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In which part of the time series does the anomaly occur?
[ "Beginning", "Middle", "End" ]
Beginning
multiple_choice
78
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
1
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null
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 flip", "speedup and cutoff" ]
cutoff and flip
multiple_choice
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.
[ "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
2
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null
You are seeing two time series that are random walk. Are they likely to have the same variance?
[ "No, time series 2 has higher variance", "No, time series 1 has higher variance", "Yes, they have the same variance" ]
Yes, they have the same variance
multiple_choice
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", "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
3
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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 1
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
4
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What is the most dominant pattern in this complex time series?
[ "Noise", "Trend", "Seasonality" ]
Seasonality
multiple_choice
13
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", "Gaussian White Noise" ]
Identify which component (trend, seasonality, or noise) has the largest impact on the overall pattern.
Pattern Recognition
Trend Recognition
5
[ 0.11681606574585326, 1.579946338574453, 2.67181316740565, 4.114339617156449, 4.93448618140805, 6.168402682590406, 6.522535903226298, 7.081508214336502, 6.671025184769849, 6.497452139394053, 5.760875074868962, 5.088025114685672, 3.9459692513737377, 2.6320545285856154, 1.1358875352976097, -0.35181607908482515, -1.735252969348148, -2.9810398281845587, -4.618176533513837, -5.53706283936872, -6.3851919387369875, -6.737969986778071, -6.862495644570686, -6.591408788298141, -6.285545028062437, -5.56029589634224, -4.970855484598015, -3.4023198182167143, -2.499584504307904, -0.7011491495832357, 0.8993890628074144, 2.0491352433998986, 3.580819737716404, 4.47743630695248, 5.637460879874152, 6.300027613953265, 7.129513816976256, 6.964914095932833, 6.817872956650146, 6.1409097150002845, 5.657408066823015, 4.42812850422703, 3.1424607689552078, 1.7718209257468902, 0.33439423587044964, -1.104266530687216, -2.813667043217117, -3.5822507276391087, -4.875824810944584, -5.714822884057987, -6.4001643921862295, -6.729740955274168, -6.921391172935659, -6.505588834163363, -6.005089420740233, -5.105400389642313, -4.2057656331026765, -2.5615920713521656, -1.3671214503732614, -0.016026901602526268, 1.5649932150532986, 2.995979872063059, 4.3555520973124375, 5.054482789789271, 5.830302080583276, 6.758735199865892, 6.964579309304863, 7.07922683432365, 6.622356243267391, 5.915810849903995, 5.145277508214719, 4.056667983935315, 2.7928053799052397, 1.0210582564977764, -0.08991283272690677, -1.732728857792679, -3.223407115870659, -4.267984774800139, -4.998021623621612, -6.069907760698207, -6.529544886863574, -6.9779799061541645, -6.955851748381221, -6.28167418635158, -5.453674157800249, -4.593225945639881, -3.3616478298954773, -2.0199919134350672, -0.8933438578430521, 1.0407529672519236, 2.1561966866108495, 3.6664607145430193, 4.816474307513139, 5.547906633680949, 6.426068185906342, 6.734973433829863, 7.178171346449865, 6.9421184898475286, 6.191701776496545, 5.583500475242237, 4.3854449450117166, 3.3586831140881594, 2.127235165614056, 0.5049780068526833, -1.122537428964199, -2.340105383478199, -3.774424703579705, -5.0544835978974065, -5.512507775238806, -6.435309824458506, -6.427125601239022, -7.01216416362775, -6.668307950623735, -5.963006431789016, -4.94090681234329, -3.90221824156465, -2.7242385789064385, -1.3527215283883174, -0.03645013888756486, 1.5430795446094434, 3.291307408347715, 4.349261550574562, 5.345726822168405, 6.227492446597843, 7.0210100146445376, 7.1728655223476965, 7.17239683165099, 6.51353756891795 ]
null
Is the given time series likely to be stationary after removing the cycle component?
[ "Yes", "No" ]
Yes
binary
36
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
6
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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?
[ "17.92", "5.37", "1.63" ]
5.37
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
7
[ 0.019337875134129316, 0.5263825241014467, 0.9973064139606924, 1.3358394177412576, 1.8675268289910865, 2.170106141611915, 2.4171528134942255, 2.3275509163436094, 2.406763721915604, 2.3328576753828703, 2.0785478624159226, 1.4646124373565734, 1.281899101696567, 0.6893422971904652, 0.1640958766421608, -0.5939892131182323, -0.7312174950083126, -1.3438219550989294, -1.9304671342606317, -2.070627426278523, -2.3037131183801955, -2.3341074094049685, -2.488066598288128, -2.3391338544528244, -2.175933574458554, -1.7221965309950922, -1.4454629315771963, -0.976159097409708, -0.3709756710410202, 0.0532979412542242, 0.8677667629676848, 1.3981139193956014, 1.600219370070823, 1.8684172841268065, 2.3062545587059358, 2.381226550475988, 2.5875689710895076, 2.3139282779605894, 2.255218456262905, 1.9150484433797819, 1.4478710336895764, 1.0788781170887474, 0.631657557723495, 0.015415213800796326, -0.5209369622547892, -1.1299627648340718, -1.3904210265538879, -1.7905813441069363, -2.235664449974806, -2.401662168915127, -2.3281812145752703, -2.545232141376628, -2.217424006490296, -2.0707634697760806, -1.4777895037219082, -1.2107759801234814, -0.5944025894339421, -0.26544099120316467, 0.22602391545980915, 0.8508567012314805, 1.3821480394085521, 1.721564442948854, 2.1804574828271703, 2.3149757682387757, 2.1278274088431584, 7.763387716397564, 7.619852812563548, 7.671946780310612, 7.863419638832199, 7.885387690890373, 7.6505571749689825, 7.765885181541448, 7.652879069436, 7.679419220588404, 7.647528976988409, 7.535672150438615, 7.717612040851635, 7.736923057172881, 7.64100634394715, 7.816885689621975, 7.664498496768742, 7.644385335992363, 7.760756830289075, -3.190432467435879, -2.9454963652683452, -3.076381184178062, -2.937235660799217, -2.9073512158557104, -2.9721489242029118, -3.117361597711457, -3.161247439087066, -3.1795715347721494, -2.9258731982684947, -3.049644279658644, -3.096086447891711, -3.049372483592515, -2.928102147543209, -2.9582902899026706, -2.9923136528677405, -2.972375662695985, -3.018147032888931, 7.738317824207906, 7.730209041593368, 7.708100393915508, 7.783443906861392, 7.744234729098303, 7.620035015367568, 7.7609939570305295, 7.732831225116194, 7.769247865369774, 7.697685827116761, 7.78928054985498, 7.701965663391648, 7.780494487138318, 7.662459366883213, 7.6693811130683684, 7.768311770799277, 7.674929179103789, 7.92868478795308, -2.979519769760723, -3.0336719198232056, -2.954174190762741, -3.0842323094362776, -2.943862786515324, -2.946640746772273, -2.910810862660671, -3.0802452215734837, -3.1584375938524003 ]
null
Which of the following time series is more likely to be an MA(1) process?
[ "Time Series 2", "Time Series 1" ]
Time Series 2
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
8
[ -0.7909328420989361, -0.8904654210399249, -0.4849101798874821, -0.3634868239199933, -0.2959709966387569, -0.1419510638774289, 0.3268358027066576, 0.7514866360187838, 0.4256668247081739, 0.17725663852862278, -0.15567229200177315, -0.3068759896920422, -0.28983760963896715, -0.2335519393982054, -0.5490841563718538, -0.9352825905599705, -1.090195774030611, -0.8924916726376435, -0.6582472083780246, -0.2948966509017667, -0.29616069965678554, -0.11692017856324353, 0.10044443995357596, 0.0017357052554519414, 0.08861223127646832, 0.23230739258038896, 0.047110354785685454, 0.39709247901481354, 0.3944686877048722, 0.41824405970833023, 0.22503717424449177, 0.06705403167705466, -0.38819322024208636, -0.3711052130247766, 0.1600337215661904, -0.048125238429141876, 0.5817125898920033, 0.8838994505671462, 0.7900721407825785, 0.8013093879094219, 0.778487157355516, 1.1419088511410327, 1.2558816804874573, 1.5093435082724829, 1.5899954906180769, 1.5720248000774923, 1.646016870674554, 1.5661696568875678, 1.2670572051272986, 1.4432634060677185, 1.133880479228445, 1.0830047558339715, 0.9962518681161219, 1.136726793342426, 1.4704744040049547, 1.7287602522254815, 1.8753334498000265, 1.7487225208687573, 1.7157539072228585, 1.6521997206712875, 1.5590661938335166, 1.4801615076048416, 1.3956586770458566, 1.3018654735732658, 1.5070608664344107, 1.2913464904102032, 1.1438418504926533, 0.8172068765272531, 1.1196520786084505, 0.9580867257422947, 1.1022161353386186, 1.2074421688945178, 1.4896142204697753, 1.4510767007298724, 1.257828195151062, 0.9369948053995709, 0.3583767900830432, 0.3977419258072644, 0.5659315159320848, 0.6703959222303788, 0.35501357408201784, 0.5784471171858231, 0.4374995159764779, 0.25277532789728085, 0.10712545562144193, 0.12909127851400354, -0.17683821352194884, -0.17908937405805236, -0.08348566710843719, 0.15431672053009526, 0.19674523324355897, -0.07875212923605512, -0.042001369619035556, -0.25889494944118174, -0.4878895666186196, -0.7682274179590197, -1.1636351896460146, -1.2770916959577958, -1.0347656279646191, -0.5559027262908441, -0.670706380212643, -0.43735499201883066, -0.5146090338989576, -0.8553676819242353, -0.7028123927042805, -0.6480372957410474, -0.26115152909443884, -0.5775647296455342, 0.014479862802322607, 0.35389396367840315, 0.3556520186256896, 0.2985243598978561, 0.15388608044722618, 0.18242271198406168, 0.1493561348819824, 0.26265343507725525, 0.20642173589779256, 0.5087580435213493, 0.5405069812289028, 0.49215210765800593, 0.712535671431447, 0.37769510272625395, 0.45474248584616006, 0.46562451331960847, 0.17518683102812205, -0.1776897781973451, 0.03976924607546273, 0.24725275271031766 ]
[ 10.579014925568757, 12.623131540574995, 10.773099132673536, 10.72403468992698, 9.278728418314273, 9.175916092615644, 8.896852727606106, 10.880404098184496, 10.564221741531888, 11.42084154992798, 11.485945554387806, 10.791638970286575, 10.957945537158087, 8.923247571047032, 11.348707661747138, 8.342560631267961, 11.999866335911886, 10.818400813489708, 10.200793028542689, 11.89788431380465, 9.102981165899823, 10.404740536830026, 9.96868325117794, 10.00044672705216, 10.244530103017018, 8.893290055779675, 9.909394572796373, 11.211048315743643, 7.118838459610506, 12.692523422779137, 8.829921550314692, 9.337444632896577, 10.376261033275501, 7.912604666627733, 11.478414246584242, 10.302451540423107, 12.634597676314236, 11.00306743941702, 12.233232249321428, 10.088281213733758, 12.408831187010271, 9.844714322238117, 10.408084185055008, 11.691993127042167, 9.435757705964111, 10.54996030482309, 9.07368709397792, 8.374381400386987, 10.11673523303739, 9.175874184539552, 12.973512856820577, 11.107087880687947, 12.095505310891637, 12.35284008705758, 9.710203167605695, 9.26833222879932, 8.614011073249674, 8.663379186042157, 8.985792081769068, 10.942181651753142, 9.697353040919618, 11.407567036567693, 11.401280605489514, 10.470731930158609, 11.755922593162552, 8.143056478936149, 10.320222252228337, 7.36421240179379, 10.0461115941369, 9.250433256080512, 10.348857779617273, 9.708677215545572, 12.48460994806587, 8.347880416519898, 10.50962926222635, 10.64056116642213, 8.232404207680894, 10.379292013052837, 11.739488593251199, 10.22997016679442, 11.247864970040268, 11.006086079152412, 11.470299646317105, 10.865627005505717, 12.84284548296859, 11.358099723494501, 11.959172110038695, 10.683584238897472, 10.75555115573905, 10.298843742076794, 10.743531590631276, 9.930324992446149, 10.709616180463245, 9.463002131377925, 10.213327969596934, 8.500727176253365, 12.698525324555142, 8.266262816435647, 11.723321248808185, 8.594383511422098, 10.326540169356996, 9.148585853913827, 9.528759489234414, 10.500081261230477, 10.020603139845017, 10.458630368502208, 9.969693366956156, 12.137564945977903, 9.80916686941957, 10.47878381949445, 11.686094565422954, 8.124970062624769, 13.873110709072131, 9.395038057997528, 13.206818708271287, 7.983708725175168, 9.52651194475432, 9.669845571083194, 9.290502358357166, 13.109484118522644, 10.739427157732898, 11.779213377912297, 12.101714075005876, 11.126373991018276, 11.174597993381475, 9.714005498881908, 7.471375375813475, 8.687051049798537 ]
Based on the given time series, how many different regimes are there?
[ "3", "4", "1" ]
3
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
9
[ -0.04207401948519687, 0.09231675752437826, 0.23225853953270997, 0.06741278828357439, 0.19017141127316278, 0.14532821334199886, 0.04275950114618929, 0.10396686129862523, 0.14889917735711536, 0.03380782262492009, -0.14058620220982954, 0.04896497336914554, -0.0714076988556985, 0.08129491965784193, -0.002270325970318565, 0.2685188653943892, 0.0742821112459733, 0.25898653654712567, 0.2932698003016101, 0.29879433768574026, 0.053843708242723776, 0.36497563252185916, 0.30677889591924623, 0.3572054997668014, 0.4718004188993855, 0.38027987202214947, 0.19461526154899045, 0.3902427350612764, 0.1865865679309564, 0.34268556175754206, 0.31069310999575506, 0.37406491034238215, 0.23412950545988878, 0.25767968133432595, 0.36421621380169567, 0.3989330108976023, 0.39063968008038696, 0.5902983041029057, 0.49965113307920644, 0.5089399329418408, 0.4431234191621604, 0.35420533566277057, 1.4929764411467235, 1.703845558197147, 1.5761704417163276, 1.6965757920441789, 1.7416569203536056, 1.7070983151568566, 1.7075917110629877, 1.6222346021952923, 1.7366602073388355, 1.7589976315332918, 1.8667862659387038, 1.7322301438845058, 1.8609425744821555, 1.997328039972598, 1.930226013096834, 1.9536811489405224, 2.0122372915405426, 2.1116461771653334, 1.949738698572082, 2.1635671140760335, 2.385331150063796, 2.3758586814138014, 2.440477705699826, 2.272342998015058, 2.4720143415763998, 2.561902378117671, 2.68176795705421, 2.810097411328461, 2.8600577255432382, 2.7735704078897485, 2.8453899095583792, 3.114437090866292, 3.010954388251699, 3.0146198066127115, 3.1803409614400553, 3.4164891388679517, 3.2739582939789527, 3.40691406753037, 3.451345261981127, 3.7238431843339463, 3.7501873461583424, 3.909958938650913, 3.9738728023703977, 3.6542254106596843, 3.717585125664005, 3.738212745563216, 3.7765134475474453, 3.808284046707503, 3.6966135975150767, 3.6646294817505396, 3.8175542521774184, 3.764562735330279, 3.729605835775253, 3.47150643563809, 3.7948146561723277, 3.6806085947665674, 3.6340784366149017, 3.556407765185545, 3.56311426509004, 3.5253789690823596, 3.4027775648948166, 3.5088475466321616, 3.418760611357476, 3.560682345286773, 3.4397176630466944, 3.615851833004593, 3.364491029250787, 3.6384622676983196, 3.5907139367820227, 3.3884935495019177, 3.4737550810308546, 3.3858086863291983, 3.5171710790420256, 3.6273615011491556, 3.5535468942870327, 3.3547323553241597, 3.423033303347547, 3.551860748594279, 3.4401262671203714, 3.476775137877943, 3.4289513944073726, 3.359519037536551, 3.333011334441871, 3.206932172050913, 3.239505766607787, 3.213971412923804 ]
null
Are there any granger causality between the two time series?
[ "Yes, time series 1 granger causes time series 2", "No, they are not granger causality", "Yes, time series 2 granger causes time series 1" ]
Yes, time series 1 granger causes time series 2
binary
105
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
10
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What is the direction of the linear trend of the given time series, if any?
[ "No Trend", "Upward", "Downward" ]
No Trend
multiple_choice
4
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" ]
Check if the time series values increase or decrease over time.
Pattern Recognition
Trend Recognition
11
[ 9.901424393644616, 10.001894946442674, 9.98412340318394, 10.001154978801644, 9.865234265039811, 10.04382999407754, 10.096841029845905, 9.998019875756741, 9.834298502447748, 9.835001046744159, 9.877318796237047, 9.858580298183137, 9.907487174689425, 9.97723941240149, 9.943283116616538, 9.934591699096895, 9.890621545741636, 9.907214197632126, 9.993512441327502, 9.715059381956458, 9.913406372315379, 9.943088311276437, 9.992224301329163, 9.814394313409114, 9.809153118731642, 9.972432104741076, 9.72571808158903, 10.04661604311843, 9.937001222268936, 10.069075649202508, 9.806757499802602, 9.871272663215652, 9.675806714065189, 9.835646732986156, 9.896308113845073, 9.719942335144776, 9.875410262335867, 9.71750012754138, 9.889009696537132, 10.028266499712569, 9.911067598622632, 10.07893924000784, 9.992492935162504, 10.048198277876017, 9.838694909600607, 9.836295950127608, 9.948801643904881, 9.758113841653678, 9.961247393594766, 9.882420532646877, 10.046398689408447, 9.981906163297914, 10.023269028751606, 9.839759647399136, 10.018460859509247, 10.057772214132374, 9.910697382596393, 9.841232497482153, 9.84297382883921, 10.0373780635817, 10.18067609479284, 9.81721012770987, 9.809588330403137, 10.005889616116987, 9.83978865257437, 10.015500886330424, 9.96067259083042, 9.912158440217036, 9.95828570215682, 9.952230581386436, 9.896728528124136, 9.740400637304118, 9.932248068653653, 10.070497309664562, 9.755033735331141, 9.818782578029333, 9.95685359112625, 9.918361882427483, 9.955302480343235, 9.845201525207104, 10.029788019998957, 9.91918565174666, 9.9836385567141, 9.946289696608595, 9.931935189640258, 9.976683324998369, 9.933025093159944, 9.796532971143089, 10.022342058865352, 9.99564920011795, 9.705651244685653, 9.849674757775544, 10.017880878379597, 9.733404195867992, 10.0080859535838, 9.9005341197445, 10.047418472055435, 9.914421979615877, 9.84294598963986, 9.945080941184006, 9.911523098229388, 9.834143553434606, 10.134474134521165, 9.81825580274218, 9.692157067516401, 10.071353786947652, 9.856678069758885, 9.885111987585443, 9.879050953955018, 9.858057383745617, 9.838571252499078, 9.815705871323116, 9.920956308107385, 9.874680478599329, 9.986947698370328, 9.962392552393053, 9.822577151079075, 9.9252950590628, 9.873108948704765, 9.81621715003415, 9.98288961746499, 9.902506840323941, 9.874128986270678, 9.829710159519795, 9.812620521499628, 10.111712793720095, 9.947661991153769, 9.80635530073676 ]
null
What type of trend does the time series exhibit in the latter half?
[ "Linear", "Exponential", "No trend" ]
Linear
multiple_choice
15
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
12
[ 1.0287865898322812, 1.1086809882162731, 1.0217166496047014, 1.1448587028996267, 0.8556731126127428, 0.8133262733310047, 1.0410204799745775, 1.0451348357107564, 0.6860579264273643, 0.9601793127767874, 0.9242059383755026, 0.88841907947938, 0.9290573622284247, 1.09229447101643, 0.9335356735842408, 0.9395307955024583, 0.8785356754530319, 1.1698867478783044, 1.089044993189632, 0.7989385209534294, 0.9525489454045519, 1.1062299972676235, 1.1841291786214054, 1.142691989963739, 1.0256645047691357, 0.8707262990421151, 1.153526597532337, 1.039456265896888, 1.0786829614608795, 1.0567120974866167, 0.9415651612908537, 1.116213707380376, 1.1051117855237649, 1.042570832136798, 1.1349507846493683, 0.9531374088728897, 1.0663409322354485, 1.098564507162503, 0.9251762671585028, 1.095683376911914, 1.1774883141114032, 1.0765382390562173, 1.106194160582527, 1.1685911783154332, 1.0763347081181374, 1.0880997616296983, 1.0029807876307109, 1.121935970768067, 1.0927301985102338, 1.1789163307812653, 1.1881525742567502, 1.213733650624552, 1.0865998370485628, 0.9225878637707459, 1.217237039248051, 1.189019262689005, 1.0852191342765436, 1.2070904873779844, 1.0095927215211409, 1.2603380365952337, 1.1268209704000889, 1.0801671888815765, 1.103773451131097, 1.1456859143810294, 1.1676332056511043, 1.1808292299085654, 1.1402072463603863, 1.2103587369899207, 1.1983294959646902, 1.139911057861481, 1.1320160838643685, 1.2798384894835528, 1.2786013276814336, 1.2390491484853434, 1.3329218484558114, 1.0515363251276018, 1.1983964154812692, 1.146370957286049, 1.4947966839208726, 1.3476582283342602, 1.2755968368164081, 1.3691688819544252, 1.4094641793328953, 1.415566570997365, 1.4043405392425672, 1.2930829472918999, 1.2763672265592847, 1.2374516393971855, 1.3910820729557287, 1.3321105616375242, 1.3133238210062566, 1.31527157677277, 1.514523764896593, 1.4719393320048655, 1.5668774652210888, 1.4439064984850574, 1.4038671014089104, 1.4027982011965021, 1.3104750804324214, 1.2935301248710025, 1.4775729151230044, 1.3405377307729656, 1.4623181660955886, 1.55988584790596, 1.3889605751809233, 1.663720920830745, 1.3707700341647513, 1.57602581079572, 1.5266487421475454, 1.6107494379164986, 1.3868869406734883, 1.7363755823923925, 1.494962771206315, 1.5876718624021078, 1.6716226062544037, 1.473874439497806, 1.6240800714296197, 1.4715272595003266, 1.6955371709558338, 1.4869897286747504, 1.574025288934774, 1.607953449673968, 1.6629381454326078, 1.7885225881905749, 1.5536448472740454, 1.7198820125504288, 1.810201168874056, 1.6369154489847082 ]
null
How does the noise in the given time series influence the detection of periodic pattern in the time series?
[ "Distort the pattern", "No influence" ]
Distort the pattern
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
13
[ 1.5591680930425154, -4.665622296788548, 1.8047866793925156, 2.131058513284418, 8.456594507023153, 3.25806884460796, 2.195271733195069, 5.399878062790664, 1.8071157813687124, 2.6715726641310282, 2.6150190365128494, 3.5820947649172643, -0.43523316932213096, 3.3744469178371, -0.37283395824616394, 5.341497030758326, -3.785560225346723, -2.4855566802361766, -6.041352627509112, 5.535820300571853, -4.9404944937629125, -0.4611174790871917, -0.7542127274294435, -4.800155126079203, -0.7673859279472057, -5.107887951795779, -4.297511865323162, -5.810999788809535, -0.06814627975559207, -5.96025085145893, 0.18961797437728456, -0.5390890269255905, 4.481104266150339, 0.8774204775271733, 3.323356539845224, 2.9446562465279245, 1.8287235186025586, 5.042733638527379, 3.460342399069097, 4.795601745535645, 0.379465052560755, 3.7628481635506006, 4.1998794309465275, -0.6642196231060051, 1.3904458229732737, -3.0689897322076334, -3.200840577147742, -0.04482899460553223, 3.9089798427040736, 3.587195161402332, -2.1383927743303657, -4.110146125153198, 0.07041643339319448, -7.242628442780208, -3.549884722678897, -4.438555737262857, -2.7981391081313487, 0.8709212294625468, -8.42556116982465, -1.1123005207305798, -0.625132739198232, -1.132685159101358, 0.22062712377491633, 1.2813031082530049, 0.946629387380326, -3.83450997944819, -0.618229366985158, 5.7662535355919164, -0.5696078859502158, 2.665941120747548, 0.8683547045766933, 4.066958547972846, 2.071864412243016, 3.9593816506150983, 3.0336332381419395, 0.8173948570294977, -4.036512051286671, -1.2337216969975875, -2.5641962018161824, -3.107981206171641, 0.5086940235362593, 3.6807819264800252, -7.572255609380127, -5.641173096886421, -1.7533398837965293, -3.1280315571215014, -1.5320268429409067, -2.737454801429613, 0.6505321876448593, -0.9452442799141492, 0.08850032696429677, 0.803871563712387, -4.077177114104171, 0.6974235230205287, 1.3492962801377533, -0.4955300447258347, 0.001809868118423097, 0.5485317698263026, -0.3714337215704884, -1.2202282785572804, 7.543355428604455, 5.157255736885961, 2.6967275644397057, -0.9260223132622594, 3.79052708455822, 1.3704374772067824, 1.5515805962494742, 6.945699700242031, 5.647005494370519, -5.116152128300552, 0.9358418439720969, -0.06931945375604376, -0.11849612502476192, -2.7836208716073223, -1.8432231013761835, -4.820086229884296, 0.062573123645838, -0.1633490193742042, 1.3137908270217924, -4.444795694165904, -1.7744899535020062, 2.750641500927167, -3.4547467554773013, -3.845750515484588, -0.22269648014531218, 2.3667939080562848, -1.5200458236129388, 5.261220000199819 ]
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
82
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
14
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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
15
[ -0.0008542674321323052, 0.053535430684782497, 0.10500614433980744, -0.3368972736064882, 0.06687838884650224, -0.10495931732559274, 0.03931498649472892, 0.03776488609071538, 0.16360455360867365, 0.10786463561486956, 0.09354126016708159, 0.09661237783906737, -0.10932180848835384, -0.1658534042793661, -0.03839965764054118, -0.07511494180652943, -0.2624562818417781, -0.15620474084611366, -0.24296924086117536, -0.3931211320518789, -0.04756646996100686, -0.26738039326373575, 0.05293339994945584, -0.5748805849140164, -0.4092720236496163, -0.3238428967244407, -0.1522072320416532, -0.28882156080001636, -0.31688155495268, -0.5705666948045058, -0.5887034555463128, -0.35438513654082787, -0.649703400435389, -0.52365548294702, -0.36405556584016613, -0.6253530587964704, -0.20564281030760306, -0.28262104327607834, -0.7634168052800847, -0.6696850884877878, -0.9092629188440711, -0.6709732624199545, -0.4250229235747422, -0.6356397903881992, -0.5024882549367133, -0.8474102798072697, -0.47242736773980193, -0.7119514125402614, -0.6302257774117467, -0.6609703026386822, -0.8713179396660526, -0.8646726700735652, -0.5230517102045743, -0.631376421917649, -0.5356359147168182, -0.6701556705268299, -0.7137182114924439, -1.0395478472924529, -0.8092112894872354, -0.7817358853813897, -0.4635997355233692, -0.6885809636340933, -0.5597098784329275, -0.7298837204453559, -0.9620064441088837, -0.8365943468648199, -0.8298428104290593, -1.0396392733597186, -0.9600065045386563, -0.9432979531394888, -0.6534506305548995, -1.283298783289276, -0.7466759945909062, -1.1182771218514982, -1.2042660973609558, -0.7905210822349282, -0.8786446437217302, -0.8043897077679176, -0.8934789594553274, -0.6960142222118183, -0.960302713669249, -1.093117894450968, -1.0227468146472907, -0.8852708446608148, -1.2368362755652091, -1.2286816601585424, -1.1844866694496512, -1.4980411234437598, -1.1360476865540108, -1.4878410710285275, -1.1766144138119168, -1.0539118459477326, -1.2916094190580882, -0.9444490331709562, -1.4825001318743636, -1.05206997896417, -1.1515822902900847, -1.5647634352971407, -0.8373898102877184, -1.314703222607188, -1.464002339727383, -1.5657695890016912, -1.3803617953759484, -1.378041373305298, -1.3527289715163129, -1.4328893276406214, -1.2903146989437586, -1.4742614663099518, -1.7462807601746233, -1.460746770953344, -1.8449784007056806, -1.4029241035051228, -1.6391001520498465, -1.461121287127842, -1.2817950948015444, -1.673505661220639, -1.3504323304016421, -1.6136375889771635, -1.2610250153478322, -1.6285667432286708, -1.721256592204218, -1.4788608111884423, -1.6798996849941321, -1.7609329555252806, -1.7132783095592208, -1.6539766091868384, -1.4351588984553576, -1.9964043696125384 ]
null
Is the two time series lagged version of each other despite amplitude difference?
[ "No, they are not lagged versions", "Yes, they are lagged versions" ]
No, they are not lagged versions
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.
[ "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
16
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What is the type of the trend of the given time series?
[ "No Trend", "Exponential", "Linear" ]
Linear
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
17
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null
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?
[ "Square wave with log trend", "Sawtooth wave with exponential 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
18
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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
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
19
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null
Is the given time series likely to be a random walk process?
[ "Yes", "No" ]
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
20
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null
What type of noise is present in the given time series?
[ "No significant noise", "Gaussian White Noise", "Red Noise" ]
No significant 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
21
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null
Two time series are given. Both of them have a noise component. Do they have the same type of noise?
[ "No, they have different noise", "Yes, they both have Gaussian white 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
22
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In which part of the time series does the anomaly occur?
[ "End", "Beginning", "Middle" ]
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
23
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null
Based on the given time series, how many different regimes are there?
[ "3", "4", "1" ]
1
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
24
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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?
[ "Exponential -> Linear -> Log", "Linear -> Exponential -> Log", "Linear -> Exponential", "Log" ]
Linear -> Exponential
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
25
[ -0.04858626884043041, -0.08471983199047571, -0.14712338959800905, 0.24232272224171966, 0.2775535251621048, 0.1929036565996457, 0.08321757373846156, 0.26640214522428474, 0.31387861599058664, 0.2209591016301667, 0.2778967597014891, 0.4243127187807093, 0.16446575065627922, 0.4557301592042975, 0.3523484862865887, 0.2993820277512951, 0.3349852011531262, 0.37891962556081127, 0.37176075753275983, 0.6972827175119416, 0.5966401044533002, 0.681344076494217, 0.6585086208251879, 0.6357705430406974, 0.6644993050604033, 0.6446484993630138, 0.6801975161401431, 0.5983414069330311, 0.8747103499485065, 0.6125803967743356, 0.7154186568518803, 1.0498591195310212, 0.8896489852716029, 0.9211787319983001, 0.9945175328022131, 0.8041259192434607, 0.8461563224387579, 0.9684222149610356, 0.9499515443913111, 1.0601680341753001, 1.1435945507366139, 1.2613319165236199, 1.2309004362456795, 1.0777399216279848, 1.167047175532261, 1.1672250567322386, 1.1576394764861253, 1.162254043649737, 1.4804787842201343, 1.3424877603011054, 1.3463765058475254, 1.4446012736975904, 1.4769261179424775, 1.5628100634691224, 1.4039373272919637, 1.5459517008460824, 1.4419380720538773, 1.5414156658452474, 1.5934817074654857, 1.6306318408513465, 1.6535915423943195, 1.7501185205942524, 1.637612573772343, 1.7428548306904275, 2.6487969194480403, 3.063624133101896, 2.7293199155125145, 2.8018974579777436, 3.0139905426757285, 2.939061646107327, 3.1292326760790923, 3.117911298976436, 3.126861550655566, 3.159502292797558, 3.2266592333636925, 3.340392006135158, 3.4397372463630407, 3.4551757627973037, 3.6124321958998933, 3.60291829074914, 3.881063793340531, 3.997718621392307, 3.9346279739718497, 4.035904829707253, 4.241583152119847, 4.467439778812635, 4.612169260716734, 4.4515735504562866, 4.826837666649143, 4.860707488373067, 5.009890821024105, 5.218728206413064, 5.281531965458024, 5.608230589080127, 5.817806006907599, 6.006674877900383, 5.869967418839554, 6.234287955110893, 6.27613335630073, 6.61548464633712, 6.685038944025315, 7.2134999078442394, 7.445508031759572, 7.647375322348223, 7.891093735133062, 8.294286029734314, 8.46813013110236, 8.782073459657916, 9.105556076352961, 9.556926681794202, 9.88706551690514, 10.292102313569393, 10.78598926883753, 11.25231873643558, 11.743001844190136, 12.066643269674055, 12.579745958161471, 13.070926864486324, 13.415440192485057, 14.101580435079589, 14.683772213296812, 15.278193461439797, 15.96271181503374, 16.612264338450174, 17.23426202184639, 18.049215689346962, 18.766112418248753, 19.36967414971007 ]
null
The given time series has square wave pattern. How does its period change from the beginning to the end?
[ "Remain the same", "Decrease", "Increase" ]
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.
[ "Square Wave", "Period" ]
Base on the definition of period, check if the time interval between two peaks remains the same.
Pattern Recognition
Cycle Recognition
26
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null
Is the given time series likely to be stationary after differencing?
[ "Yes", "No" ]
No
binary
31
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
27
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null
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
28
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null
The following time series has two types of anomalies appearing at different time points. What are the likely types of anomalies?
[ "speedup and flip", "speedup and cutoff", "cutoff and flip" ]
speedup and cutoff
multiple_choice
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.
[ "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
29
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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?
[ "Remain the same", "Decrease", "Increase" ]
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
30
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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
31
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Is the given time series likely to be stationary after differencing?
[ "Yes", "No" ]
Yes
binary
31
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
32
[ -1.7269309737575353, -2.35563068247083, -2.579246222726851, -2.8279685581767264, -2.979318302417806, -3.187071884502339, -3.1592600874260603, -2.941876683856995, -2.6763010032915715, -2.469693422485337, -2.6912097840502516, -2.676674215431855, -2.290421767833936, -2.681503336358384, -2.3487864200053257, -2.594605322961075, -2.522109771463244, -2.4202424441460186, -2.3733756055349704, -1.8234318977817419, -1.897671351708254, -2.302265027986556, -2.2143008340116395, -2.2562633904820126, -2.1193492578004927, -1.9016653321088108, -1.9099792869333643, -1.802306370389008, -1.7667112579425202, -1.3245083361863081, -1.4159557596006735, -1.5855113028443333, -1.368164069386887, -1.5974675507747034, -1.5006906421627604, -1.542541942309231, -1.5675459138962513, -0.9660666025080494, -0.6615180293765375, -0.40941209720205807, -0.2784775967161, -0.449129813710917, -0.3846012261349991, -0.2406481497234191, -0.19154242107650488, -0.16815988567931495, -0.26624263175569446, -0.1987583629929239, -0.3284591363158383, -0.15486799572033663, -0.6523210682844026, -0.31700961946074047, -0.640703217567003, -0.9040809712664019, -0.8031837212454763, -0.6699365936143539, -0.15705806632372912, -0.08394081503381123, -0.09392426336933583, -0.046715302560156095, 0.3457861000165717, 0.9440807992302922, 0.8984756846963421, 1.0324213457777083, 1.014063543874604, 0.9908004468181633, 1.4545135437252639, 1.2260609841582566, 0.6500058451024397, 0.7283449302551348, 1.0247299503204532, 1.078996154893783, 1.2029302102357486, 1.3886062428149888, 1.4159769355887029, 1.5532628222092955, 1.6864285291224785, 1.2030830610081662, 1.2311831926682875, 0.8430510215754563, 0.8336310375568448, 0.711405345652362, 0.9665791844569355, 1.0268954931595553, 1.143670271500838, 1.0964239630704846, 1.3560818060227422, 0.9618930220619689, 0.7409004580048046, 1.0583360030398086, 0.9508264383001341, 0.4212768924163842, 0.7797604673230851, 1.0455273149421722, 1.2209807173989833, 1.2442782812294708, 1.654118300007499, 1.9647208149969653, 2.346701546175844, 2.518337518933847, 2.548641143406649, 2.4501350275181415, 2.1369893372126447, 2.2608844170895797, 2.405339206688102, 2.3190199864398298, 2.47046451190759, 2.388489492683302, 2.602553752575442, 2.3848668528652897, 2.124485875755169, 2.065115731475035, 2.269643825363899, 1.9836781416066522, 2.24272045381791, 1.8373616938862558, 1.776469617500603, 1.427749950908259, 0.7836776191623004, 0.8741107874342793, 0.8302304689369352, 0.48545366271340257, 0.3579634243192251, 0.4669972851790694, 0.37614511758086866, 0.32711448784313035, 0.22878316677022834, 0.08508234185811304 ]
null
Covariance stationarity in a time series means constant mean, constant variance and that autocovariance depends only on time lag, not absolute time. Is the given time series covariance-stationary?
[ "Yes", "No" ]
Yes
binary
36
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", "AutoRegressive Process", "Linear Trend" ]
Check if the covariance between any two points depends only on the time distance between them.
Pattern Recognition
Stationarity Detection
33
[ 7.849151583288315, 8.112245256970924, 7.2143466110412, 0.6228861071576588, 9.343094850241371, -4.446572954773801, -22.76371131248101, -21.574227461414626, 3.2406342979498257, -1.381763058634244, 2.070578660683152, -1.7611163366139073, 4.7983747718094065, 3.1459529647832523, 0.9276634468374642, 6.548416280476784, -1.5209069851030883, 3.058188135918338, -0.1595326095349222, -1.2872238462284322, -8.789742507128741, -6.41573953600329, -8.807716067542481, 6.927144071764357, -13.214243970422173, 2.226891507248, -16.389618003795533, -2.79705519369718, -9.692886646089523, 0.755132908506357, -0.7660901376553688, -14.712958717594969, 6.249664372741764, 10.941595515510697, 10.439992443896173, -1.2634108930691252, 7.573805786178419, -9.08257351444325, -26.85593889924743, -28.976184051319255, -23.60655694526981, -19.430972505901792, -14.05534806840504, -11.050605579239436, -11.986866712414905, -27.123317302763542, -11.653533907486604, -8.508707866607677, -11.127097820121612, 8.386172688017286, 2.027412626364249, 1.4903554083104058, 8.418642973474677, -10.663164953776596, -5.4488695052035885, 5.110106843606878, 1.6158068580284195, -12.320383908845502, -10.970658158742888, -3.5522332228150213, -22.816008329253762, -25.055895466508492, 7.3389566200033824, 8.355973372204497, 19.11605635865443, 18.233012066420148, 12.946054307716086, 3.3236211210663096, 5.5648441247460125, 17.206961197106047, 16.867814021626465, 10.180268608338, 3.3802105373999205, 6.55778983383759, -2.0010918492618712, 3.8934056188391426, -4.899122445450646, -5.878615358649208, -13.377697716223032, -11.047341243691765, -12.26764275037691, 10.741880586168893, -3.519077300871808, 2.065899674425071, -8.544134043687544, -3.738373967970468, 1.1367491486230763, -17.967597139906363, -22.81416062828666, -21.21214632661476, -23.51196196587765, -10.998882134483985, -3.1288016965467547, -12.017896983035264, -4.8591855503896095, -6.692783190157482, -4.289217079189056, -8.661272075214269, 0.7890438036550094, 16.86651420562151, 16.172889087793056, 22.01579633249373, -3.06260669455877, -8.385086830531952, 1.6329819102265632, 15.931363675487955, 14.469280651138009, -3.0167434519706666, -5.841567277260025, 0.34563743457919877, -1.1973627802352245, -8.740026762750142, -7.300947057141101, -3.6614378752879033, -12.738882885264433, 3.4752101198310643, -2.5161365027042417, -1.9866974585090171, 9.396189400385273, 3.2698660623750966, 11.549460858173978, -4.637865982570217, 2.0154071509829743, 9.441240959924555, -3.590462548513913, -3.5116948772143526, -3.2882442350302568, 0.49829845531811867 ]
null
What is the direction of the linear trend of the given time series, if any?
[ "Downward", "Upward", "No Trend" ]
Downward
multiple_choice
4
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" ]
Check if the time series values increase or decrease over time.
Pattern Recognition
Trend Recognition
34
[ 0.15128609002876245, -0.10170483074844683, -0.08170879269423675, 0.07349558735341727, -0.13443536349522356, 0.004508704544300239, -0.021534847538441794, -0.06254941033704896, -0.26954792223153834, 0.07961427752081238, 0.2189731800754583, -0.1309781710474876, -0.30421604320547163, -0.15194011268709082, -0.017187776681446082, -0.27443258275596305, -0.21216839402888224, -0.15246096179538016, -0.03273638199263662, -0.11009741685241792, -0.11579539196806989, -0.31774831979795154, -0.20324967606138056, -0.38698324651030097, -0.15953595320671335, -0.12486259764477528, -0.22823123345693325, -0.3809344654744192, -0.3679570458684356, -0.07286694603235522, -0.4144722182490673, -0.21250588100557646, -0.33317602607504393, -0.448029243287079, -0.614442481371396, -0.38871240932173606, -0.41915173508355, -0.1691018793548827, -0.5885473629225761, -0.11857019226933663, -0.42331506790118084, -0.435494708875807, -0.5958562458973742, -0.4691979040830048, -0.4570361384587077, -0.39813490616636027, -0.7028326403900784, -0.3504724336990776, -0.5222103859563891, -0.49653259158493246, -0.6352409525036894, -0.7553149306223937, -0.6144347171875117, -0.6089605848609277, -0.8612670134080194, -0.5404384481462873, -0.5214177995021931, -0.7971702841502051, -0.8539516803242393, -0.7560390954209931, -0.7181325212649784, -0.7741722411211042, -0.7551494614742486, -0.7240355161672866, -0.9789426472391358, -0.9734070389532806, -1.2098640761134396, -0.6619915459151083, -0.8156945614463063, -0.6699626186943684, -1.0159010366044436, -0.8503811735222584, -0.8333191410771635, -0.9639971906960376, -1.1275279348618774, -0.635499198214955, -0.7004797419483678, -0.9846390119593895, -0.8603668283317703, -1.0244128935157182, -1.1144527454458817, -0.6952429323544184, -1.2393399856506782, -1.0420852170286936, -0.997613636062479, -0.7702544457720202, -0.8975773384755348, -1.3020676012642822, -1.0590354656416485, -1.0674274870218312, -1.1175596742587548, -1.0000116034838595, -1.3220139084190883, -1.1811942331131788, -1.057640906445852, -1.038999495970999, -1.1320251208333512, -1.2109425841580976, -1.1972368030364127, -1.0778247019429548, -1.197792646637076, -1.3741724352980167, -1.4154819556257467, -1.4666440619633951, -1.0287108958419942, -1.139758570202508, -1.2914191822809364, -1.3565092074111063, -1.3868932290894365, -1.1442174343014033, -1.0323146489440143, -1.427789210300154, -1.173404349922182, -1.3550785299072319, -1.4038423372739006, -1.153607711311542, -1.3970005216087873, -1.3621993495279525, -1.3815762129024416, -1.6798914865110457, -1.3995035904918964, -1.5415626685906914, -1.6847458742718313, -1.55866233956952, -1.5719527459622675, -1.346372090134711, -1.6782676689126392, -1.648445205246097 ]
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 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.
[ "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
35
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[ 1.0518985905480467, 2.342664739973105, 1.4214384844624346, 2.277245578554883, 2.3291386567191044, 3.1542370645673827, 3.616066648824218, 3.7480923100855796, 4.210001129763634, 3.8851377308138244, 3.956687211011999, 3.2884799451613977, 4.556354482436614, 4.3459638180720965, 4.201854827477336, 4.070293860893515, 4.032588427617278, 3.7758661573676378, 3.433424049439103, 3.5846933759596036, 3.4425132305432715, 2.5233476825066905, 2.394150243988086, 2.1611667607256253, 1.9235767470754528, 1.5093480154927263, 1.5560892400127608, 0.0592894583915049, -0.18049900994930168, 0.34331368952447894, -0.3419557660213699, 0.1427419651424316, 0.05971876721264413, -0.5970690551157678, -1.3981463998610282, -0.4396605836384132, -0.9266881729869723, -1.7816844885088634, -1.7016919454865498, -0.16030120352928157, -0.11240866077521838, -1.8700751339000474, -1.0704256602810276, 0.4395215069897872, 0.1576426330329435, 0.8487258374053706, 0.8262895668251335, 1.5675264633786234, 1.6443986542967344, 1.8364302329283906, 3.0050877096167454, 2.9980383715048595, 3.63939967592734, 3.7972014580459095, 3.86401392165637, 5.278184316920852, 4.991352967255171, 4.944743908222018, 6.0343019570546765, 4.96858852725957, 6.93915452467349, 5.8794295285327305, 5.437508702491188, 7.080791083372501, 5.906352918573223, 6.224250549405117, 6.382237172314286, 6.494520342548277, 5.892524600868032, 5.2238563883701765, 5.430648508883913, 4.8584930005635725, 4.91805345067454, 5.316815324684593, 4.579365043147685, 3.9987153364918986, 3.959907725771461, 3.6982065176109353, 2.4698267938801775, 2.7639915877601844, 3.7829299170222574, 2.895823638046578, 1.8592572552550832, 1.6688411399809813, 1.5530793471569468, 2.249715779525275, 2.6121211152060564, 2.139165949256721, 2.0152555586783425, 1.8520279686120134, 2.424347783389244, 2.081832829186409, 1.800763861451107, 3.9055018841113576, 2.9408541471366147, 3.6722100354112044, 4.583320070905857, 5.417556411424433, 5.293394728942732, 5.046189373283337, 5.978495471079958, 6.278064647577834, 7.082462439121199, 8.192144053095646, 6.766752202173469, 8.268420012438815, 8.645155372884865, 8.641724002979997, 9.911607639869727, 9.22251457936105, 9.550758572729453, 10.85436266433521, 11.363221843470757, 10.714281969545626, 10.238358405100405, 10.545128769280517, 11.410404475974262, 10.933004229344077, 10.755442838150207, 10.860002185719324, 10.552618750431765, 11.18736254980747, 9.86314825395586, 9.61453956155835, 9.15488294243083, 9.37388997368162, 8.898340352605265, 9.3629680928318 ]
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" ]
Log trend and sawtooth 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
36
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null
What is the type of the trend of the given time series?
[ "Exponential", "Linear", "No Trend" ]
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
37
[ 0.7706903615285006, 0.8682347029878075, 0.28150679215723307, 1.4650556933350996, 0.5196387554219519, 1.2466001498511157, 2.5286445737639016, 0.355798915705707, 1.1121018931802942, 1.0082648627944049, 0.9371810807328811, 1.6450265528797303, 1.8453784422496358, 1.7059356132106176, 0.9869521452364174, 2.594666382448964, 0.5223702053695731, 0.9215690984297165, 1.5537963564484545, 1.5453471733295747, 1.777075647421549, 2.356223732576799, 1.5400490941890859, 1.6913873787605547, 1.372558710721448, 2.000037186558936, 1.5834684200543327, 1.6208092820259705, 2.0905220296775906, 2.3755136660012437, 0.7941206885408796, 2.1195502623376705, 1.8459315064350397, 2.4976178908969446, 1.9424480413592153, 2.7626790864225024, 1.8195538708970238, 1.0891877371752907, 2.7777475843840125, 1.8788047430211092, 1.5601273958088724, 2.409028865595171, 2.333257429077886, 2.9173633313115657, 3.0061239829451445, 2.663004868518475, 2.2292563180041043, 2.872823906476877, 2.8708851255047185, 3.1329635026258913, 2.472599087320347, 2.7726514070939006, 3.2917190999946815, 3.726271863476879, 3.6525636595941537, 3.2790710127685507, 3.0642648249661875, 3.5813011249732933, 2.9066664845286354, 3.1184074937097446, 4.3579500552716155, 3.8818822578708287, 3.5865822109543335, 4.256111696121291, 4.567979885820596, 3.7869148071959273, 3.8821006056193523, 3.907921999666547, 4.75652003818686, 4.8536745136705, 5.154141406224611, 5.061821256377219, 3.83982082269905, 4.8969470631307495, 4.329978084843548, 4.707637200522716, 5.156580696658159, 5.598570027010688, 4.847233893023857, 4.244579529875217, 5.613956296745111, 6.964749186885337, 5.663388244593507, 5.912748082268101, 6.907539047578007, 6.441507323277853, 6.387518501588254, 6.635730051295252, 6.678305066869374, 6.124808131234287, 6.168520455337913, 7.930336199329086, 7.229731748873269, 7.341963400382087, 7.404255472445419, 8.000759444467581, 9.043895161813705, 8.204401037385606, 7.819881294099026, 8.222427464613327, 9.003612458810107, 8.359565090584093, 9.263888089317277, 7.8682291537391364, 9.10861168923426, 9.736784730771964, 10.261241259042125, 9.42479851215513, 9.294998485662292, 10.132943938817352, 9.922216703921903, 10.636807865314479, 10.939288095210344, 10.51932511651019, 11.822502042607887, 11.588272588844786, 12.45903126405462, 11.253710226202301, 11.930485460053806, 12.966012076498238, 12.582517778229839, 13.180125874459375, 13.549116838391091, 13.92045248296797, 13.801415758420088, 14.520170084044006, 14.366175803642177, 15.41324402121794 ]
null
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 cutoff
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
38
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null
Is time series 1 a lagged version of time series 2?
[ "Yes", "No, they do not share similar pattern", "No, time series 2 is a lagged version of time series 1" ]
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
39
[ 3.4282390744125766, 1.7728300371008434, 0.19392640970115083, 3.4854235206086828, 3.4451525078317418, 1.5198132690492219, -4.635382080311568, -0.34401997635009784, 1.0462373057375498, 0.4072709750849617, 0.9856795466490558, 1.6291693148621964, 2.105778729773081, -0.8920889454751408, -2.0067380459262836, 0.2513498098621123, 1.5902553638985046, -2.247114031552961, -0.09987920417369, 3.7001399984318364, 4.800446145973537, 3.065785112556836, 1.887412742807808, 1.373689445124179, -2.6156428713246926, 1.562486418192075, 0.4950652245261131, -0.6480854757075803, 6.218263597823894, 5.069790513257041, 2.1219446490229346, 0.1924854705305763, 0.613427822814541, 2.2395936301231276, -0.06386866295132336, -2.226519535598164, -1.5332162892323007, 0.6372091566608259, -0.7981926515786543, 2.135290089452468, 1.713488957516661, 1.7542080479996556, -0.806461725069002, 0.0305559869441277, 2.013197379324736, -1.370259613007674, 4.038478455925843, 0.7894800243270059, 2.772026745213984, 4.698505161077303, 0.7597937266466859, 2.4783042509867537, -1.5348668279305677, -3.864683628117534, -1.758901105462738, 1.5524659341693423, 0.02345012903623167, 4.587906370769391, 4.709334033344963, 0.4304539878299978, 3.5020643038140866, 0.1419054651241951, 2.368226204902236, -0.8406114554451006, -3.6720862996257586, 1.5939834712583434, -1.1614623555885117, 1.290577395197868, 2.6124743698973836, 2.7212948187640937, 4.72478688370803, -0.12759316419233524, 0.9071800350253034, 1.2963987916022885, -0.46150537061731334, 0.3299354124974353, 0.44305180949827117, 1.0237310721865973, 0.02224696551934935, 1.212584783052451, 3.3809103040025237, 0.027307902305520715, 0.3331952404581474, 0.5815293276544455, 0.6964826170852123, -0.014758046690254822, 1.846953462188762, -0.5236067375488462, -0.3323423893264785, 1.699359000259419, 0.6248579286539617, 3.7027195599341716, 1.050648318185021, 1.2427275970549891, 4.170053748484531, 1.2984812000845791, -0.012645559225720415, 1.596720395751745, 4.749209982835206, -1.3149162872336237, 0.7918166892317067, 1.4948679795963755, 2.239673823372634, -1.0318822818832794, 3.1994290822729234, 3.365891930286075, 1.6013646536837252, 1.8906645011861984, -0.941956354497854, 2.792628324295927, -0.9679097019350701, -0.07609318041659335, 2.4830547685810975, 0.8570928578241366, 1.104661910155254, -1.001950219659241, 0.220750559542069, -0.821288796131985, -2.8069770241606142, -0.47277874213366944, 0.6239184060203529, 2.5369551694386123, 2.2986909594461893, 2.333354126689153, 2.6490529220002386, 3.401938354324339, 0.6146071905822331, 1.3131704259259218 ]
[ 1.599076031569918, 0.5193428962826687, -0.10222740778161121, 1.080378572421013, 1.967688939713514, 3.4282390744125766, 1.7728300371008434, 0.19392640970115083, 3.4854235206086828, 3.4451525078317418, 1.5198132690492219, -4.635382080311568, -0.34401997635009784, 1.0462373057375498, 0.4072709750849617, 0.9856795466490558, 1.6291693148621964, 2.105778729773081, -0.8920889454751408, -2.0067380459262836, 0.2513498098621123, 1.5902553638985046, -2.247114031552961, -0.09987920417369, 3.7001399984318364, 4.800446145973537, 3.065785112556836, 1.887412742807808, 1.373689445124179, -2.6156428713246926, 1.562486418192075, 0.4950652245261131, -0.6480854757075803, 6.218263597823894, 5.069790513257041, 2.1219446490229346, 0.1924854705305763, 0.613427822814541, 2.2395936301231276, -0.06386866295132336, -2.226519535598164, -1.5332162892323007, 0.6372091566608259, -0.7981926515786543, 2.135290089452468, 1.713488957516661, 1.7542080479996556, -0.806461725069002, 0.0305559869441277, 2.013197379324736, -1.370259613007674, 4.038478455925843, 0.7894800243270059, 2.772026745213984, 4.698505161077303, 0.7597937266466859, 2.4783042509867537, -1.5348668279305677, -3.864683628117534, -1.758901105462738, 1.5524659341693423, 0.02345012903623167, 4.587906370769391, 4.709334033344963, 0.4304539878299978, 3.5020643038140866, 0.1419054651241951, 2.368226204902236, -0.8406114554451006, -3.6720862996257586, 1.5939834712583434, -1.1614623555885117, 1.290577395197868, 2.6124743698973836, 2.7212948187640937, 4.72478688370803, -0.12759316419233524, 0.9071800350253034, 1.2963987916022885, -0.46150537061731334, 0.3299354124974353, 0.44305180949827117, 1.0237310721865973, 0.02224696551934935, 1.212584783052451, 3.3809103040025237, 0.027307902305520715, 0.3331952404581474, 0.5815293276544455, 0.6964826170852123, -0.014758046690254822, 1.846953462188762, -0.5236067375488462, -0.3323423893264785, 1.699359000259419, 0.6248579286539617, 3.7027195599341716, 1.050648318185021, 1.2427275970549891, 4.170053748484531, 1.2984812000845791, -0.012645559225720415, 1.596720395751745, 4.749209982835206, -1.3149162872336237, 0.7918166892317067, 1.4948679795963755, 2.239673823372634, -1.0318822818832794, 3.1994290822729234, 3.365891930286075, 1.6013646536837252, 1.8906645011861984, -0.941956354497854, 2.792628324295927, -0.9679097019350701, -0.07609318041659335, 2.4830547685810975, 0.8570928578241366, 1.104661910155254, -1.001950219659241, 0.220750559542069, -0.821288796131985, -2.8069770241606142, -0.47277874213366944, 0.6239184060203529, 2.5369551694386123, 2.2986909594461893 ]
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
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
40
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What is the primary cyclic pattern observed in the time series?
[ "SawtoothWave", "SquareWave", "No Pattern at all", "SineWave" ]
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
41
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null
The given time series is a random walk process. What is the most likely noise level?
[ "3.8", "6.88", "1.91" ]
3.8
multiple_choice
55
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
42
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null
Covariance stationarity in a time series means constant mean, constant variance and that autocovariance depends only on time lag, not absolute time. Is the given time series covariance-stationary?
[ "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", "AutoRegressive Process", "Linear Trend" ]
Check if the covariance between any two points depends only on the time distance between them.
Pattern Recognition
Stationarity Detection
43
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null
What is the type of the trend of the given time series?
[ "Exponential", "No Trend", "Linear" ]
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
44
[ 0.9427300773736911, 1.6421142810077933, 0.24973694488343479, 0.7715589333625861, 1.0987277736258776, 1.1450325917524165, 0.9225362098415872, 1.485624540176405, 0.6676379814253425, 1.1581394106514056, 1.3180049350383174, 1.544266525778122, 1.6727219239068127, 0.7851539211211978, 0.6116875542202067, 2.049578371015672, 1.6096347739417232, 1.102732025221867, 2.2868261545753903, 1.6041577442697483, 2.171853124309679, 1.6526806091677497, 2.686864222579504, 2.572601401433059, 1.6097816862007794, 2.26029477756177, 2.1383767615923794, 2.542139666551798, 1.418475050902641, 2.288075887793407, 2.51939947835299, 1.1570020255057054, 1.4919988102385902, 1.11236491110168, 2.0467526003875576, 2.5908502865804204, 3.035055592743746, 2.3739243936480987, 3.20541463612449, 1.7565444590407604, 1.651679962282726, 2.53369087713469, 2.81293912173478, 2.665380104741517, 1.7102389319138114, 2.763076640570903, 2.2205562774281438, 3.274293649843332, 3.1909699138250107, 2.607527282005868, 2.8919498045164, 2.6923498809224675, 3.2653862218739644, 3.8508011611517965, 2.9586465748591166, 3.78362901902902, 3.3484318369050166, 3.3009809700844492, 3.7297049363579124, 3.3533928341273773, 3.6840205773975487, 3.453822153374825, 5.129172546886867, 4.260673147258956, 3.991643165808102, 4.54924540432617, 4.489178959437685, 4.54033798207337, 5.065833706787879, 5.2479363675129616, 4.716926796819243, 4.809885281241988, 5.07856860720288, 4.186179213473381, 4.703398598099077, 6.27115977542208, 6.539875888656768, 5.725552526414777, 6.274106496197839, 6.280360965204735, 7.806307678896946, 6.972084435852997, 6.497142749788537, 6.235589067970137, 6.065927183096477, 7.130288522812236, 6.813486897847514, 6.647426029449069, 7.206029940332601, 7.163268637941025, 8.726394433950098, 8.506573285250024, 8.24894196806368, 9.18441884382495, 8.679093815783714, 8.410277988144411, 9.807645624325485, 9.525463154173504, 8.952181137082794, 9.595415541850018, 9.477656678472641, 9.454165478799581, 10.84409337583633, 11.57661581294545, 10.169117019038811, 11.40209889217552, 11.053359354418843, 11.399173032580316, 11.6167215431523, 11.757375796630892, 12.49650006700856, 12.346196538229188, 13.193048955869237, 13.335722904277727, 13.551421304456355, 13.534362002997625, 14.024368783359092, 15.02259363068712, 15.235207945907613, 14.843709696570164, 15.737961089291913, 16.42805303192871, 15.590169890431621, 17.077710272591496, 16.864721134309924, 17.880385640063597, 17.621770500063775, 17.518748181024822 ]
null
You are given two time series which both have a trend component. Do they share the same direction of trend?
[ "No, they have different direction of trend", "Yes, they have the same direction of trend" ]
No, they have different 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
45
[ -0.04101262451847562, 0.5196031547774996, 1.076198168104769, 1.4797427375817134, 2.055594688672651, 2.366122241618876, 2.794177929126308, 2.677304627200189, 3.1848848733304984, 3.3319737554924007, 3.478864918099358, 3.474524446990768, 3.595243121410732, 3.3140809423195923, 3.416410783111508, 3.1264178656190564, 2.933201055908647, 2.7657363878341927, 2.4352239738647907, 2.2135985808430627, 1.676673811989418, 1.4250437067577313, 1.1852065853722233, 0.8089552531742141, 0.5144497326940419, 0.3130339690964295, -0.06876069901853152, -0.2737919162665422, -0.2860731473929151, -0.4329351041514205, -0.3193913114755113, -0.34547038436906174, -0.3322155540218163, -0.06092160599590221, 0.05034365990193394, 0.5272364942413502, 0.6363070509976311, 1.287053364585641, 1.623851135243701, 2.032179304713579, 2.602964808024458, 3.06756326032307, 3.6414767136699266, 4.1251157491735775, 4.4958994568154464, 4.8151626988089, 5.255387945971173, 5.667423199875755, 6.098956361154965, 6.20691883390405, 6.41830497447806, 6.781796594179278, 6.664697589849086, 6.626570937655212, 6.72078970630176, 6.531603836436601, 6.237574973621638, 6.27065336417364, 5.839221083505357, 5.630598151891098, 5.305119735872195, 5.00306233555786, 4.420940341984778, 4.26805103232427, 4.0866811760374535, 3.793849487705923, 3.290627530114126, 3.241805172596727, 2.8784511538379007, 2.7731326645456993, 2.6906196583945374, 2.7059648994004544, 2.829924002565391, 2.854339898002503, 2.9762390420300338, 3.3074587198913656, 3.4098575647265132, 3.8146015637933584, 4.300963293451833, 4.673212385945513, 5.024431780265695, 5.393740740483472, 6.064062665202582, 6.367464566438902, 6.991198286646344, 7.602688420003538, 7.992853548933388, 8.14660089225433, 8.744325679689254, 9.020262755553164, 9.199450648921665, 9.57710354073215, 9.650077288110978, 9.743369234963875, 9.833631744129814, 9.725656397523736, 9.705072913264766, 9.487567352407448, 9.293804129271031, 9.203421589480461, 8.933206243654775, 8.343875093058644, 8.260762219837064, 7.986919796728143, 7.663112804254733, 7.228669534521542, 6.758516296776992, 6.642247056426209, 6.24305087340553, 6.089678517836999, 6.006088448320942, 5.78629572162276, 5.710409987252173, 5.891919065175454, 6.115658142551708, 6.199976963109089, 6.354572084180562, 6.648387198935312, 6.934850084626172, 7.284999352137169, 7.7403313290335065, 7.957867119617991, 8.584121268552174, 9.04165944395577, 9.549841591919273, 9.984976601318598, 10.559710884247997, 10.880516035422342 ]
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The given time series is a sawtooth wave. What is the most likely amplitude of the sawtooth wave?
[ "6.12", "7.25", "2.62" ]
7.25
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.
[ "Sawtooth Wave", "Amplitude" ]
Check the distance between the peak and the baseline.
Pattern Recognition
Cycle Recognition
46
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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
47
[ -0.07974803986236183, 0.07600677972487446, 0.09161130865620315, 0.11582013679410719, -0.1818397485697192, 0.18460987925204922, -0.012822035993658581, 0.0254907650932662, 0.4308116562942862, 0.13322411677690096, 0.05287636692255314, -0.1765475351286763, 0.3077886630896516, -0.04239658762736159, 0.013041579033057332, 0.11202701961278683, 0.35282468015437307, 0.2784126877401553, 0.166044573937956, 0.2378776160123602, 0.1284625777329319, 0.2364065903998527, 0.2380444078622239, 0.3664747982339925, 0.3766456754474804, 0.3246418623751387, 0.22212877124972497, 0.3780780186543026, 0.2785357268734585, 0.15840668152180887, 0.2582543210551633, 0.3329462373790954, 0.4521818631735565, 0.31836857458516105, 0.1935297625201411, 0.37080607129870624, 0.38866375225932914, 0.4085869268190828, 0.5157392034468353, 0.5391784421986495, 0.3368912178128786, 0.34438045875310397, 0.29885575372865353, 0.5384998940456996, 0.6477576524008257, 0.42559389974299244, 0.4456844753313672, 0.6812679236115181, 0.5649253449444303, 0.5661669706084764, 0.36203166660293096, 0.6188974723747683, 0.4173049806067133, 0.4006747948417407, 0.5148426481396203, 0.49371196242364657, 0.552106173768695, 0.40172936898393097, 0.7284880810106151, 0.7611318286647945, 0.36611534372489296, 0.7622197102969059, 0.536748949369489, 0.766965522049468, 0.6553429981848137, 0.6785410222627336, 0.6607257208295411, 0.8553102139424379, 0.5424681688528942, 0.7964050929817351, 0.8718451810525137, 0.831470642640706, 1.053889775026194, 0.6880593872954713, 0.894380478960078, 0.7645681924493157, 0.9515418173476828, 0.7983024561917892, 0.7585611618430467, 0.9922639622392164, 0.7656531285670929, 0.6545919868898054, 0.7830811395091014, 0.9432108800516483, 1.05550102957366, 0.8970127393115118, 1.0665275500979325, 0.7240680849738641, 0.8550664028289218, 0.8858405102506316, 0.9191626428120477, 0.9557329491001106, 1.0461134976784663, 0.9067665770587684, 0.9941174137480467, 0.9802204719229649, 0.8744850536668584, 0.9919454405666257, 0.9983720556821675, 1.0059287370231136, 1.0422599212912844, 1.0584300749822226, 1.001842616331031, 1.2370037687831352, 0.9254170397265418, 0.9949272694197495, 1.466854503683127, 0.9738941493947724, 0.9426461394239661, 1.2283293984377064, 0.8680425618296672, 1.1212435278256456, 1.4455370383781354, 0.9693453554165156, 0.9221103106193043, 0.9961388989038227, 1.3226000362483747, 1.3628305291162208, 1.157348751244454, 1.3253782412779909, 1.4289721572380698, 1.4917034925592378, 1.233973268650155, 0.9734145534214167, 1.178989617033399, 1.241323289826263, 1.2738345971382747, 1.2935860967102155 ]
null
What is the direction of the linear trend of the given time series, if any?
[ "Upward", "Downward", "No Trend" ]
Upward
multiple_choice
4
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" ]
Check if the time series values increase or decrease over time.
Pattern Recognition
Trend Recognition
48
[ 0.05091851046423075, 0.03141784784430655, -0.10022316595790726, -0.06593013531323708, 0.20799771106644116, 0.2534757563561078, 0.03245679135787436, 0.082715100682186, -0.03804735960469907, 0.26059261501405606, 0.20122784663687165, 0.38884339628994036, 0.00921896814142005, 0.08942311368053954, 0.18474390023648182, 0.25313720072308565, 0.14462720410375723, 0.06449259545356498, 0.3183939310921703, 0.30710104644846403, 0.09121193854919829, 0.4167704619786125, 0.40201875081800253, 0.26944357190868073, 0.2727735296166804, 0.3493964979107121, 0.16420763094204133, 0.2986267267405791, 0.007249660063297192, 0.437676133886221, 0.11090543146014248, 0.5463284453378181, 0.30327358153751366, 0.3305865457985762, 0.28386388662733364, 0.34182076014719665, 0.5891016061386023, 0.05894609927382344, 0.5913058813404064, 0.47216053908478667, 0.2690646860660929, 0.29821374014239027, 0.6902548026874921, 0.3380052988197374, 0.32012335712155954, 0.6483063625138137, 0.5485771893028965, 0.38268013138025814, 0.5535015045065987, 0.39232769988770877, 0.6977826941530895, 0.7032246589229129, 0.6408092739592862, 0.6281211961480825, 0.8328739236494191, 0.599796959886506, 0.4470468615353733, 0.6839087883550391, 0.9214944362612428, 0.5029122433828697, 0.6043056494500643, 0.7229589003870307, 0.6687174453474003, 0.5510324233392689, 0.8533830733954648, 1.030247897353695, 0.7469743818633953, 0.605493440960726, 0.5270765076329369, 0.7882589478428842, 0.9163297528987375, 0.8401542542202803, 0.7849126700691919, 0.7145326187053936, 0.6557839422238328, 0.9335844303043215, 0.9554356101779898, 0.625679695529438, 1.0708891336399373, 0.9411027499159361, 1.066351035271218, 0.6975050862056194, 0.7051291191924445, 0.8845801729945694, 0.9857598616962148, 1.175837510253977, 1.0357302754647075, 0.9152250161821645, 0.8175836849776774, 1.1410165000795474, 0.8479370276688112, 1.218020121981238, 0.9639796863023334, 1.2345848966781752, 1.1192196096615037, 1.0171129205718294, 0.9750532978111348, 1.0106816790189388, 1.12813208868857, 1.0903995697305657, 1.008370931924314, 1.0785837344051445, 1.123314893454401, 0.8284895026986046, 1.197703902727882, 1.0094500483985795, 0.9963095958233755, 0.9332505367478141, 0.9293988904496991, 1.0010334833243566, 1.1014753102182053, 1.4811301959201488, 1.1486543316926994, 1.2570192989804128, 1.298775686631811, 1.272365414336472, 1.2543913621612552, 1.1104656676680098, 1.4878962737338275, 1.5481487975913093, 1.075679999653976, 1.17781212428276, 1.2917989433377608, 1.2078644897273723, 1.4224480432675715, 1.2624016852661857, 1.6740587308967856, 1.5499872514402866 ]
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Based on the given time series, how many different regimes are there?
[ "1", "4", "3" ]
3
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
49
[ 0.05277647609316608, 0.1085535680701791, 0.15712696701028184, 0.11712439267062243, -0.05296226209999099, 0.02247661714918752, 0.1388518286553897, -0.0173126796011637, 0.19118567306070264, 0.11083901898308332, 0.11237520679937005, 0.23593901313011192, 0.22425507621379975, 0.15871785723872073, 0.3257331829124865, 0.11667959857150495, 0.301365220781354, 0.314067514639199, 0.2387884736663946, 0.31734214857743837, 0.17460321747012925, 0.40710300578478265, 0.3111958189752266, 0.29239945932305456, 0.46455841271408044, 0.30420884983154856, 0.24878281800490146, 0.24895175904430003, 0.48020140028668734, 0.3065431986579281, 0.6250512808614259, 0.2563646506300501, 0.6491889570028592, 0.5156307956495502, 0.4998434664976821, 0.4700085977592593, 0.5793998466307944, 0.5507084937085354, 0.6797878809081054, 0.5958661863280902, 0.6144593263635069, 0.5780536577513665, 1.6087203166006454, 1.6746517688693823, 1.5031791636631395, 1.5705951291372897, 1.8118773190685724, 1.7877213492035324, 1.7862949103014298, 1.8415983254389263, 1.9106075929509792, 1.8590311697076998, 1.873428924678534, 2.0102229680380543, 1.933340187312493, 2.113735909543884, 1.9456147644262245, 2.26301671322401, 2.252891734602935, 2.278106985457876, 2.399025831893984, 2.51697826598689, 2.5030051514389804, 2.270124382659797, 2.380448479184675, 2.5017150761595928, 2.624240209370121, 2.732522998690704, 2.6690503650095048, 2.822962033341711, 2.7932534498502277, 2.874046495083113, 2.8628948161579175, 2.98161399066712, 3.0112183012581477, 3.1233830056179395, 3.4031150664622762, 3.2818532566033976, 3.721401935784974, 3.5912630131386427, 3.6466498441920843, 3.6311056624811098, 3.8783626629609262, 3.844850182827006, 3.9146149469153197, 4.129971138465718, 3.8359054138544293, 3.9319874556435175, 3.7182911996904164, 3.7566587123413644, 3.908786344142667, 3.640558293988395, 3.8560485747549196, 3.7171276316888298, 3.561654479741911, 3.6526906504249452, 3.6582540406701214, 3.5947283111172235, 3.3470735620945136, 3.402931035689128, 3.4224416089045193, 3.411298848737721, 3.452358120590849, 3.3796097301171617, 3.1998539133408817, 3.3429568535005436, 3.337544362116385, 3.304013551569162, 3.3276612985195753, 3.274524160607059, 3.208598672263068, 3.127212812382415, 2.9396820093647364, 3.1202886438176494, 3.069644309808757, 3.047582144000039, 2.864298121886526, 2.855416044615786, 3.040385703177958, 2.9026636216470574, 2.946317925958041, 2.8525484130218803, 2.824240908546464, 2.8866423943825446, 2.7127582601512628, 2.7455235298551544, 2.661232642478607, 2.635559267793935 ]
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Dataset Card for TimeSeriesExam-1

This dataset provides Question-Answer (QA) pairs for the paper TimeSeriesExam: A Time Series Understanding Exam. Example inference code can be found here.

📖Introduction

Large Language Models (LLMs) have recently demonstrated a remarkable ability to model time series data. These capabilities can be partly explained if LLMs understand basic time series concepts. However, our knowledge of what these models understand about time series data remains relatively limited. To address this gap, we introduce TimeSeriesExam, a configurable and scalable multiple-choice question exam designed to assess LLMs across five core time series understanding categories: pattern recognition, noise understanding, similarity analysis, anomaly detection, and causality analysis.

Spider plot of performance of latest LLMs on the TimeSeriesExam

Figure. 1: Accuracy of latest LLMs on the TimeSeriesExam. Closed-source LLMs outperform open-source ones in simple understanding tasks, but most models struggle with complex reasoning tasks.

Time series in the dataset are created from a combination of diverse baseline Time series objects. The baseline objects cover linear/non-linear signals and cyclic patterns.

time series curation pipeline

Figure. 2: The pipeline enables diversity by combining different components to create numerous synthetic time series with varying properties.

Citation

If you find this work helpful, please consider citing our paper:

@inproceedings{caitimeseriesexam,
  title={TimeSeriesExam: A Time Series Understanding Exam},
  author={Cai, Yifu and Choudhry, Arjun and Goswami, Mononito and Dubrawski, Artur},
  booktitle={NeurIPS Workshop on Time Series in the Age of Large Models}
}

Liscense

MIT License

Copyright (c) 2024 Auton Lab, Carnegie Mellon University

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

See MIT LICENSE for details.

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