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Does the given two time series have similar pattern?
[ "No, they have different shape", "Yes, they have similar 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
701
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What is the most likely mean of the given time series?
[ "-15.41", "7.17", "26.75" ]
7.17
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
702
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null
Does the trend of the time series change direction?
[ "Yes", "No" ]
Yes
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
703
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null
Is the given time series likely to have an anomaly?
[ "No", "Yes, it's pattern is flipped at certain point in time", "Yes, it's pattern is distorted by random spikes" ]
Yes, it's pattern is flipped at certain point in time
binary
64
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
704
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null
Does the given time series exhibit any monotonic increasing trend?
[ "Yes", "No" ]
Yes
binary
3
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", "Log Trend" ]
Check if the time series values increase over time.
Pattern Recognition
Trend Recognition
705
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null
You are given two Autoregressive processes AR(1). Which of the following time series has higher standard deviation for their random component?
[ "Time series 1", "Time series 2" ]
Time series 2
multiple_choice
61
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", "Variance" ]
The standard deviation of the noise component is related to the average distance between the data points and their past values. You should check the degree of variation of the time series over time. Which time series has a higher change in average?
Noise Understanding
Signal to Noise Ratio Understanding
706
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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
707
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null
The given time series is a random walk process. What is the most likely noise level?
[ "3.58", "8.11", "1.44" ]
8.11
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
708
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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", "Linear", "Log" ]
Linear
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
709
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null
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 2
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
710
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You are seeing two time series that are random walk. Are they likely to have the same variance?
[ "Yes, they have the same variance", "No, time series 2 has higher variance", "No, time series 1 has higher variance" ]
Yes, they have the same variance
multiple_choice
93
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", "Variance" ]
Random walk is a time series model where the next value is a random walk from the previous value. Variance refers to the distance of the values from the previous steps. At a high level, you should check the distance of the values from the previous steps for both time series.
Similarity Analysis
Distributional
711
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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 cutoff anomaly", "No. They have different types of anomalies" ]
Yes, Time series 1 and time series 2 both have cutoff anomaly
binary
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.
[ "Cutoff 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
712
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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
713
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null
Which of the following best describe the cycle pattern in the given time series?
[ "Amplitude increase over time", "Amplitude remain the same over time", "Amplitude decrease over time" ]
Amplitude remain the same over time
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", "Amplitude" ]
Check the distance between the peak and the baseline, and see how it changes over time.
Pattern Recognition
Cycle Recognition
714
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null
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
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
715
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null
The following time series has a noise component. Is it a white noise or random walk?
[ "White Noise", "Random Walk" ]
Random Walk
binary
52
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", "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. This can help you distinguish between white noise and random walk.
Noise Understanding
White Noise Recognition
716
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null
The given time series has sine wave pattern. How does its amplitude change from the beginning to the end?
[ "Increase", "Decrease", "Remain the same" ]
Increase
multiple-choice
17
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
717
[ -0.08030424010642451, 0.3817549007772821, 0.4039064967730728, 0.3911432928372608, 0.9524166637770852, 0.983750777250265, 0.9964228459552442, 1.298031544057805, 1.5091577271995757, 1.6018315667383425, 1.821002683841924, 1.6097261794508457, 1.7267745345802876, 1.6520753763207008, 1.540574129005356, 1.7293683530111819, 1.6072774660868763, 1.484825982948434, 1.3716661076002918, 1.112001197660964, 0.9129147432016679, 0.834194920757883, 0.750395479433601, 0.5889192018384343, 0.2947375524224627, 0.0017993772252868278, -0.19043437987984724, -0.42911795226908345, -0.7389477110814255, -0.8299248704705332, -1.1487758312439968, -1.1945860367441443, -1.1668016280693463, -1.3753700030424676, -1.6542140538209593, -1.6487489739554981, -1.7786494324813442, -1.728423394682662, -1.6178505811162247, -1.6292823657115818, -1.3920549486272653, -1.441225972607704, -1.435458288783011, -1.260558728275781, -1.1999771410546036, -1.1253295893745996, -0.6988722901185265, -0.5323352728496271, -0.45113371494225385, -0.1866913267452902, 0.12633004917208085, 0.3031570242837818, 0.2850498672655896, 0.6617544976569317, 0.816605644077014, 1.1274970289236341, 1.2860967592382817, 1.4629846096176757, 1.3464644672003483, 1.483965811503639, 1.753258502446808, 1.6362553435962437, 1.5700974919913835, 1.7751493471153972, 1.6671678543273933, 2.6077570544080295, 3.1537948724043265, 3.8128078636142115, 4.3987375384022505, 5.189515502969524, 5.607280049669109, 6.008996524618628, 6.378512895737087, 6.781668775849366, 6.9399845861120815, 7.302965639682325, 7.092529245729254, 7.242463342410238, 7.210520618477902, 6.988590635211725, 6.602472376766115, 6.379553121404723, 5.789616909628644, 5.373118519486511, 4.878293422168427, 4.246907801852016, 3.4803303847887492, 2.9851223965972444, 2.1729947593543035, 1.530385803873361, 0.9050777221314479, 0.17576300371608183, -0.48518544064799574, -1.2014450071462588, -1.7170047208162105, -2.293537171420438, -2.8887135019342365, -3.1174153027524554, -3.4228115346738743, -3.6067934195103186, -3.8071229775501774, -3.909964631049432, -3.7173611644006868, -3.7740544282433617, -3.2693636429819626, -3.1274061614898034, -2.6902855011718163, -2.197441403658046, -1.668074192216376, -1.2858262497873894, -0.433706419364517, 0.1793898221730593, 0.776302528862359, 1.46995331667002, 2.2194825326451433, 2.822350599396115, 3.8037904335856956, 4.428477703449673, 4.931753896661871, 5.41952605528485, 5.916972218519587, 6.438798996774737, 6.889647533647324, 6.926557477325744, 7.056046486233507, 7.418258602698403, 7.090396250517223, 7.083707485165503 ]
null
The given time series is a square wave. What is the most likely period of the square wave?
[ "38.18", "52.14", "17.59" ]
17.59
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
718
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null
Does time series 1 granger cause time series 2?
[ "No, they are not granger causality", "Yes, time series 1 granger causes time series 2", "No, time series 2 granger causes time series 1" ]
No, time series 2 granger causes time series 1
binary
101
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
719
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The following time series has two types of anomalies appearing at different time points. What are the likely types of anomalies?
[ "cutoff and flip", "speedup and cutoff", "speedup and flip" ]
speedup and cutoff
multiple_choice
68
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", "Speed Up/Down Anomaly" ]
You should first identify the two places where the anomalies appear. Then, you should check the type of anomaly based on the given definitions.
Anolmaly Detection
General Anomaly Detection
720
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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
99
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
721
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What is the primary cyclic pattern observed in the time series?
[ "SineWave", "SawtoothWave", "SquareWave", "No Pattern at all" ]
No Pattern at all
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
722
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null
What is the most likely variance of the given time series?
[ "varies across time", "0.23", "1" ]
varies across time
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
723
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null
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" ]
No
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
724
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null
Does any part of the given time series, composed of several concatenated patterns, appear to be stationary?
[ "Yes", "No" ]
No
binary
32
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
725
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null
Which additive combination of patterns best describes the time series?
[ "SawtoothWave + SquareWave", "SineWave + SquareWave", "SineWave + SawtoothWave" ]
SawtoothWave + SquareWave
multiple-choice
17
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" ]
Imagine the shape of the time series as addition of two different patterns.
Pattern Recognition
Cycle Recognition
726
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null
The given time series has square wave pattern. How does its period change from the beginning to the end?
[ "Decrease", "Remain the same", "Increase" ]
Increase
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.
[ "Square Wave", "Period" ]
Base on the definition of period, check if the time interval between two peaks remains the same.
Pattern Recognition
Cycle Recognition
727
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null
Does the given time series exhibit regime switching?
[ "No", "Yes" ]
No
binary
39
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
728
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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?
[ "30.16", "53.1", "18.75" ]
30.16
multiple-choice
25
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
729
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null
What is the type of the trend of the given time series?
[ "Exponential", "No Trend", "Linear" ]
No Trend
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
730
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null
The given time series has a decreasing trend, is it a linear trend or log trend?
[ "Log", "Linear" ]
Linear
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
731
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null
Are the two time series flipped versions of each other despite noise?
[ "Yes, they are flipped versions", "No, they are not flipped versions" ]
Yes, they are 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
732
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The given time series is a random walk process. What is the most likely noise level?
[ "0.35", "8.59", "3.72" ]
8.59
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
733
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null
The given time series has multiple cycle patterns with same amplitude and period. How are they combined together?
[ "Additive", "Multiplicative" ]
Multiplicative
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.
[ "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
734
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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" ]
Different
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
735
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null
Based on the given time series, how many different regimes are there?
[ "3", "1", "4" ]
4
multiple_choice
41
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
736
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null
You are given two time series with different underlying functional form. Are they likely to have the same variance?
[ "No, time series have different variance", "Yes, they have the same variance" ]
No, time series have different variance
binary
96
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", "Variance" ]
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
737
[ 0.42359906559346105, 2.062524919243145, -1.0675329142542729, 0.02421945667275807, 1.4122205554154292, -0.0796413912457152, 0.4523717962497342, -1.0623935281468797, 0.4283070972076486, -0.18714426500454878, 0.985729995679863, 1.187386051564751, 2.5895636420186134, 0.5796331732135757, 0.32579631658216646, 0.19438430157733602, -0.35316629281068834, 0.33848384346169114, -0.29540141013902943, 0.1684609762696143, 1.3175975356079597, -1.0065425652796411, 1.1398785611290454, 1.3171150673398653, -0.11806852699107874, -2.1218548990085946, -0.6078219870944325, 1.2969945465611092, -0.022868062298882122, -0.9993022322949108, -0.5047749212282174, 0.840620026504553, 0.5467335682013793, -0.23893209916969452, -0.36682441181468783, -0.3917581490438219, -0.9224101844985025, 1.6153756894694418, -0.3223204692113399, 1.2171585208254965, 1.5213160519224513, 0.9983108981479604, -0.4316203127180484, 0.40373009033660945, -0.024195606390916165, -0.9037018607301281, 0.324359281721603, -1.1790397911598025, 1.1876793884615637, -0.4646172972983931, 0.2011596558728393, 0.28328787154614216, -0.25890497370407733, 0.5866938014752747, -0.47490365662252443, 0.8712972974572442, -1.3459796802467485, 0.12637957954641182, 1.9389289990582848, -1.0003313246055747, -0.6777449705248515, 0.513907849658915, 0.17958178193959795, 0.3506300992735592, 0.4891871301476635, 0.6347214685617699, 1.1096998419562232, 0.40981865692851255, -0.24125765461854246, 0.6725737012027311, 1.899881934895215, -0.13263374638257355, -0.9745293046706415, 1.1070806692869728, -0.12038116395359824, -2.172669546014036, 0.8474216771504216, -0.5353281859539227, -0.09053328230416077, 0.3319803305690149, 0.1904996797790666, 0.7094518171390395, -0.43548637056984335, 0.5131057981760827, -0.2595466775839172, 0.738810480887503, 0.6153674840130534, -0.9354387020445952, 1.085982116175032, -0.535963445114048, 0.8080577982811451, 0.3672873134013406, 1.8381836767951223, -0.22346598237185214, -0.3493167961181975, -0.019419605887732585, -0.30317978283427505, 0.7999419019420501, -1.616310608436588, -1.0536824191463543, -1.067802921579193, 0.9503075919735757, 1.7106133725819253, -0.1044492185374715, -0.16882172319001063, 0.07005216311318137, 1.1618783026081902, -0.9273531341905741, 0.23836898273478513, 0.9751976297824295, 0.501094169939845, 0.1895816165987434, 1.0010460925671412, -2.703232292999237, 0.6778753195309076, -0.6540756831274238, -1.830632896856457, 0.5112025995249807, 1.3736585451629577, -0.13744851462769184, 0.9528745472029384, 1.6122782579886454, 1.3149144535840473, 1.639964529371393, 0.7421274910718922, 0.0754336389015928, -1.6019658118971685, -0.24606248812994846 ]
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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 1 with speed up/down anomaly", "Time series 2 with cutoff anomaly" ]
Time series 2 with cutoff 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
738
[ 0, 0.28967248751287666, 0.5717899469821527, 0.838957345087602, 1.0840962497073703, 1.3005947316500026, 1.4824473871369364, 1.6243825157442315, 1.7219737605243766, 1.771733846077317, 1.7711884294560714, 1.7189284999477823, 1.6146402180469077, 1.459111561713125, 1.2542156391644892, 1.0028710215949974, 0.7089799358605546, 0.3773456260423267, 0.01357063394237179, -0.3760618473489873, -0.7847210342088135, -1.2051732096992192, -1.6299349138048786, -2.0514314225423336, -2.4621571597892102, -2.854834644751866, -3.222568609001052, -3.5589920193004922, -3.858400913866327, -4.115875196596123, -4.327382831177806, -4.489865228533704, -4.60130201932842, -4.660753839836875, -4.668382225085466, -4.625446187984308, -4.534275556895123, -4.3982216362718045, -4.221586235245615, -4.009530567134507, -3.7679659491344526, -3.503428616872876, -3.2229413049077387, -2.933864524516802, -2.6437406883045647, -2.360134382639206, -2.0904721705102016, -1.8418853173415706, -1.621058770395799, -1.4340895899693216, -1.2863578304177397, -1.182412605395636, -1.1258757501359637, -1.1193651209371294, -1.1644391561636889, -1.2615638728063225, -1.4101029975231554, -1.6083314411598768, -1.8534718313953435, -2.1417533298516704, -2.4684914880841355, -2.8281874513205727, -3.214644409087753, -3.6210988266207087, -4.040363677934451, -4.464980647275475, -4.887378075744729, -5.30003130821676, -5.695622044848213, -6.067193322548719, -6.408296844332798, -6.7131295365221035, -6.9766564418918575, -7.194717346222584, -7.364114880199846, -7.4826822309059775, -7.549329028960601, -7.564064439546408, -7.527996968315795, -7.443310986288683, -7.313220470879692, -7.141900942692478, -6.934401039472882, -6.696535599841358, -6.434762520997428, -6.156045998211262, -5.867709042314126, -5.577278398461705, -5.292325150364514, -5.020304385549644, -4.768397317102796, -4.54335920531797, -4.3513762998562875, -4.197934831985657, -4.087704831285498, -4.0244412272592704, -4.0109043302508, -4.048801375659953, -4.138750369390469, -4.280267000183969, -4.471774896000911, -4.710639007246567, -4.993221409877061, -5.314958346629082, -5.670456874851855, -6.053609074205976, -6.457721395624092, -6.875656412277948, -7.299983970656095, -7.723138540788014, -8.137579433369417, -8.535950490830508, -8.911235870529541, -9.256908621011666, -9.567068904896605, -9.83656894121432, -10.06112202125341, -10.2373932892665, -10.363070365546587, -10.436912316271986, -10.458775933073026, -10.429618765791615, -10.35147884420812, -10.22743151817366, -10.061524330155125, -9.858691299413394, -9.624648433040209, -9.365772676642639 ]
[ 0, 0.5112382930910787, 0.9901451562843151, 1.4066913423642005, 1.735288040908853, 1.9566089479108442, 2.058966409131825, 2.0391436479152025, 1.902623818077866, 1.663199572005329, 1.3419909449344303, 0.9659414876784862, 0.565899731744075, 0.17442259749350109, -0.17654284474799087, -0.45793418877517866, -0.6456431020057537, -0.7222319766134795, -0.6781755869150112, -0.5125393399045206, -0.2330458236197852, 0.1444750852844512, 0.5972133992707536, 1.097003221460931, 1.6123283185485218, 2.1105662568224703, 2.560311305984947, 2.9336107067289294, 3.207955067036906, 3.3678811596029474, 3.4060729920368242, 3.3238827473555936, 3.131234500820899, 2.8459175690337197, 2.492319808871688, 2.0996910626277674, 1.7000604019861336, 1.3259554749735654, 1.0080863514243508, 0.773158790405513, 0.6419726374656791, 0.6279407566968878, 0.7361339581154394, 0.9629199269934621, 1.296221865437387, 1.716378429454039, 2.1975437290680135, 2.709527703476737, 3.219945826008681, 3.6965250675996133, 4.109401921001636, 4.43324885326105, 4.649077770889471, 4.745592080695562, 4.719991071815063, 4.5781693423389935, 4.33429707022382, 4.009811015594773, 3.631888100847883, 3.2315102583756694, 2.841258339823694, 2.492992173153575, 2.2155819607151983, 2.0328525557573247, 1.9618869966439652, 2.0118100968407155, 2.183138706019623, 2.4677449074071496, 2.8494347719345128, 3.3051014585855, 3.8063705536035233, 4.321620490998196, 4.818234188858358, 5.264921572091181, 5.6339476046878, 5.903107182878238, 6.057306265490327, 6.089636655990039, 6.001867905576321, 5.804321311017294, 5.5151349793024, 5.158972290709659, 4.765265725102753, 4.366121101067546, 3.99403145804527, 3.67956336612653, 3.449180411478916, 3.323358837691009, 3.315129520144147, 3.4291500931737335, 3.661373299871827, 3.999335179921531, 4.423042574841422, 4.906396755191867, 5.419051799345676, 5.928575396628226, 6.4027582132880205, 6.811907381235184, 7.130960800035609, 7.3412717017688705, 7.431936407527801, 7.400570731704788, 7.253479749639968, -0.011118801180469205, 0.0031890218468938335, 0.0027904129220013766, 0.010105152848065265, -0.005808781340235147, -0.005251698071781476, -0.0057138016575414155, -0.009240828377471049, -0.026125490126936015, 0.009503696823969031, 0.008164450809513273, -0.01523875997615861, -0.0042804606417623445, -0.007424068371191725, -0.007033438017074073, -0.021396206560762396, -0.0062947496092425085, 0.0059772046691260825, 0.02559488031037793, 0.003942330218796011, 0.0012221916522267957, -0.005154356620924533, -0.006002538501059117, 0.009474398210466388, 0.002910340012621821 ]
The following time series has an anomaly where the pattern is cutoff at certain point in time. What is the likely pattern of the time series without the anomaly?
[ "Sawtooth wave with exponential trend", "Square wave with log trend", "Sine wave with linear trend" ]
Sawtooth wave with exponential 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", "Cutoff Anomaly" ]
Cutoff anomaly brings sudden disappearance of the pattern. However, this only influences a small part of the time series. Can you check the place where the pattern disappears and try to recover the original pattern?
Anolmaly Detection
General Anomaly Detection
739
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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
740
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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 30 to 45", "Lagging step is between 60 to 75", "Lagging step is between 5 to 20" ]
Lagging step is between 30 to 45
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
741
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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
97
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
742
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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
38
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
743
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null
What is the primary cyclic pattern observed in the time series?
[ "SquareWave", "SineWave", "SawtoothWave", "No Pattern at all" ]
SineWave
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
744
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null
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
745
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[ 0.8011638346067744, 1.3986819293615635, 1.4920492756476798, 1.575774338480355, 3.50101948918198, 2.6102761485655046, 3.301333152072991, 4.745089273613341, 3.4822264431551164, 4.121823857738409, 5.215297093363612, 3.342598503965628, 4.904040231631434, 4.370933851272273, 3.9832222656746192, 4.189941594463069, 3.870110105577096, 4.682110460267227, 3.689435689031536, 3.813809345655521, 2.935981111625474, 3.05481718267283, 2.403114523432504, 1.5535184929530708, 2.575374026508344, 1.7475027933827751, 1.6118410626429467, 0.5212633411607981, 1.1493763389455305, 0.480445474601095, 0.03450319541666701, 0.2152560526314945, -0.689806045384219, -0.06657666947311902, -1.1932849947433948, -0.9503203028477997, -1.4943895669593528, -1.6123253245810663, -1.235312500585443, -0.9992187425401761, -0.5120876924066591, -0.9330278517122621, -0.09807623500687468, -0.2908804373012364, -0.08014619551355703, 0.8125221655945307, 0.5850468910966269, 2.1528826828726384, 1.8576478396396157, 1.3714360671721746, 2.416120067161621, 2.5734051364562816, 2.4925584949973674, 4.247417588932478, 4.647643134027799, 4.111607415522873, 5.16918008649126, 5.5607515919528945, 5.38881458631844, 6.105140543090544, 5.968269332891301, 6.541726368513285, 5.4852799100343015, 6.201804649996061, 6.238702695660215, 5.524384474971679, 5.492967138697336, 5.110408965918835, 5.765238779356372, 5.3273423545167375, 4.675769938206594, 5.676780139737026, 4.993699220327553, 4.140465889539162, 4.303023427210968, 3.7764007459194118, 2.8094693786128113, 3.4300985725975104, 3.828692743093801, 3.4491339072787754, 2.553357331872405, 2.0714178329615143, 2.3924078021572037, 2.1037164884410573, 1.8020361573059733, 2.746618029527544, 1.610247268325272, 2.326641812329807, 2.0086036460985452, 2.1484490505242553, 1.4341977689253835, 3.042602314213183, 3.1870241904784646, 3.1810985774584415, 3.96116006063534, 4.042399263574124, 3.6064394453582507, 4.215025863898943, 5.134521800406171, 4.79731884863573, 6.6903855842647175, 6.509532278260309, 7.170033038116451, 7.085407284710275, 8.358695193362124, 8.402757832213485, 8.7241392399343, 9.975581302882993, 10.273578698671573, 10.30486100760168, 10.305233194042673, 10.170783133382141, 10.468522011363262, 10.584953968287962, 11.043141757764698, 10.882042223382683, 10.903002879555723, 11.645229679529656, 11.377823409273667, 10.312880372717714, 10.719937223635245, 10.026641714795982, 10.539072353695856, 11.011123062105412, 9.668579903782675, 10.039182675993466, 10.251107577037976, 9.185814226302002 ]
Does the following time series exhibit a mean reversion property?
[ "No", "Yes" ]
No
binary
47
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 Reversion" ]
Mean reversion first requires the time series have constant mean. You should check this first. Then, see if the time series tends to revert back to the mean after a shock.
Pattern Recognition
AR/MA recognition
746
[ 1, 1.0131280961340403, 1.0264285391761854, 1.0399035917132131, 1.053555546035358, 1.0673867245262616, 1.0813994800580409, 1.0955961963915442, 1.1099792885818613, 1.1245512033891578, 1.1393144196949014, 1.1542714489235546, 1.1694248354698011, 1.184777157131383, 1.200331025547619, 1.2160890866436793, 1.232054021080695, 1.2482285447117734, 1.264615409044003, 1.2812174017065214, 1.29803734692473, 1.3150781060007326, 1.332342577800082, 1.3498336992449167, 1.3675544458135713, 1.3855078320467462, 1.403696912060322, 1.4221247800649053, 1.4407945708921985, 1.4597094605282748, 1.4788726666538583, 1.4982874491916949, 1.5179571108611096, 1.5378849977398443, 1.5580744998332716, 1.5785290516510797, 1.5992521327915308, 1.620247268533387, 1.6415180304356096, 1.663068036944929, 1.684900954011392, 1.7070204957119899, 1.7294304248824743, 1.7521345537574657, 1.7751367446189674, 1.798440910453393, 1.8220510156172163, 1.845971076511365, 1.8702051622644642, 1.8947573954250507, 1.919631952662875, 1.9448330654794088, 1.970365020927683, 1.996232162341572, 2.0224388900746555, 2.0489896622487778, 2.0758889955124347, 2.1031414658091183, 2.130751709155747, 2.1587244224313147, 2.187064364175894, 2.215776355400129, 2.2448652804053553, 2.2743360876144862, 2.3041937904138066, 2.3344434680058184, 2.365090266273281, 2.3961393986546002, 2.4275961470306995, 2.4594658626235444, 2.491753966906457, 2.5244659525263815, 2.55760738423826, 2.5911838998516714, 2.6252012111899017, 2.659665105061602, 2.694581444245203, 2.7299561684862557, 2.7657952955078597, 2.802104922034364, 2.8388912248284988, 2.876160461742131, 2.9139189727808077, 2.9521731811822787, 2.990929594509175, 3.030194805756038, 3.0699754944708735, 3.1102784278914353, 3.1511104620964256, 3.192478543171808, 3.234389708392429, 3.2768510874191557, 3.319869903511729, 3.3634534747575384, 3.4076092153165276, 3.452344636682445, 3.497667348960651, 3.543585062162701, 3.590105587517922, 3.637236838802213, 3.684986833684282, 3.7333636950895626, 3.7823756525820347, 3.8320310437641854, 3.882338315695349, 3.933306026328665, 3.9849428459669083, 4.037257558737418, 4.090259064086404, 4.143956378292861, 4.19835863600236, 4.253475091780977, 4.309315121689624, 4.36588822487904, 4.423204025205727, 4.481272272869102, 4.540102846070138, 4.599705752691777, 4.660091132001413, 4.7212692563757175, 4.783250533048106, 4.846045505879162, 4.909664857150278, 4.974119409380866, 5.039420127169414, 5.105578119058713, 5.172604639425569, 5.240511090395331 ]
null
What is the primary cyclic pattern observed in the time series?
[ "SawtoothWave", "No Pattern at all", "SineWave", "SquareWave" ]
SquareWave
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
747
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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", "Exponential trend and square wave", "Log trend and sawtooth wave" ]
Exponential trend and square 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
748
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null
Which of the following best describe the cycle pattern in the given time series?
[ "Period increase over time", "Period remain the same over time", "Period decrease over time" ]
Period remain the same over time
multiple-choice
30
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
749
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null
Is the given time series likely to be stationary after removing the cycle component?
[ "Yes", "No" ]
Yes
binary
35
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", "Sine Wave", "Square Wave" ]
Cycle component brings the cyclic pattern to the time series. Assume this effect is removed, does the time series satisfy the stationarity condition?
Pattern Recognition
Stationarity Detection
750
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null
Is the noise in the time series more likely to be additive or multiplicative to the signal?
[ "Multiplicative", "Additive" ]
Multiplicative
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.
[ "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
751
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null
What type of noise is present in the given time series?
[ "Red Noise", "No significant noise", "Gaussian White Noise" ]
Red 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
752
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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 2 has higher amplitude
binary
83
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
753
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[ 0.0259133655084339, 9.96904181474995, 10.00158158270993, 10.051083580742718, 10.013302134911497, 10.156142669611276, 10.065811794906102, 10.412684325467175, 10.509221795417004, 10.153451063828363, 10.385213081052871, 10.437793515739797, 10.506814819959574, 10.670484924876716, 10.569779416037878, 10.653643959802142, 11.006443214273409, 10.743477038950736, 10.977298927559207, -9.045937538524443, -9.105438591752915, -9.076072479344875, -8.958657728309303, -9.02450916946599, -8.952179841812907, -8.862030693457914, -8.744321667344616, -8.544987688545236, -8.730014240581168, -8.589298381445534, -8.752171358923551, -8.437284098358615, -8.669412608122045, -8.371337091601207, -8.413199622321532, -8.371103809449334, -8.342996375149239, 11.545853303632025, 11.597220126902352, 11.851767805311129, 11.815378079543368, 11.829497339825101, 11.950661420224831, 11.96252126530135, 11.919165693803237, 12.29062708319948, 12.16467171028353, 12.149371541587174, 12.131372165847822, 12.324077876806633, 12.196113732732604, 12.233761657426285, 12.536340306915248, 12.41614387276628, 12.382810048305695, 12.505782148599172, -7.306579011612551, -7.283403609783871, -7.202034217052747, -7.378347421817342, -7.1124083035579115, -7.1791604855125115, -7.106275919419011, -6.948167934906923, -6.9527762051262725, -6.941874912539936, -7.129311217132101, -6.889393122537435, -6.917241863938459, -6.721601182923674, -6.647541282841845, -6.7307715920056905, -6.7212040254882846, -6.452801186539824, 13.320202446635804, 13.307132064451546, 13.389387311671276, 13.463223099979748, 13.47865534531421, 13.695399400754972, 13.437137529687764, 13.614741444918609, 13.744316353335673, 13.816159331699389, 14.010386805269615, 14.041795704611523, 13.7732668295587, 13.788604362914192, 14.02797489502625, 14.00422785696084, 13.998412358226828, 14.165295693989211, -5.710057909716006, -5.770955873695868, -5.703398892417201, -5.671125958834219, -5.590002318399584, -5.448640172520483, -5.564506556756617, -5.474715858173221, -5.404506961314012, -5.319185375702978, -5.244843074078219, -5.0221471275003875, -5.123091727972629, -5.074642553211554, -5.114828377425425, -5.140085043849217, -5.048851253946454, -5.020994489664966, -4.864669561270022, 14.919927698240738, 15.190377824379835, 15.165469105295507, 15.29659649932601, 15.196939468959679, 15.22526192820888, 15.320800639607256, 15.364471198053717, 15.534239576254592, 15.579353830270803, 15.736244267136637, 15.542261356149304, 15.303124122770331, 15.643005536934009, 15.753082198575925, 15.847538086978304, 15.852514056819457 ]
The following time series has an anomaly where the pattern is cutoff at certain point in time. What is the likely pattern of the time series without the anomaly?
[ "Sine wave with linear trend", "Sawtooth wave with exponential trend", "Square wave with log trend" ]
Sawtooth wave with exponential 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", "Cutoff Anomaly" ]
Cutoff anomaly brings sudden disappearance of the pattern. However, this only influences a small part of the time series. Can you check the place where the pattern disappears and try to recover the original pattern?
Anolmaly Detection
General Anomaly Detection
754
[ -2.818640804157564, -2.550139931729983, -2.2816390593024023, -2.0131381868748215, -1.744637314447241, -1.4761364420196603, -1.2076355695920795, -0.9391346971644989, -0.6706338247369181, -0.40213295230933754, -0.13363207988175685, 0.13486879254582385, 0.40336966497340465, 0.6718705374009855, 0.9403714098285662, 1.2088722822561464, 1.4773731546837277, 1.7458740271113085, 2.014374899538889, 2.282875771966469, 2.5513766443940504, 2.819877516821631, 3.0883783892492116, 3.3568792616767924, 3.625380134104373, 3.893881006531954, 4.162381878959534, 4.430882751387116, -0.9378979845004316, -0.6693971120728508, -0.40089623964527066, -0.13239536721768985, 0.13610550520989095, 0.40460637763747176, 0.6731072500650528, 0.9416081224926336, 1.2101089949202142, 1.4786098673477945, 1.7471107397753753, 2.015611612202956, 2.284112484630537, 2.5526133570581173, 2.8211142294856986, 3.089615101913279, 3.3581159743408597, 3.62661684676844, 3.895117719196021, 4.163618591623601, 4.4321194640511825, 4.700620336478764, 4.969121208906344, 5.2376220813339245, 5.506122953761506, 5.774623826189086, 6.043124698616666, 6.311625571044248, 0.9428448351567003, 1.211345707584281, 1.4798465800118619, 1.7483474524394427, 2.016848324867023, 2.285349197294604, 2.553850069722184, 2.8223509421497655, 3.090851814577346, 3.359352687004926, 3.6278535594325074, 3.896354431860088, 4.16485530428767, 4.433356176715249, 4.701857049142831, 4.970357921570411, 5.238858793997992, 5.507359666425573, 5.775860538853153, 6.044361411280734, 6.312862283708315, 6.581363156135896, 6.849864028563476, 7.1183649009910575, -0.011118801180469205, 0.0031890218468938335, 0.0027904129220013766, 0.010105152848065265, -0.005808781340235147, -0.005251698071781476, -0.0057138016575414155, -0.009240828377471049, -0.026125490126936015, 0.009503696823969031, 0.008164450809513273, -0.01523875997615861, -0.0042804606417623445, -0.007424068371191725, -0.007033438017074073, -0.021396206560762396, -0.0062947496092425085, 0.0059772046691260825, 0.02559488031037793, 0.003942330218796011, 0.0012221916522267957, -0.005154356620924533, -0.006002538501059117, 0.009474398210466388, 0.002910340012621821, -0.006355597402746391, -0.01021552194675598, -0.0016175538639752096, -0.005336488038424868, -0.00005527862320126283, -0.0022945045383195653, 0.003893489132561233, -0.012651191139226421, 0.010919922643576711, 0.027783130415524406, 0.011936397242823174, 0.0021863831605386246, 0.008817610389486107, -0.010090853428651077, -0.015832942135368875, 0.007737004168336819, -0.005381416616629597, -0.013466780973613462, -0.008805912660471066, -0.011305523046815669, 0.001344288826280219, 0.005821227947130392, 0.008877484595933573 ]
null
Is the noise in the time series more likely to be additive or multiplicative to the signal?
[ "Multiplicative", "Additive" ]
Multiplicative
binary
59
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
755
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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
756
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What type of noise is present in the given time series?
[ "No significant noise", "Red Noise", "Gaussian White Noise" ]
Red 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
757
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null
Is the given time series likely to be stationary after differencing?
[ "No", "Yes" ]
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
758
[ 0.5003488838525446, 0.7628079544146305, 1.4509317439476506, 1.3196492397316175, 0.9427151021966808, 0.8949092293112086, 0.8988279024391732, 0.6501364115616133, 1.9359166439346545, 0.9842124694454828, 1.7713563780645476, 1.941104024501665, 1.6975388144812562, 1.0007831416491524, 1.4369449832608985, 1.241749687150122, 0.8210492929790602, 1.4544221113888147, 0.7223587356055481, 1.9256528656844285, 1.1197419766854297, 1.4731754236628718, 1.5350966912432062, 1.2851743615604057, 1.729469591222506, 1.2204933424877136, 1.9157479014870344, 0.8296001350644289, 1.5886122432520107, 2.5180663802827152, 1.071967866743122, 1.2571502652379327, 1.8772289034189786, 1.7346866203196694, 1.8452056522731222, 1.939858848469825, 2.0383862772418935, 2.302027161339474, 1.9786356521216768, 1.6800500039835236, 2.1643277440691193, 2.805759700981111, 1.8177017962163675, 1.425382462675876, 2.4952509163707988, 1.9110250979055543, 0.9148343472423062, 2.4552885541494205, 1.7947842891485364, 2.0485215001151658, 2.291594286340562, 2.253153397751833, 2.5454197065855304, 2.006239114192827, 2.5143295326229245, 2.162311147731676, 2.696318902021048, 2.6699558224075335, 1.9304484340512054, 2.977599997963763, 2.2036221105933214, 2.91318977832226, 2.7309322768153996, 3.5050875662929184, 2.5135580150573475, 2.490524994595258, 2.6959721574895763, 2.5952060293408645, 3.1885055757441925, 2.0227522615003113, 2.34708317151452, 2.3836933940299407, 3.4370827155110217, 3.8622433450329927, 3.00040369996801, 3.0146034017290715, 3.181131152791859, 3.774850594820804, 2.778767686370698, 3.410899030972344, 3.8293323230815983, 3.6430596207327035, 3.5388539800332683, 3.99692018729716, 2.19791020017697, 3.942400532435238, 3.331181144996942, 2.798490693899228, 4.025841282954309, 4.5143596170758435, 3.8169669993002038, 4.421173221533312, 4.810816976833777, 4.722987816585796, 4.947290279103422, 4.56108791818419, 4.29141014838288, 3.517347058521602, 4.260917536446376, 4.02894140403786, 5.603664238199389, 4.498905789217457, 4.718150168427014, 5.003048628945856, 4.82094053985204, 5.719589750578666, 4.634772587523109, 5.11855899677466, 4.726320034087085, 4.515003540150509, 4.9477667479096725, 5.314964306657022, 5.199876076176429, 5.1505926863107945, 4.877170650006182, 5.62357201648191, 4.99884853834885, 6.21862871070797, 5.968540566592595, 5.288613038287766, 5.954220969518548, 5.825573444181058, 6.455475572825409, 7.061782176588154, 5.551093079343131, 6.644790528906859, 6.607307506909718, 7.124661364852441 ]
null
The given time series has a cycle component and a trend component. Is it an additive or multiplicative model?
[ "Additive", "Multiplicative" ]
Additive
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
759
[ -0.11152465363768141, 0.19514437184008562, 0.4027136077746781, 0.6730677122483606, 0.7773624025926058, 0.9383745873692099, 1.2800032265836065, 1.2730615876749232, 1.2636703134358864, 1.3351143488820187, 1.5296867935821332, 1.3114308268083288, 1.2019919519323239, 1.1068863121108574, 0.996667796419664, 0.8441099690644575, 0.6081199915394806, 0.44206239385500623, 0.281558384077747, 0.23124777179048572, -0.054788701844516605, -0.21654680012860184, -0.23273058348698047, -0.3736674043137618, -0.6497019399677069, -0.7738926670267742, -0.8545084080958596, -0.7218682105195748, -0.7993916361715957, -0.7699405834863371, -0.7305530077178204, -0.6115069562269597, -0.3582261943118177, -0.35154791934519136, 0.07113390565187112, 0.1262173301189507, 0.3833027605473066, 0.4880375630311021, 0.8427270994843057, 1.0261102404735776, 1.2558650822076982, 1.5915084058309692, 1.6222238221789365, 1.6575544438125203, 1.7675036663881891, 1.9663124484518446, 2.069853192123644, 1.9658710326198903, 1.9692790064474361, 1.8906825723274427, 1.8700006618133886, 1.4040160513578375, 1.5132843798294744, 1.37411878866793, 0.9580748704827389, 0.8124035024444226, 0.623746638696947, 0.44867647915270736, 0.2968930157725894, 0.2092019712364381, 0.13286686833034522, 0.04175771147604444, -0.23312801960367957, -0.28421730124622147, -0.08407430569620428, -0.13148174073504737, -0.1330714253564976, -0.005066883811714523, 0.0656031888548342, 0.27098893092952364, 0.3599269994576278, 0.6158383636041862, 0.6485191286789569, 0.9509315958247333, 1.1757174579869694, 1.4272083006178067, 1.5847649380535707, 1.822637227099435, 1.9036108826382243, 2.2647150661257287, 2.3280710023800135, 2.2607397630464, 2.408870190153768, 2.551938637819241, 2.454435404030569, 2.3947691375163918, 2.3797394158782486, 2.31400632357568, 2.0017554863012084, 2.0438045773942286, 1.7348307222965424, 1.6273175685701162, 1.4338590977153827, 1.193057470303312, 0.9578629934268077, 0.8580793108677758, 0.8930585751359225, 0.4606908262190326, 0.6592210603978474, 0.3875116206043081, 0.37355811397343747, 0.25264990819091665, 0.3109651778459616, 0.3997199275819465, 0.44116194964489247, 0.6520328819008137, 0.7876443994095541, 1.193007785120875, 1.090309750512601, 1.4302148427895052, 1.6660884563349962, 1.7579655173172564, 2.1536581226126343, 2.2554609704970887, 2.241050924419435, 2.730732104973632, 2.702351910524922, 2.8295213447127923, 3.0912531619411094, 3.0417128947167087, 3.1868597919884456, 3.199352823432887, 2.962639495406375, 3.0227419133924527, 2.754530553220669, 2.9141789635084865, 2.460996826072515, 2.4560869814690083 ]
null
You are given two time series with different underlying functional form. Are they likely to have the same variance?
[ "Yes, they have the same variance", "No, time series have different variance" ]
Yes, they have the same variance
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.
[ "Gaussian White Noise", "Red Noise", "Variance" ]
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
760
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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
761
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null
Both time series have a cyclic components. Which time series has a higher amplitude of the cyclic component?
[ "Time series 2 has higher amplitude", "Time series 1 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
762
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The time series has three cyclic pattern composed additively. Which cycle pattern is most dominant in the given time series?
[ "SineWave", "SquareWave", "SawtoothWave" ]
SineWave
multiple-choice
20
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", "Amplitude" ]
The cyclic patterns have different period and amplitude. The dominant pattern is the one that has the highest amplitude. Identify the pattern with the highest peak.
Pattern Recognition
Cycle Recognition
763
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