6.258012820482083, -7.027556415666073, -7.344254338021732, -7.5639199321642625, -7.351777891882888, -6.9849460833187145, -6.159453058557496, -5.187649501885512, -4.471047792305604, -3.293708395580489, -1.7881311028945504, -0.5144308101611914, 1.0560607425745705, 2.502652312485143, 3.866420852666242, 4.893084262498911, 5.834800082780885, 6.4274910417006685, 7.161545648137892, 7.44289974282568, 7.509827906161164, 7.118197516960866, 6.630821233336196, 5.772432838123549, 4.724682191200292, 3.6988725566600213, 2.3719654305339826, 1.1912428998203766, -0.30718419012768816, -1.7129781220189464, -3.10187404464615, -4.563250004753167, -5.173656456476277, -6.31804680463085, -6.929785748827951, -7.457500486359983, -7.376041710379822, -7.3520890200353195, -7.078069770954396, -6.4127674968074, -5.355251735024736, -4.481807896121745, -3.283647950422073, -2.033460692388344, -0.7330751294199006, 0.8555813803647367, 2.2880767628865972, 3.66853556102803, 4.509148555016392, 5.627125620934894, 6.4813471377425715, 7.104323913104505, 7.400611514953951, 7.447447054820964, 7.277388699386112, 6.663674261798188, 6.122610995452722, 5.131499243797562, 3.9326421350907474, 2.8589969014878807, 1.4920326336978058, 0.01923605420906689, -1.783697754178962, -2.6785901470587272, -4.009921338661173, -4.995003319980193, -5.991803813543081, -6.658288913054028, -7.184371493599837, -7.332663901729891, -7.195595268786988, -7.0356058862484385, -6.623630641246309 ]
null
In which part of the time series does the anomaly occur?
[ "Middle", "Beginning", "End" ]
End
multiple_choice
77
medium
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Linear Trend", "Spike Anomaly", "Cutoff Anomaly", "Wander Anomaly" ]
Identify where in the time series sequence the unusual pattern or disruption occurs.
Anolmaly Detection
General Anomaly Detection
611
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null
You are given two time series following similar pattern. One has an anomaly and the other does not. Which time series has the anomaly, and what is the likely type of anomaly?
[ "Time series 2 with cutoff anomaly", "Time series 1 with flip anomaly", "Time series 1 with speed up/down anomaly" ]
Time series 1 with flip anomaly
multiple_choice
74
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Linear Trend", "Speed Up/Down Anomaly", "Cutoff Anomaly", "Flip Anomaly" ]
You should first identify the time series with the anomaly. Remember, both time series share similar pattern. Then, you should check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
612
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The given time series has multiple trends followed by each other, what is the correct ordering of the trend components?
[ "Linear -> Exponential -> Log", "Log", "Linear -> Exponential", "Exponential -> Linear -> Log" ]
Exponential -> Linear -> Log
multiple_choice
9
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend", "Log Trend" ]
Identify the different components first, and then check the assignment of each component.
Pattern Recognition
Trend Recognition
613
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null
You are given two time series following similar pattern. Both of them have an anomaly. What is the likely type of anomaly in each time series?
[ "Time series 1 with cutoff anomaly and time series 2 with flip anomaly", "Time series 1 with cutoff anomaly and time series 2 with speed up/down anomaly", "Time series 1 with flip anomaly and time series 2 with speed up/down anomaly" ]
Time series 1 with cutoff anomaly and time series 2 with speed up/down anomaly
multiple_choice
74
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Sawtooth Wave", "Linear Trend", "Log Trend", "Cutoff Anomaly", "Flip Anomaly", "Speed Up/Down Anomaly" ]
You already know both time series have an anomaly. You should treat them separately and check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
614
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Two time series are given. One has noise and the other does not. Do they have similar pattern?
[ "No, they have different pattern", "Yes, they have similar pattern" ]
No, they have different pattern
binary
83
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Sawtooth Wave" ]
Noise refers to the random fluctuations in the time series. You should focus on the overall pattern of the time series. Pattern refers to the general shape of the time series. In this case, you see both time series have cyclic patterns. Do their behaviors at peak and trough look similar?
Similarity Analysis
Shape
615
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The following time series has an anomaly. What is the most likely type of anomaly?
[ "Scale: the pattern is at obviously different scale at certain point in time", "Cutoff: the pattern of time series disappeared for certain point in time", "Wander: the pattern deviates off for certain point in time" ]
Wander: the pattern deviates off for certain point in time
multiple_choice
66
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Cutoff Anomaly", "Scale Anomaly", "Wander Anomaly" ]
Anomaly is an observation that deviates from the general pattern in the time series. You should check if the time series has any sudden changes or unexpected patterns. If so, check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
616
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null
Is the given time series likely to be a random walk process?
[ "No", "Yes" ]
Yes
binary
53
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Red Noise" ]
Random walk is a non-stationary process with a constant mean and variance. You should check if the time series has a constant mean and variance over time. Another important property is that the noise is correlated over time. Does the time series seem to have these properties?
Noise Understanding
Red Noise Recognition
617
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null
You are given two time series which both have upward trend. Which time series has a higher slope in terms of magnitude?
[ "Time series 2 has higher slope", "Time series 1 has higher slope" ]
Time series 2 has higher slope
binary
81
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend", "Sine Wave", "Sawtooth Wave" ]
Slope refers to the steepness of the trend. You should check the direction of the trend and the steepness of the trend. If the trend is upward, you should check the magnitude of the slope.
Similarity Analysis
Shape
618
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Two time series are given. Both of them have a noise component. Do they have the same type of noise?
[ "Yes, they both have Gaussian white noise", "No, they have different noise" ]
No, they have different noise
binary
88
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Gaussian White Noise", "Red Noise", "Additive Composition" ]
When a white noise is added to a time series, it is expected the random fluctuations have similar amplitude or distribution. Random walk, on the other hand, can result in very different noise patterns.
Similarity Analysis
Shape
619
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Does the trend of the time series change direction?
[ "No", "Yes" ]
No
binary
12
medium
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend" ]
Check if the overall direction of the time series changes at any point.
Pattern Recognition
Trend Recognition
620
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null
Are the given two time series likely to have the same underlying distribution?
[ "Yes, they have the same underlying distribution", "No, they have different underlying distribution" ]
No, they have different underlying distribution
binary
91
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Gaussian White Noise", "Red Noise" ]
You should focus on the underlying distribution of the time series. You can start from analyzing whether both time series are stationary. Then, you can check if they have the same mean and degree of variation from mean.
Similarity Analysis
Distributional
621
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Seasonal stationarity refers to a time series where statistical properties remain constant within seasons but may vary between seasons. Does the time series exhibit seasonal stationarity?
[ "Yes", "No" ]
Yes
binary
37
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Stationarity", "Sine Wave", "Linear Trend", "Gaussian White Noise" ]
Determine if the statistical properties of the series are constant within seasons across years.
Pattern Recognition
Stationarity Detection
622
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null
Is the given time series a white noise process?
[ "No", "Yes" ]
No
binary
51
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Gaussian White Noise" ]
White noise is a stationary process with a constant mean and variance. You should check if the time series has a constant mean and variance over time. Another important property is that the noise is uncorrelated over time. Does the time series seem to have these properties?
Noise Understanding
White Noise Recognition
623
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null
The given time series has a decreasing trend, is it a linear trend or log trend?
[ "Linear", "Log" ]
Log
multiple_choice
8
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Log Trend" ]
Check if the slope of the time series is constant or changes over time.
Pattern Recognition
Trend Recognition
624
[ 0.01764841836629528, -0.15277338462531553, -0.3703353285217093, -0.583788160620018, -0.5271975583675841, -0.7794991157895692, -0.987069909278186, -1.133897425352378, -0.885764980458279, -1.0267340956585467, -1.1507081049706085, -1.2699158752370612, -1.3410374933344253, -1.4543116235195817, -1.445239099178486, -1.6665536524468747, -1.577988112433622, -1.5829460664692458, -1.5361831796877703, -1.644517633287487, -1.6025847665109532, -1.587057742919179, -1.6545177441650158, -1.750229725299507, -1.831723890164461, -1.9653925024848502, -1.8265784966165193, -1.7647867030535012, -1.9297355039872226, -1.8024617139222396, -2.1760985525810983, -2.1674743449139626, -1.9942637784921597, -2.0803327975801156, -2.0016527618956186, -2.160174862574634, -2.2703830867247574, -2.229294958103345, -2.3849752608912307, -2.367785185404345, -2.180374050432715, -2.2125285042630334, -2.2852139385073222, -2.5148680349644557, -2.3994045420751964, -2.5064440785230326, -2.2862636108849834, -2.4818708805712135, -2.5512790777924073, -2.4585684130389986, -2.544058669632246, -2.349828157684287, -2.589519074988248, -2.6734837109802534, -2.7660733647648783, -2.570790238103803, -2.6405523283294707, -2.7436248920145307, -2.497923069730134, -2.5659770225173695, -2.65113165850848, -2.5272456988253027, -2.6125605536766683, -2.7760098991168443, -2.8123374267599677, -2.641095649985798, -2.6975288671548845, -2.734261723987407, -2.849761971892498, -2.71800322295733, -2.867848881173349, -2.815818819650873, -2.674071777831957, -2.897825076012789, -3.001849829865229, -2.9624528711038742, -2.770257559776216, -2.856549558982589, -2.9070953351323765, -2.957155215526112, -2.869604884934628, -3.014806571149004, -2.9109481585588783, -3.0261253580769103, -3.054120612404672, -3.0393307053835406, -3.024225340805829, -3.0025482978714217, -2.9849811851768466, -3.3881080395825793, -3.1106670886185155, -3.0795777326436253, -2.900323740736887, -3.169132178766725, -3.055049180090892, -2.931919806313296, -3.222712814272242, -3.061912687412758, -3.1913347043003406, -3.1712731492900748, -3.2107298826911372, -3.213122099124005, -2.8771729917068116, -3.0742584028904663, -3.057783562529752, -3.12792651844676, -3.346836765808971, -3.1557187111561538, -3.096844629150068, -3.2983217026877028, -3.1252157192244683, -3.1600052092132165, -3.0538503963716117, -3.2893746783078446, -3.3658271036871086, -3.300627312239264, -3.1292359501433253, -3.4638933935316865, -3.496082467924708, -3.2884308940093594, -3.3496893843382907, -3.312653253850304, -3.2268270314883956, -3.3844848842553814, -3.5243368242215194, -3.1403358795533833, -3.4521950910659784, -3.4660055434272867 ]
null
Given that following time series exhibit piecewise linear trend, how many pieces are there?
[ "2", "4", "1" ]
1
multiple_choice
5
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Piecewise Linear Trend" ]
Check if the time series values increase or decrease linearly over time with different slopes. The slope change could be both positive and negative.
Pattern Recognition
Trend Recognition
625
[ 0.12347256964231687, 0.30535457701747387, -0.014616623815826218, 0.00039719247219058285, 0.36109711519853493, 0.2213539031466578, 0.000565532095485155, 0.20850612890228082, 0.031741527086614596, 0.04631145219733816, 0.196233516160113, -0.1996220023800877, -0.1487027121817682, 0.08794683717822648, 0.0170678225755109, 0.2850670630550914, 0.06706916178546993, -0.014053860390394024, 0.5495973622478025, 0.24216201580330607, 0.31308701727762944, 0.043616522192401974, 0.2264563107494143, 0.3663915964544581, 0.14083598807630687, 0.4468886234065914, 0.2757746602779572, 0.34968128730241765, 0.3055924490889749, 0.7884202897848047, 0.44774754108360987, 0.26369379808091, 0.6371484072484301, 0.2626162475930527, 0.5501802015541715, 0.1517909050487689, 0.28718501169984295, 0.5929241826215887, 0.7111841928635968, 0.6180856878445307, 0.5783807655802187, 0.5580370261610914, 0.34858973036703383, 0.5082315007032034, 0.5726560019084396, 0.8770061461625427, 0.7559974972217448, 0.3694038380063648, 0.7822949310132381, 0.6621132001184625, 0.6214888119866437, 0.8821523588063348, 0.9771010310934662, 0.9731016374837574, 0.650592234307272, 0.7666408327094479, 0.9037490847004909, 1.0415828749723288, 0.7792720905001059, 0.850237269597195, 0.689734226071745, 0.6876121659861882, 1.0855590051013415, 1.204221039774938, 0.9469562330799207, 1.1670038355451144, 1.0596460506424594, 0.8827331259921991, 1.0896215910386249, 1.328942072189199, 1.043918330472812, 1.3640357067244477, 0.5813524366512041, 1.2524640868176353, 1.1273850794371811, 1.068800004530198, 1.1583050535516106, 0.7769212309439022, 1.12895623685005, 1.253922642988859, 1.4825943105771637, 1.1170647890902439, 1.0767485321935217, 1.1502341629548583, 1.4354060039696346, 1.338580054182077, 1.189927819822644, 1.4037768289742893, 1.3394468580415198, 1.5206094296409662, 1.2171253868680258, 1.3035083604707922, 1.3062333362026837, 1.1169956188081942, 1.4674556302389032, 1.4757816743222463, 1.442000708969129, 1.4113159013077206, 1.2012270564818552, 1.4058679376906968, 1.4357350193831382, 1.3631366304308168, 1.5003432028508799, 1.6231272320918522, 1.9206857972500266, 1.6094028464882644, 1.6402310699407394, 1.5919514020813863, 1.255367810451372, 1.631110333960555, 1.6626575414539266, 2.1357681278554246, 1.644526014392969, 1.753693265727415, 1.7046009548704288, 1.503437167425584, 1.9591024790073546, 1.8995956111783439, 1.9220599472720408, 1.6129099598049188, 2.0687050778391614, 1.549050179145835, 1.9431796733774696, 2.2638935177341337, 1.672493518995101, 1.7683792348231606, 1.9103436052598664, 1.81037673925118 ]
null
Is the given time series likely to have an anomaly?
[ "Yes, it's pattern is distorted by random spikes", "Yes, it's pattern is flipped at certain point in time", "No" ]
Yes, it's pattern is flipped at certain point in time
binary
63
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Flip Anomaly", "Spike Anomaly" ]
Anomaly is an observation that deviates from the general pattern in the time series. You should check if the time series has any sudden changes or unexpected patterns. If so, check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
626
[ 0, 1.092560519338032, 2.0510989566479276, 2.7590384013056135, 3.1324215104056043, 3.1308389335060296, 2.7626892521409667, 2.084085766730511, 1.1915524304965692, 0.20945967434282303, -0.7261644439068717, -1.4853405215523632, -1.9610567614229044, -2.083198311845979, -1.8276738641966572, -1.2195515317165957, -0.3297958235584668, 0.7339695496154335, 1.8414706661758835, 2.8567406803999935, 3.655818136756503, 4.1428825858170955, 4.262727186823044, 4.007944783182165, 3.4198920653471307, 2.5833063194681434, 1.6152754802466482, 0.649997216458361, -0.17868909594489857, -0.7547237630477923, -0.9949338450510457, -0.8598594780911275, -0.35889022250660707, 0.4509571423912808, 1.4724602869939698, 2.580846411652931, 3.6400334723306447, 4.520343489835353, 5.115382265014988, 5.355888328217732, 5.2187484551793135, 4.730006232125775, 3.961472056015113, 3.0213758339688517, 2.0402790863209423, 1.1540802240576278, 0.48632514243520353, 0.132125697051944, 0.14577933638664708, 0.533701398617259, 1.2535900501710693, 2.2199325629456634, 3.315136197939528, 4.40483482828533, 5.355378893730856, 6.051232082226029, 6.410010275271343, 6.393205191711882, 6.011196871911949, 5.321902545310392, 4.423237753397334, 3.440371036564522, 2.509431196308093, 1.759787899743845, 1.2972120962852025, 1.19010819435487, 1.4606101060689336, 2.081700155666973, 2.980725872994543, 4.048856903704713, 5.155251064260537, 6.164085597412803, 6.952236731007972, 7.425306255673297, 7.529908999521078, 7.260621783573988, 10.796480486273461, 10.707128452206796, 10.248140996174397, 9.471070277941585, 8.468872209147056, 7.363806717296568, 6.291523611622493, 5.383405536295822, 4.749466365135497, 4.464031092141688, 4.556061214892993, 5.005384920783382, 5.745322779170284, 6.671367162549531, 7.654785627783893, 8.559377554276283, 9.25920288788808, 9.654975303900239, 9.68698595007553, 9.34287553276457, 8.659243081617397, 7.716881985796262, 6.630263409686516, 5.53263599398096, 4.558681360346875, 3.8269830901241297, 3.424591126915546, 3.395690799154847, 3.7358513751476674, 4.3926027954479085, 5.272265511394529, 6.252144414341143, 7.196499615757194, 7.974215219313436, 8.475866204567485, 8.627961887508679, 8.402511938036458, 7.820669780352784, 6.949979127970431, 5.895582061951547, 4.786533065146211, 3.7590004652702564, 2.9385418944350703, 2.423760904683447, 2.2734720989858763, 2.4990454463388043, 3.0629262938775597, 3.8835237206933577, 4.8458309339555665, 5.816395288651696, 6.660689337427482, 10.512759049325949 ]
null
The time series shows a structural break. What is the most likely cause of this break?
[ "Sudden shift in trend direction", "Change in variance in underlying distribution", "Abrupt frequency change" ]
Change in variance in underlying distribution
multiple_choice
72
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Gaussian White Noise", "Sine Wave" ]
You know the time series shows a structural break. Can you first identify the place where the break happens? Then, you should check the type of break based on the given options.
Anolmaly Detection
General Anomaly Detection
627
[ -1.120086361375929, 1.46696509467062, 0.9727780843128846, -1.8984062472582302, 0.19290272359007707, 1.4591891524374634, -3.241974744393895, 1.055202137387204, -1.2868112469937734, 1.1080990899472976, -1.4822445675241178, -3.5050698911366114, -3.160677361402732, 0.09338066940642091, 0.5043794940951949, -1.7561773001908123, 1.2401426105025766, -3.226661698087748, -0.1283265608129216, -2.351785979761924, -1.2658616951056456, 0.09204792692546272, -1.670917440800123, -0.7468044915805573, 1.9542144198483664, -1.1203204472816395, 1.6229089197468562, -2.1938837337980046, 1.028876441029325, 2.799517357070032, -4.799918352450792, -1.5475656638795405, 1.120670506538882, -0.3943128855294621, 0.720762993601862, -1.1729355019204353, 0.16815683242658133, -0.30232422954788263, 2.267825550614201, 0.49408370619019376, 0.6556222844537521, -0.7998625241377432, -0.9469282753139705, -0.840025328930325, 0.766023624055811, -0.8175492614257768, 0.5627409822182207, 4.030415531681939, 1.6917187933214892, -0.6331356856953579, 2.3327500172120956, -0.7924798538173564, -3.9580252582750495, -1.9576973890774618, -3.633066355168078, -0.6826370147878886, 0.03576837861989214, 3.2556309054595034, 0.6348909404925865, -0.42549187361175134, 1.610700515605185, -4.2940111124040365, 0.457562016508299, 1.4970154450662447, -26.086116332444977, 22.833828623792023, 7.811690047769665, -6.250210181729661, 13.301606248643893, 43.85695251457292, 4.8897433927789935, 6.127588170434831, -7.072394869427697, -14.356891826308212, 16.986989271549113, -14.47328933088949, 2.8320887001282014, -7.413718261700252, 10.432418225959758, 7.721505795602143, 20.85239703919379, -8.017376818796928, -3.5375207038333647, -16.7618914185174, -6.791306981520288, 8.53558302885108, 15.618692030791548, -15.706044389990682, 17.71957585183325, 26.78653630238918, 9.209673025637265, 36.508775066816796, -12.938077203608868, -21.722106737982816, -31.685137547962213, 29.40582868242849, 13.704253393754106, 0.460079448326987, 6.7198501193299816, -19.499062933441238, 47.122692906511226, 3.907645802978541, 3.537783133777606, 15.036243531256511, 10.470276939322519, 5.673587871731649, -13.249341849637686, 10.292291243773525, 36.6063165378783, 26.595922279293433, 31.218025493814125, -8.03974942744463, -16.964132995047894, -0.8495485128352589, 2.536567654710013, 21.909236193069336, -30.076032825498874, 30.030885648738135, -1.450633162400136, -6.466481333895342, -17.383863796896932, -29.37445369192165, 16.853321347138852, 2.86476734752653, -22.567297060849217, -22.66277133372077, -4.76707204785277, 32.63273093204427 ]
null
Are the given two time series likely to have the same underlying distribution?
[ "No, they have different underlying distribution", "Yes, they have the same underlying distribution" ]
Yes, they have the same underlying distribution
binary
92
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "AutoRegressive Process", "Moving Average Process" ]
The difference between AR(1) and MA(1) is that AR(1) is a linear combination of past values and white noise, while MA(1) is a linear combination of past white noise values. You should check if the time series exhibit any dependency on the previous values. This could give you a clue about whether the time series is AR(1) or not. Check this for both time series.
Similarity Analysis
Distributional
628
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What is the type of the trend of the given time series?
[ "No Trend", "Linear", "Exponential" ]
Exponential
multiple_choice
1
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend" ]
It would be helpful to check if slope of the time series changes over time.
Pattern Recognition
Trend Recognition
629
[ 0.9371268512521137, 0.6647962237441689, 1.663163982609725, 2.1921275706519854, 0.5500800616218647, 1.0284028771215554, 1.314487116608539, 2.3124357643459312, 0.8323450951757108, 0.7569881230376697, 0.7817501758818668, 1.8944982142657192, 0.9593596006358256, 0.9183743245231253, 1.4897841994855288, 1.5599791398910097, 1.9736717910066077, 1.5171594223850668, 1.6294561226588387, 1.4869246747223948, 0.9227705111627429, 1.5112979448541095, 1.6795243523962253, 1.4640531754796178, 0.9424648620357722, 1.1968131267883722, 1.7851442158281112, 2.3126688184686657, 2.7298440089420684, 1.8401705198708025, 1.6180290592266373, 1.8356112558804096, 1.5451010400398921, 2.5096908784989944, 3.233224673483333, 1.8678685362111085, 1.6689743377505484, 2.820264150350491, 2.529270713841968, 2.5921544371634195, 3.274472484582334, 1.8541172950735683, 1.8984358329246624, 2.5744094045675556, 2.7479603043275618, 2.601177399480854, 4.072854160061981, 2.7526489287706233, 2.6991993547667787, 3.1050600524082235, 3.5982274475329703, 2.821571369958825, 3.1839355640273763, 3.8318949805104565, 3.936198364714569, 3.595909881743499, 4.776390707160947, 4.639459781342413, 3.0298974867927475, 2.9727216787154838, 4.304275842261588, 4.678832631470566, 3.975562650341147, 3.930745068176629, 3.8677554083705883, 3.7921589495729138, 5.0448576634334374, 4.388869133990953, 4.835609374807406, 3.8794147966115, 5.403533648632691, 5.308896277497041, 4.457858247435697, 5.377559009441383, 5.370964877406072, 5.266833361284886, 4.166597413471504, 5.416944392465362, 6.030336801481078, 5.73988330444062, 6.041464811910986, 7.042010526829008, 6.399444075010156, 5.537684994662027, 6.64494319428544, 6.941824073371187, 6.637763190287925, 7.5797647982911, 6.646946018197227, 7.478665430984868, 6.984024890344531, 7.7504111475449875, 8.433744380843915, 8.18443128586918, 8.345099374168159, 8.66322704875682, 8.886902801956024, 9.398135736232245, 9.609076824201512, 10.18270180527305, 9.773232670667056, 9.081629876796898, 10.568646799368642, 11.04749496659516, 11.841690476199952, 11.580429022166438, 10.858758587567284, 11.452558714960077, 11.484570988898504, 11.683531889680541, 12.103094643916178, 13.082022704729463, 11.930295218045577, 12.515901017341285, 13.925927344153141, 14.348890167816963, 13.605209488105222, 15.080420178364578, 15.070428210301692, 14.783569149860357, 14.042473635631112, 14.776626444261176, 15.640124953364651, 16.71599770462783, 17.092820974911803, 16.861907491187402, 17.372173443197383, 17.87326829044139 ]
null
The given time series has a trend and a cyclic component. It also has an anomaly. What is the most likely combination of components without the anomaly?
[ "Linear trend and sine wave", "Log trend and sawtooth wave", "Exponential trend and square wave" ]
Exponential trend and square wave
multiple_choice
71
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Sine Wave", "Exponential Trend", "Square Wave", "Log Trend", "Sawtooth Wave", "Cutoff Anomaly", "Flip Anomaly" ]
The anomaly only influences a small part of the time series. You should focus on the overall pattern of the time series without the anomaly. Can you recover the original pattern?
Anolmaly Detection
General Anomaly Detection
630
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null
What is the most likely autocorrelation at lag 1 for the given time series?
[ "Negative autocorrelation", "High positive autocorrelation", "No autocorrelation" ]
Negative autocorrelation
multiple_choice
46
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Autocorrelation" ]
While it is hard to directly measure the autocorrelation for higher order lags, the autocorrelation at lag 1 can be approximated by observing the time series pattern. You can tell this by checking the sign and magnitude changes at each step compared to the previous step.
Pattern Recognition
AR/MA recognition
631
[ 8.031536184728376, -4.2889247034975995, 6.096945229747443, -8.89135375712022, 12.493306553664613, -9.515104740100634, 19.701903233145167, -30.176465067152286, 25.89663035262691, -16.63218079832727, 11.442020695030898, -13.200274789095182, 6.930647041589072, -3.798124939592978, -15.06108905813268, 21.699020857138443, -22.160535362669265, 19.00645526380324, -11.53414154316192, 3.9692593613999696, -4.485791559109935, -16.76376915896709, 20.732251400504392, -5.7851111171818665, -12.381846625642043, 5.840548533551016, -16.971132609248958, 11.799502872525107, -2.9532389508104755, 12.23568015321463, 1.4299877716967782, 11.961448029564707, -11.793286208207423, -2.034957320768454, 0.4820628535350753, 5.9470247402076994, -17.030217601374734, 30.225543615582207, -15.201549504862351, 10.095567919576592, -15.185173639773684, 5.456928100692517, -3.6234803425524604, 0.604758246738446, 9.021220955435492, -10.646735047374685, 13.572406144014659, -11.147173756960427, 11.614432579539049, -11.592110419595066, 16.35084374817226, -5.855274195637038, 9.283509614731074, -1.351664420289814, -8.362356239198675, 9.922342620448735, 4.554143578516347, 1.2707308073818973, -11.32375967392075, 8.561342642645752, -3.0992947307195124, -5.09455938440748, -9.507064459707543, 4.444672883400765, -10.964062386397636, 8.628359595218422, -22.816734151137624, 23.90039794627166, -25.466368709950896, 30.330617334774274, -27.033482265783203, 21.372895348781693, -18.82866506599453, 8.1813351517929, 18.177726501292277, -19.50084298110667, 25.835889609541937, -31.6050011482675, 29.00531482954561, -18.415530224318132, 14.49065440847321, -17.302570723174306, 11.208837552399807, -12.999965061651048, 34.4202348676754, -27.762218788588513, 27.458662817510316, -4.150679349754583, -5.442643199938148, 4.730716891629896, -6.476434830117807, 4.319763409260607, -5.24593039858334, -3.1220265374354987, 4.451724079914729, -14.1877070380928, 21.238993003564424, -10.758096336305503, 3.671848905404244, -7.3873123380619905, 8.664955493932123, -14.91741755120752, 30.053735282314733, -20.4637309389341, 20.303616264984054, -9.428442208414388, 1.7481210260308089, 9.49160299702309, -6.447948735463833, 14.659813698359383, -13.70738222437081, 24.138688046808507, -15.297514167198909, 34.06308157553, -30.9456814286463, 26.802039103824495, -31.757393751761175, 20.112932625946744, -9.903480622278341, 19.216028873217677, 14.277280418633078, -12.388113401138671, 0.5783566444549599, 7.070572288208445, -16.93473003557982, 19.19055790873122, -20.375003488926215, 18.415952494944907 ]
null
The given time series has a decreasing trend, is it a linear trend or log trend?
[ "Log", "Linear" ]
Log
multiple_choice
8
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Log Trend" ]
Check if the slope of the time series is constant or changes over time.
Pattern Recognition
Trend Recognition
632
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null
You are given two time series which both have a trend component. Do they share the same direction of trend?
[ "Yes, they have the same direction of trend", "No, they have different direction of trend" ]
Yes, they have the same direction of trend
binary
81
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Sine Wave" ]
Trend refers to the general direction of the time series. Are the values going up or down? Check this for both time series to see if they have the same direction of trend.
Similarity Analysis
Shape
633
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Is the given time series likely to be stationary after differencing?
[ "Yes", "No" ]
No
binary
32
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Stationarity" ]
Differencing is a common technique to make a time series stationary. Focus on checking if the trend is removed after differencing.
Pattern Recognition
Stationarity Detection
634
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null
Based on the given time series, how many different regimes are there?
[ "4", "3", "1" ]
1
multiple_choice
40
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Regime Switching" ]
First identify the different patterns in the time series. It might be helpful to identify their individual starting and ending points. Then, count the number of different patterns.
Pattern Recognition
Regime Switching Detection
635
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null
Is time series 1 a lagged version of time series 2?
[ "No, time series 2 is a lagged version of time series 1", "No, they do not share similar pattern", "Yes" ]
Yes
multiple_choice
99
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Lagged Pair" ]
Focus on the time delay between the two time series. If time series 1 is a lagged version, then it should look the same to time series 2 after being shifted by a certain number of steps. Can you check this?
Causality Analysis
Granger Causality
636
[ 0.6754001291485567, 3.2279552599799484, 0.6931141736261732, 1.752093158010961, 3.4612437966014027, -0.1373010984688474, 0.39584573799877587, 1.696465334657064, 0.5885446316062444, 0.7416305969875353, 0.1452941287633326, 0.3382431183962167, 1.1897407426744344, 0.07994256135292466, 2.101735164914733, -1.3275026005555222, 1.761084874646404, 2.5727845797120033, -3.0803413652173197, 2.5554892203474076, 1.226108793760537, -3.4266573041199164, 1.542734883358904, 0.2226389082723248, 1.029394051368897, 1.8567474337053365, 1.9587821283576996, 2.5776023794187766, -0.718839774013755, 0.3474387967522401, 2.0836348744428106, -0.7220344686976756, 2.652543348035478, 1.4537995957010044, -0.7805999450253037, 2.4081771461670463, 1.1321490939836398, 0.04525286623194802, 3.113519642718306, -0.33599223502933806, 1.1767748083715122, 2.6571070108893173, -0.17624506402344253, 2.099806349076365, 0.28524793857645014, 1.0057821851916549, 1.3360248990419685, 0.009765516149708109, 2.9812035620817916, -0.18049101405854617, -1.0798942450833073, 0.6392588898143248, 0.4708980166825787, -1.1098053959883591, 3.095961371925562, -0.5652263778094455, 1.132734478989237, 1.8159994552391636, -0.6385385976070048, 1.8220662806519154, 1.4976525353808574, -0.19995770155589102, 2.7321857386722397, 1.6831893213886804, 0.9896673960242474, 1.0244740730130293, 0.7061549386078255, 1.3275047129938757, -0.4389748680905339, -0.11674223517410964, 1.8201360097578556, -0.2398739598603229, 0.9242064469921999, 2.151842327089725, 0.18086703157891565, -0.3514250639272113, 0.7263534214225335, 1.3996755553134574, -0.6089560896984859, 1.2715305116885105, -0.18752848034557879, 1.141787346545223, 1.5985211426809571, 0.28832889437906306, 2.9248761757479613, 2.6073680517150826, 1.2446151384291544, 0.2844900570930715, 0.5361586713015296, 0.1400954589839717, -0.04241098741810513, 2.4587141518837434, 0.9463190151368207, 0.585024315699959, -0.21278303985056812, -0.5396076179600098, -0.011903976232774172, -0.2668325172313807, -0.836727497798645, -0.5069305511354235, 1.655539280723179, -0.7313303719036263, 3.0973572601921004, 1.9180203800271398, -0.25917173793212966, 1.652378612696494, 1.253176337623426, -0.14914836944896015, 1.951099052114138, 4.535241441425743, 0.32932255112034325, 2.3572300988025345, 1.9673592614754098, -0.4314065563331317, 3.544256275038333, 0.7046226947903124, 3.304092226911979, 3.1745649220106222, -0.8872950757853901, 3.055711015377549, 2.3119857653062836, 0.8159112600639835, 1.0632317681148027, 0.9080886083340414, 0.2317390256764287, 0.04492315465895842, 2.4240307217765658, 1.6103006459955835 ]
[ -2.529761994373178, 2.287844330845748, 0.25990232561749793, -0.4253498390369529, 3.910826125271198, 1.8501301838477864, 0.08643684252587974, 0.6754001291485567, 3.2279552599799484, 0.6931141736261732, 1.752093158010961, 3.4612437966014027, -0.1373010984688474, 0.39584573799877587, 1.696465334657064, 0.5885446316062444, 0.7416305969875353, 0.1452941287633326, 0.3382431183962167, 1.1897407426744344, 0.07994256135292466, 2.101735164914733, -1.3275026005555222, 1.761084874646404, 2.5727845797120033, -3.0803413652173197, 2.5554892203474076, 1.226108793760537, -3.4266573041199164, 1.542734883358904, 0.2226389082723248, 1.029394051368897, 1.8567474337053365, 1.9587821283576996, 2.5776023794187766, -0.718839774013755, 0.3474387967522401, 2.0836348744428106, -0.7220344686976756, 2.652543348035478, 1.4537995957010044, -0.7805999450253037, 2.4081771461670463, 1.1321490939836398, 0.04525286623194802, 3.113519642718306, -0.33599223502933806, 1.1767748083715122, 2.6571070108893173, -0.17624506402344253, 2.099806349076365, 0.28524793857645014, 1.0057821851916549, 1.3360248990419685, 0.009765516149708109, 2.9812035620817916, -0.18049101405854617, -1.0798942450833073, 0.6392588898143248, 0.4708980166825787, -1.1098053959883591, 3.095961371925562, -0.5652263778094455, 1.132734478989237, 1.8159994552391636, -0.6385385976070048, 1.8220662806519154, 1.4976525353808574, -0.19995770155589102, 2.7321857386722397, 1.6831893213886804, 0.9896673960242474, 1.0244740730130293, 0.7061549386078255, 1.3275047129938757, -0.4389748680905339, -0.11674223517410964, 1.8201360097578556, -0.2398739598603229, 0.9242064469921999, 2.151842327089725, 0.18086703157891565, -0.3514250639272113, 0.7263534214225335, 1.3996755553134574, -0.6089560896984859, 1.2715305116885105, -0.18752848034557879, 1.141787346545223, 1.5985211426809571, 0.28832889437906306, 2.9248761757479613, 2.6073680517150826, 1.2446151384291544, 0.2844900570930715, 0.5361586713015296, 0.1400954589839717, -0.04241098741810513, 2.4587141518837434, 0.9463190151368207, 0.585024315699959, -0.21278303985056812, -0.5396076179600098, -0.011903976232774172, -0.2668325172313807, -0.836727497798645, -0.5069305511354235, 1.655539280723179, -0.7313303719036263, 3.0973572601921004, 1.9180203800271398, -0.25917173793212966, 1.652378612696494, 1.253176337623426, -0.14914836944896015, 1.951099052114138, 4.535241441425743, 0.32932255112034325, 2.3572300988025345, 1.9673592614754098, -0.4314065563331317, 3.544256275038333, 0.7046226947903124, 3.304092226911979, 3.1745649220106222, -0.8872950757853901, 3.055711015377549, 2.3119857653062836 ]
The following time series has an anomaly. What is the most likely type of anomaly?
[ "Wander: the pattern deviates off for certain point in time", "Cutoff: the pattern of time series disappeared for certain point in time", "Scale: the pattern is at obviously different scale at certain point in time" ]
Scale: the pattern is at obviously different scale at certain point in time
multiple_choice
65
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Cutoff Anomaly", "Scale Anomaly", "Wander Anomaly" ]
Anomaly is an observation that deviates from the general pattern in the time series. You should check if the time series has any sudden changes or unexpected patterns. If so, check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
637
[ -2.9014286128198323, -2.700193726625713, -2.4989588404315937, -2.2977239542374743, -2.096489068043355, -1.8952541818492357, -1.694019295655116, -1.492784409460997, -1.2915495232668777, -1.0903146370727583, -0.889079750878639, -0.6878448646845194, -0.4866099784904001, -0.2853750922962809, -0.08414020610216155, 0.11709468009195767, 0.3183295662860772, 0.5195644524801968, 0.7207993386743159, 0.9220342248684352, 1.1232691110625543, 1.324503997256674, 1.5257388834507934, 1.7269737696449126, 1.9282086558390321, 2.1294435420331514, 2.3306784282272703, 2.5319133144213897, 2.733148200615509, 2.934383086809629, 3.1356179730037477, 3.336852859197868, 3.538087745391987, 3.7393226315861057, 3.940557517780226, 4.141792403974344, 4.343027290168465, 4.544262176362584, 4.745497062556703, 4.946731948750822, 5.147966834944941, 5.349201721139061, -0.25242061830648455, -0.051185732112365656, 0.15004915408175412, 0.35128404027587345, 0.5525189264699928, 0.7537538126641121, 0.9549886988582315, 1.1562235850523508, 1.35745847124647, 1.5586933574405895, 1.7599282436347086, 1.9611631298288281, 2.1623980160229475, 2.3636329022170663, 2.564867788411186, 2.7661026746053055, 2.967337560799425, 3.168572446993544, 3.3698073331876635, 3.571042219381783, 3.772277105575902, 3.9735119917700215, 4.174746877964141, 4.375981764158261, 4.577216650352379, 4.778451536546498, 4.979686422740619, 5.180921308934738, 5.382156195128856, 5.583391081322977, 5.784625967517096, 5.985860853711214, 6.187095739905335, 6.388330626099454, 6.589565512293572, 6.790800398487693, 6.992035284681812, 7.193270170875931, 1.8486262642675126, 1.8989349858160425, 1.9492437073645723, 1.999552428913102, 0.5991468440517157, 0.6494555656002456, 0.6997642871487753, 0.7500730086973052, 0.8003817302458351, 0.850690451794365, 0.9009991733428947, 0.9513078948914246, 1.0016166164399545, 1.051925337988484, 1.1022340595370141, 1.152542781085544, 1.2028515026340738, 1.2531602241826036, 1.3034689457311335, 1.3537776672796633, 1.4040863888281931, 1.4543951103767228, 1.5047038319252528, 1.5550125534737824, 1.6053212750223125, 1.6556299965708423, 1.7059387181193721, 1.756247439667902, 1.8065561612164318, 1.8568648827649616, 1.9071736043134913, 1.9574823258620213, 2.007791047410551, 2.0580997689590808, 2.108408490507611, 2.158717212056141, 2.2090259336046705, 2.2593346551532, 2.30964337670173, 2.35995209825026, 2.41026081979879, 2.4605695413473194, 2.5108782628958495, 2.5611869844443795, 2.611495705992909, 2.6618044275414388, 1.2613988426800526, 1.3117075642285827 ]
null
Given that following time series exhibit piecewise linear trend, how many pieces are there?
[ "4", "1", "2" ]
2
multiple_choice
5
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Piecewise Linear Trend" ]
Check if the time series values increase or decrease linearly over time with different slopes. The slope change could be both positive and negative.
Pattern Recognition
Trend Recognition
638
[ 0.25460483334044753, 0.05041437202525957, 0.07614645172377116, 0.14339440550963645, -0.009860031955970683, -0.06259836964133382, 0.07230343949612236, 0.09030141336134294, -0.08895133029818561, 0.1194856592880496, 0.19807223633651705, 0.008901097810653541, 0.1528602085971771, 0.2076397084433505, 0.18618988190598643, 0.20473140357377542, 0.12125947416563093, 0.04209778321884278, 0.11924228940115235, 0.1144599440991225, 0.1741484683120717, 0.30061018212546065, 0.06920779740969207, 0.22392553115448932, 0.11226908296760628, 0.15371327438375576, 0.29270076007385837, 0.12694089812274556, 0.3284685510762547, 0.12893639609012567, 0.33995959974305545, 0.12741715108802956, 0.22969772876686054, 0.4902371536521195, 0.4805510709624934, 0.27755268738073147, 0.3669099298820775, 0.45742939181421705, 0.41426092601441705, 0.32789360257352884, 0.28948521446201925, 0.4602677788080869, 0.4956365140203854, 0.5632450852450154, 0.23205867810691078, 0.2845798602787539, 0.5351934179602086, 0.27295672171712415, 0.5610734905299763, 0.42483396308688526, 0.4033445503983973, 0.485087510605854, 0.3391165244017985, 0.5651635713318248, 0.6608345066881007, 0.5880371471466965, 0.4854373749564996, 0.36539339208201094, 0.378346935884903, 0.40445006992790683, 0.5452952910872472, 0.5669718437723807, 0.651584907165861, 0.3942463760900953, 0.7049702977776429, 0.6290212385372272, 0.5126283092407639, 0.41206711627805465, 0.6416886665246638, 0.4724965381361007, 0.48623537622968355, 0.5123297951472069, 0.3683800393945398, 0.41721320397446326, 0.5176942839833134, 0.4933035335351902, 0.47993597825937373, 0.27283861438009405, 0.3504298863255104, 0.3201798697979312, 0.38806846943446915, 0.364847716076176, 0.33255598208986714, 0.5493179764618537, 0.25939530480974426, 0.23342493612158083, 0.14426360959911697, 0.09188517594412277, 0.10936950271971951, 0.14526437980125634, 0.3338712136936568, 0.19251162659034474, 0.19365963475371945, 0.15043056914252367, 0.18231933116919952, 0.2717277784930922, -0.08214118795120848, 0.22481695913842042, -0.1627892857693311, 0.07726616254064969, 0.2793679587671857, 0.11397434915018581, 0.06894578063338236, 0.21756581568590325, -0.06720373889022119, 0.03223062506068525, 0.03237692446585699, -0.09194366679994759, -0.09738313942255578, -0.1226187328910045, -0.07377796026352684, -0.042108965182964725, -0.09872376656434251, -0.05436928020853589, -0.336498858644589, -0.1756779145172306, -0.27046339727372437, -0.1522178830660826, -0.16796705956285282, -0.2224896820215435, -0.17416823756830355, -0.13968353489082058, -0.25978552704356705, -0.3731716317186191, -0.44039656809630967, -0.2929284615670616, -0.28662147704443297, -0.4220292042434978 ]
null
What type of noise is present in the given time series?
[ "Red Noise", "Gaussian White Noise", "No significant noise" ]
Gaussian White Noise
multiple_choice
62
medium
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Gaussian White Noise", "Red Noise" ]
Observe the pattern of fluctuations in the time series.
Noise Understanding
Signal to Noise Ratio Understanding
639
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null
The given time series is a sine wave followed by a square wave patterns with different amplitude. How does the amplitude vary over time?
[ "Increase", "Decrease", "Remain the same" ]
Decrease
multiple-choice
19
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave", "Amplitude" ]
Focus on the amplitude instead of cyclic pattern change, check if the distance between the peak and the baseline changes.
Pattern Recognition
Cycle Recognition
640
[ 0.0573433791687982, 1.0396209537445404, 1.9442756828856094, 2.8138866036713384, 3.5549836380178697, 3.806558503599376, 4.489793530728784, 4.636642667260257, 4.669286128979847, 4.661859012252556, 4.107553123019415, 3.6064195496344214, 3.192282562172207, 2.3980455955188136, 1.4878876063060833, 0.45130838492962333, -0.3431307365020163, -1.289343270638689, -2.233585443873419, -3.1535469545593022, -3.7487663118705727, -4.1423890579037455, -4.441776251937083, -4.769719978184361, -4.732251195961933, -4.5025263742132005, -4.055768650705574, -3.572460356554629, -3.092163928738291, -1.8580520105629206, -0.8921520662264232, -0.18363874565708244, 0.7251282299185737, 1.7385000231826937, 2.5827259358073125, 3.4446588570084824, 3.9583701702888696, 4.320931420154051, 4.536965925668067, 4.834401838236236, 4.694030318528172, 4.438204490747871, 3.757487870941639, 3.4038002688732947, 2.2804875720633273, 1.6610356199312815, 0.4697691137099866, -0.3744833781277568, -1.0835285219010908, -2.0503385032125223, -2.995309179625278, -3.6803734804259314, -4.158891710975634, -4.488719384230527, -4.6017984006402415, -4.767459758582097, -4.6861599492846, -4.128688223303011, -3.6412448705652456, -3.0306828765687195, -2.0581877491579865, -1.211817643664883, -0.21406496573560713, 0.6215664233842761, 0.7596818964355441, 3.524114413148131, 3.5730510938539704, 3.631532809714901, 3.8300060743196003, 3.734306769678478, 3.7635434832504076, 3.7975319361579434, 4.016107446404716, 3.659983139579472, 3.797864325136614, 3.7570877582638227, 3.7554274831543815, 3.833248194627647, -2.2757338491160883, -2.2836710484112785, -2.2018259946694547, -2.2520725232098293, -2.2019524607178234, -2.0775276675123395, -2.2816172182882686, -2.264270442277014, -2.216371445664983, -2.256634388620158, -2.4252031288189895, -2.2918153102875345, -2.16506522179389, 3.7995789079168936, 3.540362376069856, 3.5398959929005445, 3.658847613095362, 3.4482647263358452, 3.611327212524916, 3.4822200268684895, 3.7927303628078755, 3.5788911173885882, 3.8211076514575315, 3.7671763681694626, 3.591192503053887, 3.548628269139021, 3.63646965790687, -2.244267208443461, -2.1991878516224004, -2.3114568749706588, -2.1591630586654205, -2.207269740517651, -2.267842061689227, -2.305006611559443, -2.2522910443275093, -2.315492671200398, -2.227958676529282, -2.2252586774956495, -2.207631817670007, -2.0571783050504555, 3.6425797608536716, 3.756284019536077, 3.678782972521199, 3.6319998026337834, 3.6439083058285053, 3.6499415919068237, 3.6838010035964506, 3.5598921563017316, 3.509290194479132, 3.7212539721710565 ]
null
What is the most likely mean of the given time series?
[ "-13.7", "3.2", "25.8" ]
-13.7
multiple_choice
41
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Mean" ]
The given time series is stationary. Check the average value of the time series over time.
Pattern Recognition
First Two Moment Recognition
641
[ -13.810695333889988, -13.848345370643338, -13.670452768991634, -13.837701740007066, -13.510311478401073, -14.012269442727186, -13.663565570185275, -13.665622938333877, -13.853729386554212, -13.738710160352955, -13.649830577156038, -13.944910902336915, -13.876600549832432, -13.72253648016103, -13.815424818648381, -13.764739586231638, -13.704035541500332, -13.826029511765821, -13.704926185433928, -13.66045528773345, -13.594569895676948, -13.87197925782575, -13.78738424845527, -13.620647032115262, -13.904350149604108, -13.686735444712593, -13.697435079221508, -14.055714954927323, -13.76901655908078, -13.655963469832628, -13.730311181827332, -13.766267689167918, -13.679887132234345, -13.56579348007348, -13.627628240820984, -13.804846446236116, -13.90118520370962, -13.630111183004729, -13.862650153649467, -13.77363232102092, -13.673752814280967, -13.544196009525425, -13.525111862637658, -13.692970150366733, -13.77109176888586, -13.865788182355004, -13.43292735261963, -13.74100293819732, -13.608413609547101, -13.674323430908027, -13.76918871106211, -13.774991730374245, -13.89079074004928, -13.54749815500142, -13.71779909125994, -13.505414926057947, -13.7627717578263, -13.742117482460042, -13.8565565770159, -13.743956201144488, -13.871197083342054, -13.64611505133513, -13.686513597163085, -13.49920788761792, -13.90101612091855, -13.53467696077569, -13.835344223722474, -13.654120691669695, -13.858224642432104, -13.673502249400547, -14.045268788561984, -13.793163132454772, -13.686747906032188, -13.460766102872938, -13.992850201707313, -13.70159693782479, -13.77235950959477, -13.963808674351988, -13.855400786216878, -13.765833053187295, -13.637289323338083, -13.68924163945027, -13.881112008492222, -13.952571223772722, -13.644061590671884, -13.728038980233306, -13.480498976379543, -13.749589549739236, -13.544647522773978, -13.626772038977803, -13.588714117269353, -13.642038779428505, -13.639035533761763, -14.015298747454597, -13.733744914715096, -13.792209075102996, -13.527188942828543, -13.838527137557417, -13.739686862419118, -13.591555950479766, -13.660048718676085, -13.678361568690066, -13.549310642106914, -13.665650111559914, -13.775947843222365, -13.878890401218264, -13.63460045199676, -13.80679902286102, -13.734323946443887, -13.553536053850374, -13.731602176035633, -13.762150604808438, -13.7395956623007, -13.735897779489552, -13.83709179401782, -13.471465228855184, -13.77654860143482, -13.593813684266355, -13.840826834103517, -13.625992654849735, -13.678080936927508, -13.697855128788543, -13.677316273059299, -13.644293065489869, -13.732373379905612, -13.725539642837518, -13.622168626889215, -13.85774726306517 ]
null
What is the most likely variance of the given time series?
[ "0.27", "1", "varies across time" ]
1
multiple_choice
42
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Variance" ]
Check the degree of variation of the time series over time.
Pattern Recognition
First Two Moment Recognition
642
[ -0.31268426883718514, 0.7636773371379586, 1.2860335408138033, 0.09790432960048834, 1.6940101851917344, 1.5048878317379195, 0.9031931669567326, 1.0577092423270373, 1.2688858960520852, 1.5321690517366573, 2.153877946948164, 0.8913946003685451, 1.8516126819486178, 1.0742236843043786, 1.0016081159378252, 1.0873732313864992, 1.7738229712771902, 0.9625091888568049, 1.3183231001583608, 1.0250672268767644, 1.0841941041741425, 1.9908575453735424, 1.3274628420664334, 1.0172673675797732, 1.151034287524361, 1.5257095554833728, 1.3781330285796125, 1.4239331521187397, 1.2919803313540557, 1.9823808583791904, 1.767807220676736, 1.3866799492044943, 1.5836737616021883, 1.1313013631653082, 1.522011566316524, 1.2342251845030943, 1.6979351422462063, 1.5694279109738516, 1.5220265127417694, 1.7355016974007786, 1.8352253394839881, 2.25327704657402, 2.1198252661177914, 2.2288281690345793, 1.6003193730092253, 1.9435312246271923, 2.6907744167754744, 1.7988676330813453, 1.9362418505883723, 1.9675309451039615, 1.869119200466272, 2.5904262424483564, 1.7508742462166476, 2.537819957090092, 2.408860518594222, 2.0203228265908955, 1.8721356211627318, 2.0886210794389135, 2.712247721411898, 2.699110646578771, 2.589049752365003, 2.1746276849003943, 2.2687771431896486, 2.589686217618787, 2.188020436946077, 2.755553335645344, 2.443336999031083, 2.905574445607273, 1.7229167174422848, 2.158476909910418, 2.3279375697487694, 2.733463174711247, 2.372501749311959, 3.6841671565221326, 2.018817350808695, 3.1725459618181966, 3.31280046624876, 2.982308786826277, 2.611309246907236, 2.7958967694592034, 3.250891302316094, 2.0804352485670443, 2.6004201438732735, 2.687125479243201, 3.267078570882118, 3.5786215130100456, 4.0645013891045725, 2.182272732372856, 2.6414667952070556, 3.025755027473686, 3.5169031148240975, 3.663613160034722, 2.7351371742069897, 3.5564206970243286, 2.132566801259796, 3.603317877580846, 3.489730301128907, 3.49901741075779, 3.399564357095544, 3.5978993912869246, 3.8514251960653683, 4.569473404506512, 3.145647670912573, 3.7016248871188093, 4.1589386226189236, 3.9094635414375265, 4.053473681619022, 3.7505504107698417, 4.5096960560652555, 3.0646818332140517, 3.709074811253043, 5.238423785515112, 3.7022635123354553, 3.9374090184341, 4.037076803074834, 4.218585086933396, 4.538503711134259, 5.14742746854758, 4.907208102822279, 4.611805747809672, 5.66658674846198, 4.6463943213772785, 4.947611090284557, 5.043104051297649, 5.472474437703888, 4.539783327158716, 4.6706645476756785, 5.722035001008669 ]
null
Two time series are given. One has noise and the other does not. Do they have similar pattern?
[ "Yes, they have similar pattern", "No, they have different pattern" ]
Yes, they have similar pattern
binary
83
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Sawtooth Wave" ]
Noise refers to the random fluctuations in the time series. You should focus on the overall pattern of the time series. Pattern refers to the general shape of the time series. In this case, you see both time series have cyclic patterns. Do their behaviors at peak and trough look similar?
Similarity Analysis
Shape
643
[ 0.2956253652346522, 0.42927844783431035, 1.1715118534582, 1.8035674461227764, 1.97633647987519, 2.136091859512665, 2.559527960263782, 3.0015613971632513, 2.95036290877155, 2.6837606926980517, 2.9638949590073556, 2.8249814784682346, 2.3389421054031674, 2.191962994541713, 1.7109587582333217, 1.160017569883872, 0.43901523123215885, 0.38865501421170556, -0.2054261709093545, -0.7591095383900431, -1.0568812887884413, -1.621865782894923, -2.059333101905557, -2.9530095128335714, -2.5023925244310714, -2.8666651851003735, -2.867755178734822, -2.817281423505242, -2.5828084576526056, -2.2798068430335734, -2.061950929680049, -1.706532608778925, -1.309006898594304, -1.5349131393352922, -0.4030424626894581, -0.003446273465736477, 0.9513538222840503, 1.3340940673467803, 1.580056847440144, 2.006726941422281, 2.337917534627598, 2.5935523581157596, 2.5584714139520206, 2.5932318140679396, 2.9134804590712235, 3.0095800803002426, 2.4821983256296076, 2.3607314887464894, 2.081786786302111, 1.3077080416888882, 1.024446097411187, 0.3834738724476337, 0.3093944434726641, -0.2275571108187886, -1.2490299131541733, -1.449450806890264, -1.7391188181409123, -2.144960304243163, -2.584408742334862, -2.540232081831444, -3.091411221384458, -2.9846613118939453, -3.0172316067831235, -2.509690549740586, -2.519783255950504, -2.095773961776251, -1.5286646741536347, -1.0490507959577742, -0.8676527435762682, 0.050077036879775466, 0.4601445941650795, 0.6708277159576616, 1.110698094636248, 1.8170258748135906, 2.3744764461579937, 2.691588497665157, 2.8171567148228442, 2.895102492065486, 3.0325532930060337, 2.707901776749781, 3.07073145514377, 2.8328665252826055, 2.2666788045751134, 1.8317056477076645, 1.2625261207926213, 0.9590309531932781, 0.19551104134539712, -0.6413984180852343, -1.2634993509073742, -1.3809497198401444, -1.6501105818870863, -2.020198419078711, -2.5207351474317177, -2.652349349297925, -2.9049988794060804, -3.1260012479124066, -2.916930323798785, -2.6283443250976743, -2.77499271856576, -2.4834153415480698, -2.139885309990681, -1.8835285215048785, -1.1133963453587181, -0.362312496290071, 0.05844193376425111, 0.5178212497889172, 1.0874087937236596, 1.438916148595217, 1.5718657260899467, 2.478605269144296, 2.8203752731779144, 2.659356921358156, 2.8816886096283234, 2.8758489063029904, 2.9090515027943415, 2.999238552001024, 2.628426361722367, 1.9777176913328587, 1.7509083021820606, 1.4287500807634532, 0.756390417835574, 0.14850129564517767, -0.29153891717698033, -1.039089616433741, -1.4981298536786598, -2.0422522880618907, -2.1508201631492874, -2.5487661767593752 ]
[ 0, 0.6492720643813447, 1.2706727421153245, 1.8375270852068173, 2.3255016632870062, 2.7136491279546995, 2.9853074223350857, 3.1288150353698487, 3.138011597024365, 3.012502325296204, 2.757674973073668, 2.3844685473643756, 1.9089037291137412, 1.3513951513430966, 0.7358750575335694, 0.08876595908665266, -0.5621536072712568, -1.1889415323604215, -1.7646916091153855, -2.2646885388473366, -2.667468888096632, -2.955742452242216, -3.1171344743720217, -3.1447168580880223, -3.0373055708045285, -2.799511470869532, -2.4415423766466087, -1.9787648741637651, -1.431044673669426, -0.8218938316958553, -0.1774614459397003, 0.47458885046766786, 1.1062664093501053, 1.6904551256941387, 2.2020774542279504, 2.619170916480237, 2.9238308869599967, 3.102979187351781, 3.148925495183154, 3.0596974673011603, 2.839125406904276, 2.496677839617097, 2.047055056855059, 1.5095580744962545, 0.9072600956537604, 0.26601604427418796, -0.38664731255698964, -1.0227130097388157, -1.6148765720723057, -2.1377181170310235, -2.568793557375927, -2.889598061417566, -3.086360412341183, -3.1506341670282643, -3.0796602376226794, -2.87648533125517, -2.549831163648731, -2.1137200608894307, -1.5868730212044022, -0.9919060762275869, -0.35435944965805105, 0.2983988112561431, 0.9383476674540538, 1.5380159508628395, 2.0716616228149562, 2.516376805901824, 2.853071153417127, 3.067291343161447, 3.149841517090708, 3.0971780331146226, 2.9115615834832025, 2.600960149755478, 2.178706960215199, 1.6629281326400815, 1.07576457207825, 0.44242152532752926, -0.20991340798351393, -0.8532373610332308, -1.4599342825256953, -2.0039604145290344, -2.461962276271228, -2.8142791620572103, -3.045787118948247, -3.146548174663651, -3.112236946213904, -2.944326316180794, -2.65002420609459, -2.2419641610457743, -1.7376630278460523, -1.1587690070590875, -0.5301323578695171, 0.12126135223649077, 0.7674496604486208, 1.380693556923082, 1.9346682408784583, 2.4055931687546304, 2.773252884709972, 3.021864812132596, 3.140756754366473, 3.1248250214901647, 2.974753517080182, 2.696984380192892, 2.3034414428204633, 1.8110183739987016, 1.2408534830714302, 0.6174223127265144, -0.03251302581960164, -0.6810526734629369, -1.300356684105009, -1.8638401136526168, -2.3473142353825938, -2.730024892570847, -2.9955434148868414, -3.132471854068993, -3.1349322651373317, -3.0028190297048027, -2.7418033898715706, -2.363089998075172, -1.882935933512988, -1.3219528323817409, -0.7042220894803156, -0.05626111303229467, 0.5941149915577542, 1.2189874443643665, 1.7915322640507376, 2.287171744416591, 2.6846295047999287, 2.966843824046605 ]
In which part of the time series does the anomaly occur?
[ "Middle", "End", "Beginning" ]
Beginning
multiple_choice
77
medium
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Linear Trend", "Spike Anomaly", "Cutoff Anomaly", "Wander Anomaly" ]
Identify where in the time series sequence the unusual pattern or disruption occurs.
Anolmaly Detection
General Anomaly Detection
644
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null
You are given two time series following similar pattern. One has an anomaly and the other does not. Which time series has the anomaly, and what is the likely type of anomaly?
[ "Time series 1 with flip anomaly", "Time series 2 with cutoff anomaly", "Time series 1 with speed up/down anomaly" ]
Time series 1 with flip anomaly
multiple_choice
74
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Linear Trend", "Speed Up/Down Anomaly", "Cutoff Anomaly", "Flip Anomaly" ]
You should first identify the time series with the anomaly. Remember, both time series share similar pattern. Then, you should check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
645
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Despite the noise, does the given two time series have similar pattern?
[ "Yes, they have similar shape", "No, they have different shape" ]
Yes, they have similar shape
binary
79
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave" ]
Noise refers to the random fluctuations in the time series. You should focus on the overall pattern of the time series. Pattern refers to the general shape of the time series. In this case, you see both time series have cyclic patterns. Do their behaviors at peak and trough look similar?
Similarity Analysis
Shape
646
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You are given two time series following similar pattern. Both of them have an anomaly. Do they have the same type of anomaly?
[ "Yes, Time series 1 and time series 2 both have flip anomaly", "No. They have different types of anomalies" ]
No. They have different types of anomalies
binary
76
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Cutoff Anomaly", "Flip Anomaly", "Spike Anomaly" ]
For each time series, identify the type of anomaly based on the given definitions. Then, check if they have the same type of anomaly.
Anolmaly Detection
General Anomaly Detection
647
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The following time series has an anomaly. What is the most likely type of anomaly?
[ "Flip: the pattern is flipped at certain point in time", "Spike: the pattern of time series is distorted by random large spikes", "Speed up/down: the period of cyclic components is different from other parts of the time series" ]
Speed up/down: the period of cyclic components is different from other parts of the time series
multiple_choice
64
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Spike Anomaly", "Flip Anomaly", "Speed Up/Down Anomaly" ]
Anomaly is an observation that deviates from the general pattern in the time series. You should check if the time series has any sudden changes or unexpected patterns. If so, check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
648
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null
You are given two time series following similar pattern. Both of them have an anomaly. What is the likely type of anomaly in each time series?
[ "Time series 1 with cutoff anomaly and time series 2 with speed up/down anomaly", "Time series 1 with flip anomaly and time series 2 with speed up/down anomaly", "Time series 1 with cutoff anomaly and time series 2 with flip anomaly" ]
Time series 1 with cutoff anomaly and time series 2 with speed up/down anomaly
multiple_choice
75
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Sawtooth Wave", "Linear Trend", "Log Trend", "Cutoff Anomaly", "Flip Anomaly", "Speed Up/Down Anomaly" ]
You already know both time series have an anomaly. You should treat them separately and check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
649
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Does the given two time series have similar pattern?
[ "Yes, they have similar shape", "No, they have different shape" ]
Yes, they have similar shape
binary
79
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave" ]
Pattern refers to the general shape of the time series. In this case, you see both time series have cyclic patterns. Do their behaviors at peak and trough look similar?
Similarity Analysis
Shape
650
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The given time series is a square wave. What is the most likely period of the square wave?
[ "38.27", "19.76", "51.43" ]
38.27
multiple-choice
22
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Square Wave", "Period" ]
Check the time interval between two peaks.
Pattern Recognition
Cycle Recognition
651
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null
The given time series has a cyclic component and a trend component added together. What is the most likely type of the trend component?
[ "Log", "Linear", "Exponential" ]
Exponential
multiple_choice
10
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend", "Log Trend", "Sine Wave", "Additive Composition" ]
Despite having a cyclic component, check the general trend of the time series.
Pattern Recognition
Trend Recognition
652
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null
The given time series is a swatooth wave followed by a square wave. What is the most likely period of the swatooth wave?
[ "53.29", "39.64", "14.48" ]
39.64
multiple-choice
26
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sawtooth Wave", "Square Wave", "Period" ]
The sawtooth wave comes before the square wave. Begin by identifying where the sawtooth wave starts. Next, measure the time interval between two peaks.
Pattern Recognition
Cycle Recognition
653
[ -2.8287525212527074, -2.8195121606508464, -2.729891002614425, -2.540571223759809, -2.2702521192628207, -2.184003507447075, -1.9822322520450533, -1.7209343499778005, -1.7261210762165793, -1.682098488953098, -1.3474508002307934, -1.3000454164720368, -1.0699251379569241, -0.9025383506161648, -0.9570473659715855, -0.5749344472146826, -0.47461106293919036, -0.4775020474862685, -0.2386550495536997, -0.09536756374574319, 0.02931651729986047, 0.26212638343154715, 0.46668226608069124, 0.4716889192184328, 0.7520580634386088, 0.8658018403888421, 0.9382228438531021, 1.0806229689377242, 1.0957599882635223, 1.208951334805837, 1.5235421026345188, 1.569458579737679, 1.7990995060136845, 1.8976084947296705, 1.920236767113658, 2.282828520502402, 2.3536565344667797, 2.551141234956882, 2.601820985036909, 2.8056629363573884, -2.723424952267497, -2.7185962176766463, -2.5284820344804566, -2.5625152009772965, -2.048512775853416, -1.9550633470635779, -1.8550495251034298, -1.7605048277410817, -1.6938554489785522, -1.5031507264208346, -1.2945445050109818, -1.3141918054610169, -1.1477730564383337, -1.122224769228438, -0.884481792398029, -0.4931580628645075, -0.5447012963433291, -0.39504962918232, -0.1834765865905187, -0.22846437185465224, 0.1753081765685875, 0.3554223417941489, 0.414522931499933, 0.6899400522988721, 0.3921217770373334, 3.415195444360828, 3.1577497242626777, 3.10283189125933, 3.2070846684649763, 3.4180244326328735, 3.2288796504956885, 3.137564698929535, 3.101329617137657, 3.2203120141110015, 3.0313277074298783, 3.100804580426299, 3.3851306297715515, 3.363150245300767, 3.217982649931672, -2.2277804344092513, -2.1753630670531123, -1.9464142644387645, -2.140716406406744, -2.090240139787815, -2.2014597098669517, -2.1751242965720805, -2.1164976876050923, -2.168604474501394, -2.3709516555326626, -2.0531598811160503, -2.2427273250609296, -1.9700821931221715, -2.1125291060072, 3.2379211061496176, 3.2747565785959867, 3.219974075729292, 3.182180587980407, 3.2515836907142153, 3.3193229113043095, 3.1843708897211465, 3.168600148095015, 3.195275000494007, 3.3260249739703127, 3.3760788893318803, 3.26702525577989, 3.2889552779892153, 3.167853778859132, 3.3184993295808756, -2.1260402562372893, -2.252226753076545, -2.359981118476975, -2.303270967711982, -2.2481342301019183, -2.0650202255091195, -2.025927979699864, -2.2251657448312243, -2.2220054925609265, -2.1550516516865503, -2.1799993063764744, -2.0881205488863888, -2.2335327666425075, -2.086299658505697, 3.2069013847986674, 3.3162213356924286, 3.203719818356789, 3.1695143962948054, 3.42205562856964, 3.337346572840335 ]
null
Are the two time series flipped versions of each other despite noise?
[ "Yes, they are flipped versions", "No, they are not flipped versions" ]
No, they are not flipped versions
binary
91
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend" ]
Both time series have a trend and a cyclic component. Then we say two time series are flipped versions of each other, we mean that the sign of each step is flipped. You should check if the sign of each step is flipped for both time series. At a high level, you should check if the time series are mirror images of each other.
Similarity Analysis
Shape
654
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The given time series is a square wave. What is the most likely period of the square wave?
[ "12.27", "50.69", "36.83" ]
36.83
multiple-choice
23
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Square Wave", "Period" ]
Check the time interval between two peaks.
Pattern Recognition
Cycle Recognition
655
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null
The given time series is a sine wave followed by a square wave. What is the most likely amplitude of the square wave?
[ "6.29", "7.63", "1.86" ]
7.63
multiple-choice
24
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave", "Amplitude" ]
After the sine wave, the square wave follows. Begin by identifying where the square wave starts. Next, measure the distance between its peak and baseline.
Pattern Recognition
Cycle Recognition
656
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null
Does any part of the given time series, composed of several concatenated patterns, appear to be stationary?
[ "No", "Yes" ]
No
binary
33
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Stationarity" ]
You can try to identify different parts in the time series first, and see if any part is stationary.
Pattern Recognition
Stationarity Detection
657
[ 0.20332937694664568, 0.24788471211586094, 0.5374901302513543, 0.6484711924867821, 0.7867940594745261, 1.121309440465204, 1.309160883249897, 1.3879008335296987, 1.6058160886459767, 1.5660315759705232, 1.5979286411700784, 1.8177546080202278, 1.8081710441238756, 1.5947382561093844, 1.75403757998773, 1.4463580713948672, 1.3475019499502707, 1.1682231346956917, 1.043626205939797, 0.813492065769804, 0.5918067839216271, 0.23260208612959787, -0.07231896924316794, -0.029163120289043706, -0.43502502353886585, -0.615014763768497, -0.7950836984837628, -0.8662626012816395, -1.1942212923929643, -1.407266387990497, -1.5507156912557467, -1.6032529499876949, -1.7602050643100164, -1.7033581578757575, -1.7149246593550675, -1.515478507300048, -1.6249221909565505, -1.7142024215164449, -1.1297161459232719, -1.149267690689174, -0.8601568206451321, -0.9865876765869379, -0.6784040840965951, -0.3612628534847018, -0.13912831965004002, 0.07764660305312601, 0.06579018452639951, 0.3476953357336643, 0.8936905385187537, 1.1199036130014117, 1.1294782222391044, 1.4465733804060137, 1.3469232701084584, 1.4830645673180518, 1.534862225997591, 1.6103819243231152, 1.7846403743862609, 1.6095119899281276, 1.8698039285941785, 1.6096051011785626, 1.5591197027700425, 1.3582478274072163, 1.2635618055477669, 0.8657914012268719, 0.8890382735282041, 0.5355779660194542, 0.40931110316090125, -0.0943335981851362, -0.1720548441353522, -0.4115926106145202, -0.7156771367447265, -0.837242913508151, -0.9123423383410972, -1.3127308459628604, -1.299335608813316, -1.6332693255450956, -1.4047347278024813, -1.6006493106720188, -1.5370603739336528, -1.6392633277623099, -1.630800760783184, -1.5211756522334072, -1.5132971839332614, -1.5311753598473494, -1.1675051219598884, -1.1068474328168487, -0.9402669951697273, -0.5489771116334415, -0.41099507456975215, -0.043270164570366504, 0.014976279917505858, 0.2848553841226916, 0.6785185810454478, 0.8119604798421753, 0.841338169093534, 1.2005225441062977, 1.4854809908689017, 1.425852594654339, 1.6409346956652853, 1.5725651641657414, 1.6876572662523153, 1.8207471078466935, 1.7105061627428049, 1.761176029054174, 1.5863979877805197, 1.6470483430173832, 1.1220079982238813, 1.0850030884763802, 0.804762904081411, 0.6001552691236703, 0.37584706940242346, 0.2587664561252389, 0.0253011297285212, -0.19395865166827414, -0.5837381636129756, -0.729326422936591, -1.0051223270066434, -1.0090524848120082, -1.3619660855963684, -1.443577261021221, -1.4855187285943485, -1.6921890090789455, -1.618299587600602, -1.5520049374362819, -1.6829616560283323, -1.5686761517109877, -1.7905143751974413, -1.5193287458413485 ]
null
The given time series has multiple cycle patterns with same amplitude and period. How are they combined together?
[ "Multiplicative", "Additive" ]
Multiplicative
multiple-choice
28
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave", "Sawtooth Wave", "Additive Composition", "Multiplicative Composition" ]
For additive composition, the patterns are added together. This changes amplitude. For multiplicative composition, the overall shape of the time series might be distorted with cyclic patterns unobservable.
Pattern Recognition
Cycle Recognition
658
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null
The given time series has an increasing trend, is it a linear trend or log trend?
[ "Log", "Linear" ]
Linear
multiple_choice
7
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Log Trend" ]
Check if the slope of the time series is constant or changes over time.
Pattern Recognition
Trend Recognition
659
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null
Which of the following best describe the cycle pattern in the given time series?
[ "Period decrease over time", "Period increase over time", "Period remain the same over time" ]
Period decrease over time
multiple-choice
29
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Period" ]
Check the time interval between two peaks, and see how it changes over time.
Pattern Recognition
Cycle Recognition
660
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null
The given time series has sine wave pattern. How does its amplitude change from the beginning to the end?
[ "Decrease", "Remain the same", "Increase" ]
Remain the same
multiple-choice
18
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Amplitude" ]
Base on the definition of amplitude, check if the distance between the peak and the baseline changes.
Pattern Recognition
Cycle Recognition
661
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null
Two time series are given. Both of them have a noise component. Do they have the same level of noise?
[ "No, they have different level of noise", "Yes, they both have the same level of noise" ]
No, they have different level of noise
binary
89
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Gaussian White Noise", "Variance" ]
Noise level refers to the amplitude of the random fluctuations in the time series. Both time series have a white noise component added to it. You should check the amplitude of the noise for both time series.
Similarity Analysis
Shape
662
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You are given two AR(1) process, which one of them is more likely to have a larger magnitude in autocorrelation at lag 1?
[ "Time Series 1", "Time Series 2" ]
Time Series 1
multiple_choice
47
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Autocorrelation", "AutoRegressive Process" ]
While it is hard to directly measure the autocorrelation for higher order lags, the autocorrelation at lag 1 can be approximated by observing the time series pattern. You can tell this by checking the sign and magnitude changes at each step compared to the previous step. You should compare the two time series to see which one has a larger magnitude in autocorrelation at lag 1.
Pattern Recognition
AR/MA recognition
663
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Which of the following time series is more likely to be an MA(1) process?
[ "Time Series 2", "Time Series 1" ]
Time Series 1
multiple_choice
50
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Moving Average Process", "Stationarity" ]
MA(1) process is a stationary process with a constant mean and variance. You should check if the time series has a constant mean and variance over time. The other option is likely not stationary.
Pattern Recognition
AR/MA recognition
664
[ 10.012528353921475, 11.794889620181532, 11.303949527461128, 12.1516307043504, 10.922369918934544, 10.63547789301224, 10.394325832129233, 9.510039694749628, 11.36276899959469, 8.661467759073876, 11.142496260769008, 6.973288361053045, 9.762856423795796, 10.24590469308534, 10.595696673110208, 13.197610156270079, 10.161645528159147, 11.332147596748056, 10.748146119210798, 10.716113204145726, 11.534159679833763, 12.137057918094364, 9.366397736272727, 11.120227536818547, 7.413550464839503, 8.757503516507995, 9.670916942043487, 8.206565892259395, 11.594872567868274, 10.924605629014383, 10.41048122830814, 11.846651473374278, 10.60096158954937, 9.194395688773284, 9.978197358333288, 8.019142737874946, 8.970115013676134, 9.913181728743657, 8.975424780991286, 10.537735331533062, 8.48138099831493, 11.198299582988248, 8.620920716231675, 12.504118283536917, 9.62484110167069, 9.811384863564884, 9.877716528533863, 7.811623510163372, 10.452527980141653, 8.888415755700201, 10.634689756929875, 9.421556664091945, 9.575225900158559, 8.730895502347124, 10.39194909373087, 9.0479492905078, 10.35428745575884, 9.663263620118082, 9.069385491555519, 9.530077454470245, 9.662540379904868, 8.716781859522415, 9.275151858675583, 10.550974494377261, 8.925761872737077, 10.551066465974131, 8.36592316820108, 10.409428990335032, 7.868976902041737, 10.665249449017933, 7.447074279874736, 10.80593867159495, 9.810308188165308, 11.139058585769309, 9.407004863489568, 11.226378420291642, 7.945066895235411, 9.500037836405772, 8.954659754530065, 8.659854823676222, 9.188182512213588, 10.950980109227503, 11.607787075498395, 9.64980286097429, 10.92062840282951, 9.047439106165385, 9.0602175936031, 10.513597418114482, 10.605012163196013, 11.068884941692854, 11.342521852606467, 12.258588274735757, 8.898839571363757, 12.807385208690393, 8.315850539577369, 11.969212254239318, 8.639940464448761, 9.719603784647223, 9.838384308858473, 7.344472863735532, 11.519135911473935, 9.716979484141712, 10.96933851645961, 11.149731837451828, 9.308591738154716, 10.787858230866515, 9.680756330480664, 9.618054125899112, 9.88665224703775, 9.103460258485137, 9.29401384341026, 8.509620246893382, 10.384778551368546, 8.666160413418126, 10.574581022760425, 9.226925047881059, 10.487563294686638, 9.736082914463461, 11.59300156830801, 10.639555660444108, 10.767543109467224, 9.644762152848628, 10.703805162446956, 9.125650447211495, 10.521044580537094, 9.60196751467816, 9.461018236065893, 9.70788372073599 ]
[ 2.5520763066228525, -1.33612100925535, -0.9748305654974104, 1.9906099206875332, -0.28793761349939617, -0.3362268372135244, 1.6840886013892058, -1.5165133426700699, 1.5056622158074864, 0.5298990796713234, 1.1374500854322542, 1.1647420417691183, -0.20608066643625933, 2.0708474430565964, 0.0013824123658670029, 1.324128105848511, 2.4744864199194883, 2.7136976439597738, 0.5849998938533914, 1.604702461803646, 0.5669514023339365, 4.412745303606548, 2.181177651980848, 1.3111041767321598, 1.6660163020535004, 1.843441113161354, 1.9348716557447945, 1.0904033888144218, 0.9380915855182387, 1.3115131471134414, 0.054865923599352495, 2.568689891392362, 0.6069967862970338, 0.31700436585385394, 1.7545001412218555, 1.6532785777703978, 2.2085897378976656, 1.177177399577952, 1.4620793769610068, 2.9513351836215236, 2.922806646774387, 2.919730075910285, 2.235821682973643, 2.4667889679819117, 2.6004555836237917, 1.4780995081637487, 4.352464418610452, 4.215880129801734, 3.5561051954142653, 1.9917196991948778, 3.322440068363364, 3.956542683674744, 1.0917989093638616, 5.009699939706698, 0.5122107016537951, 3.8024756223271714, 4.84657647972521, 2.8234515794998916, 2.826060541871994, 3.9621755727942327, 5.583339415597219, 2.8095082788870065, 2.199358178792572, 2.7247560678013043, 1.2814269663715425, 4.5800103619935495, 2.7615924181089064, 3.2188417934192177, 4.752215173639488, 3.0998226368310964, 4.657098199694563, 2.3281372252520605, 5.025915885337133, 4.260846732247292, 3.7426509137515747, 4.085597371347546, 2.2594765500262284, 4.159590882480474, 3.8809590218550167, 2.4521718909053085, 3.283862049358868, 4.053907505643677, 3.472694550011944, 1.1336074279482582, 5.80776482503826, 4.24553863857492, 1.4731506021127796, 7.36678244641109, 6.235032693715312, 4.180071737598066, 3.57836419609555, 5.280967867019151, 5.0670003650782345, 5.569322568845159, 3.7908255469178345, 6.409883073986961, 4.380281455796768, 5.9617065878657005, 4.056023852623974, 8.672655488897126, 6.137746213128009, 9.089778876378098, 6.417064826653097, 4.628821493600967, 6.523746251672965, 6.670239127205182, 6.023831031231852, 6.416589032842449, 6.642759628835413, 4.369141685173103, 4.3269994482038765, 4.737740731017013, 6.011163076481612, 5.598656993527773, 4.653948200064258, 7.025897665493048, 6.425841043926147, 6.3268086959323835, 5.813337228231357, 5.706192419800538, 5.144778934924938, 7.548773881229336, 5.43172864372599, 6.693390915324287, 8.670162486373581, 6.080073482995305, 7.8453078221669035, 7.378109510763442 ]
The given time series is a sine wave followed by a square wave. What is the most likely amplitude of the square wave?
[ "17.79", "1.49", "4.13" ]
4.13
multiple-choice
24
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave", "Amplitude" ]
After the sine wave, the square wave follows. Begin by identifying where the square wave starts. Next, measure the distance between its peak and baseline.
Pattern Recognition
Cycle Recognition
665
[ 0.09923547312467886, 0.31032895328564253, 0.4911429584914484, 0.8782079569669343, 1.0050731296474114, 1.1747725290528586, 1.1447863016670499, 1.3474100657227892, 1.3924821873195032, 1.4415863250524183, 1.1252528120334309, 1.2693645342522095, 0.8940146120940557, 0.44747433640395073, 0.25046723018278977, 0.19839857620830728, -0.1004633578106715, -0.49449303906573633, -0.7316998786620086, -1.0817563868062445, -1.010663610257128, -1.370449488413016, -1.2619303480340858, -1.2286174693689609, -1.3183675393156158, -1.1294574131996935, -0.8922917369022476, -0.8552473285018168, -0.6670155826591174, -0.3959642532680589, -0.18680029847110605, 0.09250659346177822, 0.48767528599467264, 0.6825329134498732, 0.9574257799552436, 0.9620544377413756, 1.2408696999944966, 1.439010657944375, 1.2531022536436516, 1.3375373407706024, 1.064447164466165, 0.9801785636699667, 1.00502562617521, 0.6675215277871374, 0.6251156890679493, 0.21175720798061054, -0.05999638516716603, -0.4974603817776169, -0.6884852158739834, -0.9557323438991752, -1.1839415679613883, -1.1600735474568957, -1.2368680424447467, -1.323950933071129, -1.4291195599019917, -1.2383974929052837, -1.3337713872528347, -0.8326009967147914, -0.8760408799878453, -0.6078299760656641, -0.21270827655277066, 0.07727048334333339, 0.3282514857611689, 0.48890251303799537, 0.7132501064965542, 4.56116096342317, 4.5814289844852505, 4.719057606334647, 4.603332485345656, 4.852018411157688, 4.6119344199888035, 4.885458598751127, 4.833268100107253, 4.853261457080854, 4.91846648182542, 4.737878675939672, 4.6284584239481, 4.719455095953231, 4.673089322989199, 4.658836756278723, 4.744841227210778, 4.69858546210932, 4.654534915098395, -3.5544655085163708, -3.4750274228372744, -3.4342835485983754, -3.690217660576744, -3.5602453778904994, -3.5440595898051157, -3.6481772714804084, -3.541895842561715, -3.5151257083036422, -3.4780418147295458, -3.522209466694478, -3.6180202102574004, -3.3287222665004603, -3.447012592095485, -3.4746532947926583, -3.4294421435565514, -3.505464352076597, -3.4012951807054495, 4.735443078558672, 4.729930629557513, 4.793278731409216, 4.887391638159188, 4.880960745059026, 4.789040643356095, 4.781417069387775, 4.799360124639744, 4.828317974863755, 4.8596290774714195, 4.70609747512971, 4.861562012513835, 4.764055394937226, 4.79484904578009, 4.8679508156834945, 4.8044621085391634, 4.821355439845379, 4.690814030201853, 4.879587037905063, -3.4603565981500326, -3.5173186974735953, -3.4198178305683347, -3.2711422194815953, -3.6468177194398383, -3.610298531549973, -3.2613947383740567, -3.4872557850272075 ]
null
Are the given two time series likely to have the same underlying distribution?
[ "No, they have different underlying distribution", "Yes, they have the same underlying distribution" ]
Yes, they have the same underlying distribution
binary
94
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "AutoRegressive Process", "Moving Average Process" ]
The difference between AR(1) and MA(1) is that AR(1) is a linear combination of past values and white noise, while MA(1) is a linear combination of past white noise values. You should check if the time series exhibit any dependency on the previous values. This could give you a clue about whether the time series is AR(1) or not. Check this for both time series.
Similarity Analysis
Distributional
666
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The following time series has an anomaly with short term disruption on its pattern. What is the likely pattern of the time series without the anomaly?
[ "Sawtooth wave with linear trend", "Sine wave with linear trend", "Square wave with log trend" ]
Sawtooth wave with linear trend
multiple_choice
72
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Sawtooth Wave", "Square Wave", "Linear Trend", "Log Trend", "Wander Anomaly" ]
Wander anomaly brings short term disruption on the pattern. You should focus on the overall pattern of the time series without the anomaly.
Anolmaly Detection
General Anomaly Detection
667
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null
You are given two time series where one is the lagged version of the other. What is the most likely lagging step?
[ "Lagging step is between 60 to 75", "Lagging step is between 5 to 20", "Lagging step is between 30 to 45" ]
Lagging step is between 5 to 20
multiple_choice
100
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Lagged Pair" ]
You already know that one time series is the lagged version of the other. Shift the time series by lags proposed in the options and check which one looks the same as the other time series.
Causality Analysis
Granger Causality
668
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Two time series are given. Both of them have a noise component. Do they have the same type of noise?
[ "Yes, they both have Gaussian white noise", "No, they have different noise" ]
Yes, they both have Gaussian white noise
binary
87
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Gaussian White Noise", "Red Noise", "Additive Composition" ]
When a white noise is added to a time series, it is expected the random fluctuations have similar amplitude or distribution. Random walk, on the other hand, can result in very different noise patterns.
Similarity Analysis
Shape
669
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The given time series has a trend and a cyclic component. It also has an anomaly. What is the most likely combination of components without the anomaly?
[ "Log trend and sawtooth wave", "Exponential trend and square wave", "Linear trend and sine wave" ]
Linear trend and sine wave
multiple_choice
70
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Sine Wave", "Exponential Trend", "Square Wave", "Log Trend", "Sawtooth Wave", "Cutoff Anomaly", "Flip Anomaly" ]
The anomaly only influences a small part of the time series. You should focus on the overall pattern of the time series without the anomaly. Can you recover the original pattern?
Anolmaly Detection
General Anomaly Detection
670
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null
The given time series has multiple trends followed by each other, what is the correct ordering of the trend components?
[ "Linear -> Exponential -> Log", "Linear -> Exponential", "Log", "Exponential -> Linear -> Log" ]
Exponential -> Linear -> Log
multiple_choice
9
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend", "Log Trend" ]
Identify the different components first, and then check the assignment of each component.
Pattern Recognition
Trend Recognition
671
[ 1.0572513287625522, 0.9415081542192116, 1.2085261434246461, 1.4062464491348592, 1.4049989161840488, 1.501518944732819, 1.5637543492092012, 1.6601653900843902, 1.525700704136479, 1.8105732481017935, 2.000085168777764, 2.1368947424869824, 2.3547467065274867, 2.27808480430265, 2.606412014127816, 2.6148852693365554, 2.8880511467569794, 3.1038207869488015, 3.410929206056927, 3.6286380841513446, 3.8114846192361274, 3.8464879678752935, 4.386515207566427, 4.614953524035422, 5.101275815211532, 5.419931021746506, 5.576904413499182, 6.120319308972804, 6.54070242930717, 6.980718054489569, 7.445918209185667, 7.980138850021151, 8.613716023645619, 8.992589317348484, 9.581625323288163, 10.418058601026067, 10.865108460481697, 11.881761662885616, 12.67962455090322, 13.269242947427065, 14.37219849435861, 15.589798396232405, 15.286483290600012, 15.479848113299447, 15.384486429938024, 15.440470337664122, 15.729384858245929, 15.576485418914707, 15.642224061325283, 15.605670542959237, 15.491791677325022, 15.551200696177917, 15.813924057564805, 15.737758247968051, 15.671828205670726, 15.773039869273585, 15.867792853860564, 15.873469950423397, 15.777430153776379, 15.723266754037146, 15.866480435741604, 16.044477961790328, 16.045398802840275, 16.027389440954966, 15.995649081448736, 15.987450454522182, 16.050280298415707, 16.170078313424252, 16.219308216350512, 16.11849848676761, 16.424688302345494, 16.206693557103335, 16.18914564266504, 16.397796139652378, 16.072787550948092, 16.351008581513753, 16.322113380926787, 16.50059966031015, 16.44266157232093, 16.422467461572975, 16.501208632476363, 16.355775029642526, 16.584403252435386, 16.37965070141905, 16.549959015201832, 17.0529053299331, 17.219791999467766, 17.659972590945188, 17.885537063575747, 17.961382255621814, 18.07054134933256, 18.34754851742258, 18.4468792593374, 18.534295726592525, 18.60419829027221, 18.630650964808854, 18.99200710342976, 18.80686345730855, 18.817267148412256, 18.972084670616226, 19.00769212998254, 19.049475676257664, 19.32194132684769, 19.071768623104152, 19.23631398885964, 19.171946473631557, 19.267762087787542, 19.537300984362926, 19.431979405505118, 19.46936781943023, 19.38564404898979, 19.47295979490343, 19.7323243915025, 19.63338215991353, 19.581826403167636, 19.69119663523983, 19.70428801325481, 19.62306724973414, 19.698775195478593, 19.988956708601254, 19.829795938131813, 19.660069372262445, 19.89369453311438, 19.998038318802728, 19.8017351600902, 19.870348979458562, 20.084714467176155, 19.965602042080757 ]
null
The given time series is a sine wave. What is the most likely amplitude of the sine wave?
[ "19.27", "5.9", "1.19" ]
5.9
multiple-choice
21
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Amplitude" ]
Check the distance between the peak and the baseline.
Pattern Recognition
Cycle Recognition
672
[ 0.17648737104525095, 1.1617712646708116, 2.1836371342108425, 3.2830650998990487, 4.090652596350757, 4.990628115634963, 5.595924223799604, 5.795867464565783, 5.734208099104288, 5.853140683613056, 5.200115339327498, 4.636808048027985, 3.997352405897587, 3.1050321518333557, 2.064696142254546, 0.8783279324066552, -0.11165205623232441, -1.44233855985659, -2.449171749306861, -3.4765693314363775, -4.546288996620182, -5.120672877960911, -5.375814614870551, -5.901579375148924, -5.949732581920669, -5.663234344708247, -5.300064489061421, -4.697327233350004, -3.848027236749028, -2.6876641309121285, -1.763510563088127, -0.7322961197917602, 0.42345357128320715, 1.9466539728213703, 2.7865877600058653, 3.8240137608465647, 4.525235586320514, 5.273904694309765, 5.8194475540882475, 5.815164555996191, 5.900095459140538, 5.4555141260739815, 5.318463392527299, 4.460372590471852, 3.5338886432314616, 2.5453515195474434, 1.4220574281174232, 0.2667180084019694, -1.104981880361223, -2.00878021305496, -3.0725062933854335, -3.947982919115221, -4.829105431251632, -5.444540168797196, -5.746156684594589, -6.056878570717992, -5.7979272623622204, -5.684748487270974, -4.8548823778870425, -4.170102169907202, -3.434746620921409, -2.2471699717703846, -1.1816163963720643, -0.1258854282729688, 0.9415014843093161, 2.2988796616456892, 3.221408002795633, 4.313126439761533, 4.941243114539008, 5.410333871236393, 5.983353300901084, 5.954505294566055, 5.390960162459822, 5.339318257894804, 4.667521118396369, 3.9534715737676986, 3.0866603241060493, 2.081327704337132, 0.935772103819859, -0.1549118712843423, -1.360963706200544, -2.472617689368001, -3.5151485196762717, -4.271725104950061, -5.122758950780853, -5.609134631331821, -6.038504140129096, -5.778428228153723, -5.694659864622174, -4.971164060088136, -4.6740106459320785, -3.8099158887607567, -2.7981077064546875, -1.8838825060995392, -0.5884834792675059, 0.5532236656857761, 1.6716984752789508, 2.90418728815426, 3.6709702137073315, 4.614197468359482, 5.375772068262981, 5.59597329327788, 5.8487171026509195, 6.091754679859388, 5.651369530853365, 5.077942179284594, 4.530219291984037, 3.538197759147239, 2.441101503297299, 1.6344770589375008, 0.22724908099033342, -0.5903361460438092, -2.0243932548909607, -2.823801872859928, -4.115307288018454, -4.659543513540194, -5.307058898152816, -5.655905061963286, -5.798071351101191, -5.866237766726417, -5.638440237010951, -4.985484696323704, -4.2335620523744755, -3.409868646016913, -2.3084901576741457, -1.1842627399665349, -0.14097100666062762, 1.1587658626017454 ]
null
Is the mean stable over time in the given time series?
[ "No", "Yes" ]
No
binary
43
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Mean" ]
Check if the average value of the time series changes over time.
Pattern Recognition
First Two Moment Recognition
673
[ 0.4153150887384082, 0.39868122807636647, 0.31790263417244347, 0.24221239112445186, 0.39892137227673263, 0.33214094767917274, 0.5218258008538774, 0.4523032737869306, 0.3951801624480051, 0.28553543781351953, 0.22596484327139785, 0.3613291049054415, 0.37570140780157313, 0.1874135207591322, 0.40844578438079965, 0.3660261652248504, 0.09400747172096341, 0.2755036592984938, 0.28213844915805986, 0.23907748654747557, 0.39983996442477443, 0.5399144400754254, 0.40744792631453225, 0.4243135285676643, 0.2835034058446082, 0.412058533775329, 0.3427558352045335, 0.3611697412895418, 0.30072807087629494, 0.20326856989108041, 0.4530496618391794, 0.3772242480757688, 0.33817853210902554, 0.5436428337933221, 0.26145555471649146, 0.42511311094853604, 0.5663963003562313, 0.402975747503002, 0.2450816610594384, 0.45893031727765554, 0.30654396317165455, 0.29965092115322445, 0.27083562051120225, 0.5239279541081994, 0.3205911811788941, 0.2690903030918589, 0.4857707303701169, 0.202327337552023, 0.3675137525108588, 0.2930833254901605, 0.42171524588864523, 0.3187510553441376, 0.21995192873538555, 0.37547509685138325, 0.31518071955234245, 0.445283807234857, 0.3677910292486968, 0.5752364310976065, 0.30542396021974505, 0.4783541561720207, 0.3260663278585282, 0.34898269372413404, 0.4367122728882492, 0.26691796328540246, 0.4799538382187352, 0.4570629520356286, 0.4936613645038269, 0.5348283494806279, 0.52583700399508, 0.5627223075815118, 0.6530494773702511, 0.5486986274872209, 0.556984841337687, 0.6499647194627058, 0.6383010172991929, 0.7485657282727898, 0.8682597171628028, 0.613875655663839, 0.7449976372278855, 0.6555666568448995, 0.7675689764530844, 0.800474632591193, 0.8030722968433096, 0.9592471149979833, 0.931371463874259, 0.8622496981862678, 1.0395954412071777, 0.964253523829573, 0.9491689184493594, 0.9272622089816834, 0.9092988296938107, 1.03604786007721, 1.115113643944986, 1.2287484354181586, 0.9583003353181833, 1.375818708784923, 1.1392032465772044, 1.2043171003101825, 1.2346346166663291, 1.233162789920435, 1.2925657092003757, 1.3259164613628767, 1.3612525796144799, 1.5617125766375413, 1.3564212038814951, 1.6400118456529253, 1.5378712133681265, 1.354808283570608, 1.453664416383062, 1.4684624124350452, 1.5879981193642767, 1.7489118849289509, 1.725080670863439, 1.568661111237896, 1.8186116938417793, 1.6195285444065395, 1.6613506378316307, 1.8821615735346082, 1.9067788872746383, 1.9122183128777022, 1.859439520824404, 1.8766613672620978, 1.7937841012280424, 1.9363559736460436, 1.896973178802219, 1.9732032853965207, 2.24725269960696, 2.0768211858675443 ]
null
The time series has a trend and cyclic component added together. Which components are most likely present in the given time series?
[ "No trend and sawtooth wave", "Linear trend and sine wave", "Exponential trend and sine wave" ]
Exponential trend and sine wave
multiple-choice
27
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend", "Sine Wave", "Sawtooth Wave", "Additive Composition" ]
For trend, check if the slope is constant or changes over time. For cyclic component, check the overall shape of the time series.
Pattern Recognition
Cycle Recognition
674
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null
What is the most likely autocorrelation at lag 1 for the given time series?
[ "Negative autocorrelation", "High positive autocorrelation", "No autocorrelation" ]
High positive autocorrelation
multiple_choice
45
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Autocorrelation" ]
While it is hard to directly measure the autocorrelation for higher order lags, the autocorrelation at lag 1 can be approximated by observing the time series pattern. You can tell this by checking the sign and magnitude changes at each step compared to the previous step.
Pattern Recognition
AR/MA recognition
675
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null
Does the given time series exhibit regime switching?
[ "Yes", "No" ]
Yes
binary
40
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Regime Switching" ]
Identify whether the time series exhibit different patterns over time.
Pattern Recognition
Regime Switching Detection
676
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null
The given time series is a random walk process. What is the most likely noise level?
[ "0.81", "7.7", "3.82" ]
7.7
multiple_choice
54
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Red Noise" ]
The noise level refers to the standard deviation of the noise. You should check the degree of variation of the time series over time. You can estimate the standard deviation by observing the average distance between the data points and the past value.
Noise Understanding
Red Noise Recognition
677
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null
The given time series has a cyclic component and a trend component added together. What is the most likely type of the trend component?
[ "Exponential", "Log", "Linear" ]
Log
multiple_choice
10
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend", "Log Trend", "Sine Wave", "Additive Composition" ]
Despite having a cyclic component, check the general trend of the time series.
Pattern Recognition
Trend Recognition
678
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null
The following time series has an anomaly with random large fluctuations. What is the likely pattern of the time series without the anomaly?
[ "Sine wave with linear trend", "Sawtooth wave with linear trend", "Square wave with log trend" ]
Square wave with log trend
multiple_choice
67
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Sawtooth Wave", "Square Wave", "Linear Trend", "Log Trend", "Spike Anomaly" ]
Spikes anomaly bring constant large random fluctuations. Can you check the place where the spikes disappear and try to recover the original pattern?
Anolmaly Detection
General Anomaly Detection
679
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null
Is the noise in the time series more likely to be additive or multiplicative to the signal?
[ "Additive", "Multiplicative" ]
Multiplicative
binary
60
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Additive Composition", "Multiplicative Composition", "Gaussian White Noise" ]
Additive noise is added to the signal, while multiplicative noise is multiplied to the signal. When a cyclic component is added with a white noise, the cyclic pattern still remains. When a cyclic component is multiplied with a white noise, the noise is amplified. Can you check if it is the case for the given time series?
Noise Understanding
Signal to Noise Ratio Understanding
680
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null
You are given two time series which both have upward trend. Which time series has a higher slope in terms of magnitude?
[ "Time series 1 has higher slope", "Time series 2 has higher slope" ]
Time series 2 has higher slope
binary
80
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend", "Sine Wave", "Sawtooth Wave" ]
Slope refers to the steepness of the trend. You should check the direction of the trend and the steepness of the trend. If the trend is upward, you should check the magnitude of the slope.
Similarity Analysis
Shape
681
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Does time series 1 granger cause time series 2?
[ "No, time series 2 granger causes time series 1", "No, they are not granger causality", "Yes, time series 1 granger causes time series 2" ]
Yes, time series 1 granger causes time series 2
binary
103
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Granger Causality" ]
Granger causality is a statistical concept that determines whether one time series can predict another. While you cannot perform the statistical test, you can check if one time series can predict the other by shifting the time series by a certain number of steps. Do they look simiar after the shift?
Causality Analysis
Granger Causality
682
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Is the given time series stationary?
[ "No", "Yes" ]
No
binary
30
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Stationarity" ]
Try to see if the time series has a constant mean, and degree of variation over time.
Pattern Recognition
Stationarity Detection
683
[ -1.6261249495241679, -1.4046243907506435, -1.362839820374613, -1.2210179396564693, -1.42790514061027, -1.366322890249277, -1.1953130396639637, -1.0975088992641555, -1.081875798071353, -1.0360637309205478, -0.7998041764257054, -0.8650653103349434, -0.9069616496436725, -0.8248578231170036, -0.619630888481712, -0.27352047907550436, -0.6008285085128019, -0.4641699475772011, -0.12165046975490176, -0.3400074268369638, -0.17548167629758743, 0.0371149052627843, -0.17507244165833213, -0.04029900234171664, 0.012742019925374513, -0.02005932957950171, 0.35921839471446926, 0.21429295972700893, 0.2557604194201954, 0.3694931916237318, 0.5773713143745732, 0.5663291209883399, 0.5464247301729045, 0.7370579386358352, 0.8479540173475759, 0.8348696822108321, 0.8843216415429315, 1.079936921696108, 1.030982396634931, 1.2802716653436668, 1.1142406209340219, 1.1824643549953628, 1.2407276169913968, 1.3777742427592221, 1.472460887993241, 1.4101984843277178, 1.6229893955048063, -1.5237185771146455, -1.656251557894155, -1.4912679516245515, -1.311850642701176, -1.4069895487172768, -1.2590938808926422, -1.048126078379527, -0.9068745655319158, -0.9718497272912159, -0.962214983570501, -0.9248778636229232, -0.7131110582538067, -0.6202942347910055, -0.7787268609859481, -0.501489006251401, -0.5826847245900274, -0.5373840783842405, -0.3962413279156699, -0.2111639898760017, -0.2088331882198818, -0.14098896079637824, -0.06342636844710292, 0.018646861450354234, 0.031017531257060502, 0.17617312297729493, 0.1175676202689819, 0.31918819838942725, 0.4103375615066622, 0.4651042796083503, 0.5408450967494514, 0.5827803710314448, 0.7241896919710812, 0.4502356154673427, 0.8333231830501138, 1.0160459334377743, 0.82686222665449, 0.8862303817425146, 1.1587868623045345, 1.008032620487615, 1.1045857166063866, 1.258804593262101, 1.2324662137054045, 1.4704153783484553, 1.3743843093517705, 1.5600794497765456, 1.6230159547339174, -1.4326111488815154, -1.4119181760644004, -1.5108495234109496, -1.51379441648442, -1.2329966982110625, -1.3115810724557497, -1.209258069342403, -1.2111215711300027, -0.9666860156165666, -1.0286849269106118, -0.8969881906687506, -0.8248827349993293, -0.7340247729903024, -0.6156653913813398, -0.6355596853143377, -0.6148688128851809, -0.656128924643682, -0.38935990490298145, -0.3447711784731624, -0.3295669639950694, -0.18171284133932747, -0.031818226864703536, 0.06432390779691494, -0.12982704911185328, 0.05815215605744151, 0.26089240082720666, 0.3949455764680554, 0.2241667011283004, 0.514276952795789, 0.3119866250774585, 0.6323763030413037, 0.559923806937164, 0.8149333601504624, 0.6827995053889471, 0.7687651477668317 ]
null
What type of trend does the time series exhibit in the latter half?
[ "Linear", "Exponential", "No trend" ]
No trend
multiple_choice
14
medium
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Exponential Trend" ]
Focus on the pattern of growth or decline in the second half of the time series.
Pattern Recognition
Trend Recognition
684
[ 0.08797386742198851, -0.08298546474457455, -0.17383581759029032, 0.07233607268623782, 0.14744158017432357, 0.06977017608416562, -0.1071342504232476, 0.07248690862469914, -0.0571398800632249, -0.0919900007377523, 0.06840168607420942, 0.09233516393182671, 0.0731399491014037, 0.13373266337686684, 0.01777593067749575, 0.11232081058258478, 0.062134414967868846, 0.09241744359742224, 0.15134449728751984, 0.2373839079945662, 0.1675665338194324, 0.20765469239721607, 0.15319317323911028, 0.20784900916952798, 0.26938403822104606, 0.3608399542048536, 0.3009155645189218, 0.18124638349163588, 0.3081383213088126, 0.2554927333439202, 0.14678435453747068, 0.27070334245995903, 0.10846945873216432, 0.28468607383494426, 0.4103524070557152, 0.3243511689739216, 0.3686682522049404, 0.21810395672163088, 0.3109284372536444, 0.33957346066325234, 0.24615763512176667, 0.3519616267842159, 0.3359764535672318, 0.3669060192920791, 0.2013336633795626, 0.4388679811373549, 0.36323923855587104, 0.31327815251747365, 0.32260741372918533, 0.3350428559015699, 0.26294966849314394, 0.4716751793074584, 0.4559869258552302, 0.46962574450380146, 0.5248288863387086, 0.3994043259272277, 0.22176996011269537, 0.4571473832356428, 0.46033957674675996, 0.5634772652757637, 0.5232192173894006, 0.4353260666963312, 0.4144132976882241, 0.5361250253947137, 7.79446280995336, 8.084097550641827, 8.154523620297093, 8.047856833690748, 8.021741767809804, 8.089441910330303, 8.194902222268837, 8.105061917389625, 7.9922552255069625, 8.18165575793556, 8.20112220440699, 7.979224613722895, 8.339814145218126, 8.059892246623482, 8.154800131086853, 8.132703773468245, 7.990157388483992, 8.014804952322867, 8.06672833501663, 7.872951444146498, 8.142055310197527, 7.870382939673778, 8.061424291283595, 7.992786188327294, 8.117838464993492, 7.839540215473783, 7.893737604442685, 8.000281722213106, 8.111841946309047, 8.082117355828709, 8.164985753354811, 8.07074752384178, 8.058183370563597, 7.952799659963266, 8.037620520236349, 8.05800601007463, 7.854482084771747, 7.970935619808651, 8.106293169716865, 8.07790689029416, 8.034656819254925, 7.999213464486714, 7.885668756633329, 7.842419410811118, 8.029288790377358, 8.208852060026668, 8.063648087870337, 8.16209753090322, 7.94228881185953, 8.088272503566877, 7.9895888774658355, 7.985729585464162, 8.134416514325752, 8.04791285447892, 7.921404134236119, 8.069760512259402, 7.988340702367698, 7.915524530672764, 7.96042259558042, 8.26454688356734, 8.18119599930401, 7.858503794866466, 8.04112096935307, 8.048409264375872 ]
null
Is the noise in the time series more likely to be additive or multiplicative to the signal?
[ "Multiplicative", "Additive" ]
Additive
binary
58
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Additive Composition", "Multiplicative Composition", "Gaussian White Noise" ]
Additive noise is added to the signal, while multiplicative noise is multiplied to the signal. When a trend component is added with a white noise, the general trend still remains. When a trend component is multiplied with a white noise, the noise is amplified. Can you check if it is the case for the given time series?
Noise Understanding
Signal to Noise Ratio Understanding
685
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null
How does the linear trend in the first half of the time series compare to the trend in the second half?
[ "Same", "Different" ]
Same
binary
6
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Piecewise Linear Trend" ]
Check if the time series is a piecewise linear trend with different slopes in the first and second half.
Pattern Recognition
Trend Recognition
686
[ -0.030945326415154954, -0.025507593502929894, -0.041810396413970136, -0.10156864616481634, 0.03353293356247428, 0.12977400456710853, 0.025246450072538628, -0.08005954333577472, 0.08688679878638497, -0.056443453159555124, -0.025976926537676227, 0.03867916845959831, 0.06578288253738149, 0.0009215697726798061, 0.05083134436684768, 0.11682944934918277, 0.13012228171911275, 0.15957309740515496, 0.20496155581058684, 0.1420704240814579, 0.08367089884749826, 0.15481789084026057, 0.13548104089718038, 0.14277514035105393, 0.12734742508153454, 0.06508819595319114, 0.06278999924700096, 0.12499905506784245, 0.14500813718453318, 0.09882438503905622, 0.17161837856240345, 0.27858397812034674, 0.04776981571137799, 0.1959620269705073, 0.16087625604370145, 0.1975572035591272, 0.1481069188475459, 0.17049579376025034, 0.19232435503097448, 0.17061324249848636, 0.10036718948734208, 0.18448783178992778, 0.11648370606046764, 0.24884524459224464, 0.0985162216361255, 0.28167993782226464, 0.2496209406320514, 0.25470784304374233, 0.0995140536955951, 0.21746393721465693, 0.31363164774221564, 0.21545986330918326, 0.1858429265907392, 0.21788843054922266, 0.2577584688885135, 0.21436308644328572, 0.34768333944924285, 0.2725345030182298, 0.24714109763685435, 0.20604492850468992, 0.32091920728820084, 0.32436691049302974, 0.25196648270757005, 0.16784500740635164, 0.3357843083008291, 0.3038193160155136, 0.34088498186623256, 0.44561285883421564, 0.3282288269848179, 0.303075396500854, 0.2688974994728856, 0.32518715857866154, 0.35917998473754076, 0.3574222568275085, 0.46517239978657143, 0.3945891941947906, 0.36038646290532095, 0.3300113783433901, 0.39482378594942624, 0.3273641520910436, 0.3991758534931659, 0.42297733143480365, 0.3844631287409208, 0.36381788145262794, 0.2728644221706816, 0.4828245602524459, 0.4420510962044212, 0.4484004723571175, 0.3307106537794759, 0.516769533974348, 0.4079463038925596, 0.4236668952299244, 0.38043177812655843, 0.34106780136965076, 0.5273177355835128, 0.5401321376704623, 0.45551744732299276, 0.4287098020167429, 0.45218829122148957, 0.4587294163705422, 0.41119678464701337, 0.4719657796942363, 0.5042555779620959, 0.5624031006384996, 0.5054029149964906, 0.41225702409609916, 0.5360099293499841, 0.5033109831171136, 0.6083615064686085, 0.6168506834571093, 0.6238580341805618, 0.5038841595649914, 0.6659305451725943, 0.5698078479510418, 0.6532391703888767, 0.5269220361043399, 0.544343152695728, 0.5844739023030656, 0.5817994245199087, 0.654602749682591, 0.5678430509163034, 0.658748098087091, 0.6369602099578608, 0.5835510645706002, 0.6418842549129811, 0.5772426306557321, 0.7560487341871316, 0.45195271898489814 ]
null
Which of the following time series is more likely to be an MA(1) process?
[ "Time Series 1", "Time Series 2" ]
Time Series 2
multiple_choice
49
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Moving Average Process", "Stationarity" ]
MA(1) process is a stationary process with a constant mean and variance. You should check if the time series has a constant mean and variance over time. The other option is likely not stationary.
Pattern Recognition
AR/MA recognition
687
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[ 10.021426264197476, 9.811001578444122, 10.21971083863697, 10.091297134021707, 11.117256528564413, 10.406568238386619, 12.672609438643995, 9.152507200042468, 9.872317714399907, 7.993324656884369, 8.74457179680391, 8.883175330392481, 10.117640714145601, 9.341563057112236, 12.326196842023503, 10.976484768218896, 10.63628468135754, 11.1068148222764, 9.133854658417443, 10.604086616213669, 8.515226211264551, 8.834378271559423, 7.561728484273839, 10.132807406022696, 8.370166722328932, 12.011815781872706, 10.065066753829907, 10.467139663927757, 11.29850114126474, 8.628732054750706, 10.190514643372829, 6.801272184039174, 9.72053436165207, 7.434309451560518, 12.268073480755827, 9.424826800293612, 12.571303092360614, 10.699762642575152, 10.577838898123995, 11.514339715364072, 9.970951728470395, 11.269258065335048, 12.38445388781705, 10.572734606490974, 11.358608948843715, 9.445994864940547, 9.494699518339372, 9.55092970874534, 9.992694621230594, 8.51175133978834, 7.783765235676049, 7.765682537400495, 8.247865381446497, 9.288212290749192, 10.50150105547152, 10.41355469262871, 9.864102809405374, 9.269723818528549, 10.121443412956157, 9.409572979336557, 9.323640525714156, 10.805667836039692, 10.082468854218101, 11.289286954912894, 11.73010041893966, 9.880965208054473, 11.623375892236576, 9.241672643858067, 12.726260387805837, 10.767855009053793, 12.065256807318152, 12.431560626125101, 9.837224202554191, 11.923692737337994, 11.830546002995872, 11.253737543360781, 11.939909221174677, 10.380736360998869, 9.152881439150507, 9.494593144633392, 8.406551896813154, 9.538147018272882, 9.234745439565353, 10.804581923472039, 9.503231803732126, 10.194368489935853, 10.560342480374086, 10.219391530909643, 10.466339120099633, 11.158259514289682, 9.543210659360788, 10.267537126543187, 11.34424465129445, 9.691623010643925, 10.83725290576896, 9.907617049101967, 7.709972581990532, 9.846352938578598, 8.682450526533433, 11.847025185631233, 10.296166467335848, 12.02302556821163, 10.420335327936703, 12.618935994286616, 11.27984601949058, 10.363883989873703, 12.031319063328118, 7.894274715888971, 10.329694805375864, 7.944320397100233, 11.299428743274497, 10.146552301054422, 12.688529012287924, 11.984962007593936, 11.675271349681815, 10.509018433552875, 10.758642164698259, 9.227904077443226, 9.313503516527279, 8.94644395719482, 11.673104066404031, 9.10531272883029, 12.884114104687411, 11.771328437888377, 11.581326766246882, 10.87371677246588, 9.887954307619205, 9.488437645787036 ]
The following time series has an anomaly with short term disruption on its pattern. What is the likely pattern of the time series without the anomaly?
[ "Sine wave with linear trend", "Sawtooth wave with linear trend", "Square wave with log trend" ]
Square wave with log trend
multiple_choice
73
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Sawtooth Wave", "Square Wave", "Linear Trend", "Log Trend", "Wander Anomaly" ]
Wander anomaly brings short term disruption on the pattern. You should focus on the overall pattern of the time series without the anomaly.
Anolmaly Detection
General Anomaly Detection
688
[ 0.04967141530112327, 0.07179331851347275, 0.23277487032420066, 0.3996971561172212, 0.3005794410715708, 0.374583280181079, 0.6274925598694775, 0.6156154218272265, 0.5590915613751694, 0.7254559004220134, 0.6881292407134054, 0.7493858981537594, 0.8799574837232762, 0.7226400781029316, 0.7981705588186427, 0.9696918504686329, 0.9785307234268336, 1.1638325887983814, 1.09296142494668, 1.0927083443606767, 1.4295504854523406, -1.3535317485208873, -1.3711378257876192, -1.5663134805658576, -1.5232772179574003, -1.5018375453523942, -1.6712466268831865, -1.560955469124464, -1.7001596700807926, -1.7100584312158345, -1.781104231493585, -1.5750285156643629, -1.8002326275009608, -1.942608599263176, -1.79188862763238, -2.032905929071095, -1.926007221758829, -2.178345909986917, -2.1501148979754827, -2.0319775366042565, -2.0116514009248587, 2.1359525958040697, 2.1400675020538418, 2.1538522299715845, 2.067968578473751, 2.175236032293395, 2.2321107597925782, 2.4144080158488834, 2.3731576996478285, 2.1921823144647554, 2.4301865671937124, 2.3881737253460513, 2.3875156270118927, 2.5445331748364, 2.614264444218808, 2.6317417047412786, 2.481800087432396, 2.561576066384735, 2.652074495364497, 2.742636674091019, 2.6229894083485714, -2.7149952996136273, -2.832290354618452, -2.866216607165813, -2.6900006003875583, -2.6600108675014997, -2.826948110777316, -2.74324246855297, -2.831022946860857, -2.9708264377548335, -2.9090558046399297, -2.83003077531988, -3.0258192795670014, -2.9039425894369364, -3.3603244912120287, -3.053880071264075, -3.164867703178546, -3.2407612820137732, -3.2387628302919484, -3.4835684387014685, -3.3434495915314466, 2.9831402417222677, 3.099918099502804, 2.904810758200406, 2.8801103936560413, 2.9149223305001515, 3.0605961598017126, 3.0057118402110063, 2.9392569812868015, 3.0627851011351668, 3.0402235385320657, 3.146272686341564, 2.9979330929104964, 3.053942975015876, 3.0659124252456786, 2.977031683703365, 3.1711035894973647, 3.185556412666642, 3.1777749291085704, 3.1714733172622824, 3.0709214702993917, -3.8719099196160185, -3.8813662192830414, -3.944436568852386, -3.8973182876045693, -3.85763436287237, -3.726141458254228, -3.913895698852974, -3.9220666245190716, -3.971611066926312, -4.172266871687224, -3.999144669678496, -4.006455804967626, -3.7820238867878144, -4.063338874047338, -4.029589773422371, -4.078746073273648, -4.20756332118453, -3.991725630334883, -4.046020284683124, -4.057210828448606, 3.460371918682382, 3.7064843592142642, 3.4408130970655977, 3.6543775594799786, 3.8293327639332633, 3.525731930981227, 3.5825584440862874 ]
null
Is the two time series lagged version of each other despite minor noise?
[ "No, they are not lagged versions at all", "Yes, they are lagged versions" ]
Yes, they are lagged versions
binary
102
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Lagged Pair", "Red Noise" ]
Try to shift one time series by a certain number of steps and check if it looks the same as the other time series despite the noise. If they are lagged versions, they should look very similar in general after the shift.
Causality Analysis
Granger Causality
689
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The given time series is a sine wave. What is the most likely amplitude of the sine wave?
[ "7.92", "5.57", "1.67" ]
7.92
multiple-choice
21
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Amplitude" ]
Check the distance between the peak and the baseline.
Pattern Recognition
Cycle Recognition
690
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null
What is the most likely variance of the given time series?
[ "varies across time", "0.51", "1" ]
1
multiple_choice
42
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Variance" ]
Check the degree of variation of the time series over time.
Pattern Recognition
First Two Moment Recognition
691
[ -0.0603713442254934, 0.004464017087844817, -0.08096245108330126, 0.019327085858399515, -0.005045522457030244, 0.22806842173883562, 0.00125455873531026, 0.15892577273303354, 0.14059906050095403, 0.12476698150011839, -0.053363520590181554, 0.03853607124487039, 0.11546511574686474, -0.02555539713929464, 0.0187648086207792, 0.10731273995340787, 0.24508128156174372, 0.4203089292251359, 0.25776685733322646, 0.24834706705202622, 0.2516464241600935, 0.20084069884135008, 0.2504888532553077, 0.36332083023390727, 0.43395451954742054, -0.07220714111163207, 0.4236733549223396, 0.28023795660250983, 0.41303719151397567, 0.40456572214063424, 0.3412989126733097, 0.45394128693857716, 0.42919927015910925, 0.3918432428838586, 0.39292410226501184, 0.2706345781186189, 0.4359462464347509, 0.1411650399192842, 0.5019051897827451, 0.5845220763048519, 0.26026464073535244, 0.45163327070527354, 0.7232471618658467, 0.8521052190241709, 0.5153602340675647, 0.551746362540337, 0.5433237629740789, 0.5893207476404347, 0.7674059464438764, 0.590898109955735, 0.39258349116631963, 0.6538294945272576, 0.5676415113319142, 0.46720750813386214, 0.47930992749744195, 0.645837571957061, 0.7706356523202957, 0.7741652131536846, 0.8833206161940825, 0.5950555123193921, 0.666330159567444, 0.8322071619641433, 0.857309086846781, 0.6793502415761392, 0.6659948686243929, 0.8552646530066637, 0.9297580726113245, 0.7709169826752779, 0.8896125291507695, 0.8317930934651973, 0.7437030100741315, 0.967957564734174, 0.8327164333057184, 0.6476443017092047, 0.7909090904652573, 0.5595076365138827, 1.3294581660509188, 1.1265412010775366, 0.7378889311107552, 0.8615929402196891, 0.998324508535756, 1.220702777067339, 1.0988121610821953, 1.0338253445730725, 0.9220459188134809, 1.0973216371696515, 1.1032044643328043, 1.0534868742913313, 1.0480903258597203, 1.0039196631105691, 1.2812945500539146, 0.8375882896275196, 1.1556887480565465, 1.123097931347711, 0.8313595286993724, 1.0867462718399903, 1.0007340907076714, 1.0107209330400944, 1.0609107202675336, 1.3833384431093814, 1.1958046331003789, 1.330928726157802, 1.044997063758821, 1.1462474719911724, 1.187979566930664, 1.2895653934256903, 1.358527393566828, 1.3306616898627477, 1.1776881865599311, 1.4265667431447235, 1.232128297143598, 1.3781462269179123, 1.1392000373556983, 1.3223300647240297, 1.4527228007778767, 1.401320824197035, 1.2725022213447128, 1.4926338553592247, 1.3027293023667823, 1.1663982522159575, 1.6039217998280209, 1.3043355784991268, 1.5907126545503598, 1.4457235865512463, 1.592809417326047, 1.3859547921309576, 1.6489529808360106, 1.446764211892181 ]
null
The given time series has an increasing trend, is it a linear trend or log trend?
[ "Linear", "Log" ]
Linear
multiple_choice
7
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Linear Trend", "Log Trend" ]
Check if the slope of the time series is constant or changes over time.
Pattern Recognition
Trend Recognition
692
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null
Are the given two time series likely to have the same underlying distribution?
[ "Yes, they have the same underlying distribution", "No, they have different underlying distribution" ]
No, they have different underlying distribution
binary
95
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Red Noise", "AutoRegressive Process", "Linear Trend" ]
When we say two time series have the same underlying distribution, you should check if they have the same mean and variance. They should also share similar behaviors over time.
Similarity Analysis
Distributional
693
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What is the primary cyclic pattern observed in the time series?
[ "SawtoothWave", "SineWave", "No Pattern at all", "SquareWave" ]
SawtoothWave
multiple-choice
15
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave", "Sawtooth Wave" ]
Check the overall shape of the time series against the definition of provided concepts
Pattern Recognition
Cycle Recognition
694
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null
Is the two time series lagged version of each other despite amplitude difference?
[ "Yes, they are lagged versions", "No, they are not lagged versions" ]
Yes, they are lagged versions
binary
104
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Lagged Pair" ]
Try to shift one time series by a certain number of steps and check if it looks the same as the other time series despite the scale difference. If they are lagged versions, they should look very similar in general after the shift.
Causality Analysis
Granger Causality
695
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How does the noise in the given time series influence the detection of periodic pattern in the time series?
[ "No influence", "Distort the pattern" ]
No influence
binary
58
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Gaussian White Noise", "Sine Wave", "Additive Composition" ]
When the noise level is high, it can distort the pattern in the time series. Can you check if you can still detect the cyclic pattern in the time series?
Noise Understanding
Signal to Noise Ratio Understanding
696
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null
There are two time series given. Is one of them a scaled version of the other?
[ "Yes, time series 1 is a scaled version of time series 2", "Yes, time series 2 is a scaled version of time series 1", "No, they do not share similar pattern" ]
Yes, time series 2 is a scaled version of time series 1
binary
87
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Moving Average Process" ]
Scaled version refers to the same pattern but with different amplitude. You should check if the pattern is the same for both time series. If they are the same, you should check the amplitude of the cyclic component.
Similarity Analysis
Shape
697
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One type of noise in time series is random walk. Is the given time series noisy based on your understanding of random walk
[ "Yes", "No" ]
Yes
binary
57
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Red Noise" ]
When we say a time series is noisy, it typically refers to there are random fluctuations that disrupt the overal pattern of the time series. When the time series has a random walk noise applied to it, it seems like the pattern are even more disrupted. Can you check if it is the case for the given time series?
Noise Understanding
Signal to Noise Ratio Understanding
698
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null
Does the given two time series have similar pattern?
[ "Yes, they have similar shape", "No, they have different shape" ]
Yes, they have similar shape
binary
78
easy
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Square Wave" ]
Pattern refers to the general shape of the time series. In this case, you see both time series have cyclic patterns. Do their behaviors at peak and trough look similar?
Similarity Analysis
Shape
699
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You are given two time series with same underlying pattern but different noise level. Which time series has higher magnitude of noise?
[ "Time series 2", "Time series 1" ]
Time series 2
multiple_choice
60
hard
Please answer the question and provide the correct option letter, e.g., A), B), C), D), and option content at the end of your answer. All information need to answer the question is given. If you are unsure, please provide your best guess.
[ "Sine Wave", "Exponential Trend", "Gaussian White Noise", "Variance" ]
When the noise level is high, it can distort the pattern in the time series. Both time series have the same underlying pattern, but different noise level. To tell which time series has higher noise level, you should check the degree of distortion of the time series pattern.
Noise Understanding
Signal to Noise Ratio Understanding
700
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