Manipulate a time seriesΒΆ

The objective here is to create and manipulate a time series. A time series is a particular field where the mesh \mathcal{M} 1-d and regular, eg a time grid (t_0, \dots, t_{N-1}).

It is possible to draw a time series, using interpolation between the values: see the use case on the Field.

A time series can be obtained as a realization of a multivariate stochastic process X: \Omega \times [0,T] \rightarrow \mathbb{R}^d of dimension d where [0,T] is discretized according to the regular grid (t_0, \dots, t_{N-1}). The values (\underline{x}_0, \dots, \underline{x}_{N-1}) of the time series are defined by:

\forall i \in [0, N-1],\quad \underline{x}_i= X(\omega)(t_i)

A time series is stored in the TimeSeries object that stores the regular time grid and the associated values.

import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt

ot.Log.Show(ot.Log.NONE)

Create the RegularGrid

tMin = 0.0
timeStep = 0.1
N = 100
myTimeGrid = ot.RegularGrid(tMin, timeStep, N)

Case 1: Create a time series from a time grid and values Care! The number of steps of the time grid must correspond to the size of the values

myValues = ot.Normal(3).getSample(myTimeGrid.getVertices().getSize())
myTimeSeries = ot.TimeSeries(myTimeGrid, myValues)
myTimeSeries

[ t X0 X1 X2 ]
0 : [ 0 -1.40973 0.711103 -1.75418 ]
1 : [ 0.1 -1.33661 0.269893 1.41368 ]
2 : [ 0.2 0.499241 1.15854 -0.098967 ]
3 : [ 0.3 -0.650467 1.46114 0.61372 ]
4 : [ 0.4 2.14201 -1.66772 -0.151473 ]
5 : [ 0.5 2.4158 0.137289 -0.969704 ]
6 : [ 0.6 -0.292688 -1.02522 -0.354939 ]
7 : [ 0.7 -0.869302 0.266897 0.296524 ]
8 : [ 0.8 -2.24114 -1.5607 -2.272 ]
9 : [ 0.9 0.722451 -2.16128 -0.32861 ]
10 : [ 1 1.06975 -1.77994 -0.832708 ]
11 : [ 1.1 -0.245372 -0.0205006 -0.170101 ]
12 : [ 1.2 0.529296 -0.725104 -1.16247 ]
13 : [ 1.3 0.199523 0.727148 -0.260688 ]
14 : [ 1.4 -0.136772 0.52023 -0.659133 ]
15 : [ 1.5 -0.180673 -1.04885 0.512371 ]
16 : [ 1.6 0.20648 -0.960832 0.414682 ]
17 : [ 1.7 -1.22871 2.57497 -0.00804901 ]
18 : [ 1.8 -1.8859 0.830757 -0.378346 ]
19 : [ 1.9 0.479046 1.60938 -0.570841 ]
20 : [ 2 0.269096 0.803503 0.583218 ]
21 : [ 2.1 0.449756 -0.693556 1.89666 ]
22 : [ 2.2 0.0270818 -0.258272 -0.37012 ]
23 : [ 2.3 0.0456596 -0.343048 -0.392484 ]
24 : [ 2.4 -2.41093 1.93921 -0.590044 ]
25 : [ 2.5 0.22705 -0.141765 0.855507 ]
26 : [ 2.6 0.286761 0.564812 -0.509701 ]
27 : [ 2.7 1.40334 -1.37852 0.434035 ]
28 : [ 2.8 0.0342518 0.896116 -0.870577 ]
29 : [ 2.9 1.36995 0.272597 0.579223 ]
30 : [ 3 -1.5321 0.957065 0.427663 ]
31 : [ 3.1 -0.36668 0.648699 -0.00464944 ]
32 : [ 3.2 0.171548 -0.0795761 0.455389 ]
33 : [ 3.3 -2.14009 0.933245 0.818686 ]
34 : [ 3.4 -1.54826 0.370246 -0.773089 ]
35 : [ 3.5 -0.0129833 0.187309 -2.13145 ]
36 : [ 3.6 -1.19768 -0.00500185 -0.125673 ]
37 : [ 3.7 -1.89201 3.40565 -0.103576 ]
38 : [ 3.8 0.415448 0.727255 0.978855 ]
39 : [ 3.9 1.15808 0.295275 0.283934 ]
40 : [ 4 1.29426 0.200773 0.342265 ]
41 : [ 4.1 0.164085 -0.608383 0.144346 ]
42 : [ 4.2 0.537733 0.696557 1.18791 ]
43 : [ 4.3 2.18097 -0.194809 0.628316 ]
44 : [ 4.4 0.230866 -0.648071 -0.0280203 ]
45 : [ 4.5 0.871005 1.24473 -0.106358 ]
46 : [ 4.6 -0.234489 -2.0102 0.121701 ]
47 : [ 4.7 -1.33163 -0.825457 -1.21658 ]
48 : [ 4.8 -1.02579 -1.22486 -0.735057 ]
49 : [ 4.9 0.267431 -0.313967 0.328403 ]
50 : [ 5 -1.18542 0.272577 -0.537997 ]
51 : [ 5.1 -0.154628 0.0348939 0.357208 ]
52 : [ 5.2 0.87381 -1.4897 -1.60323 ]
53 : [ 5.3 0.276884 -0.205279 0.313591 ]
54 : [ 5.4 1.52063 2.12789 0.15741 ]
55 : [ 5.5 0.056432 1.05201 -1.06929 ]
56 : [ 5.6 0.0389696 0.108862 1.56022 ]
57 : [ 5.7 0.897858 0.0713179 0.329058 ]
58 : [ 5.8 0.768345 -0.201722 0.148307 ]
59 : [ 5.9 0.498826 -0.540609 0.202215 ]
60 : [ 6 1.52964 -1.19218 0.524954 ]
61 : [ 6.1 -0.127176 1.00122 0.299567 ]
62 : [ 6.2 -0.0732479 -0.592801 0.509773 ]
63 : [ 6.3 1.56808 0.369343 0.687346 ]
64 : [ 6.4 0.26022 1.5601 0.68388 ]
65 : [ 6.5 -0.260408 0.169652 -1.01657 ]
66 : [ 6.6 0.810285 -0.934548 0.440233 ]
67 : [ 6.7 0.102655 0.16255 0.977606 ]
68 : [ 6.8 -0.685128 -0.0411968 -0.161531 ]
69 : [ 6.9 0.00948899 -0.699237 0.835643 ]
70 : [ 7 0.961209 -0.395342 0.250509 ]
71 : [ 7.1 -1.71279 -0.303372 1.71343 ]
72 : [ 7.2 0.287997 -0.346204 -1.24308 ]
73 : [ 7.3 -0.661934 -0.539626 0.78918 ]
74 : [ 7.4 0.525199 0.265505 -0.615353 ]
75 : [ 7.5 0.667728 -0.320656 -0.00603524 ]
76 : [ 7.6 -1.44043 0.0706512 0.400517 ]
77 : [ 7.7 -0.537003 -2.13043 0.186229 ]
78 : [ 7.8 -1.32629 0.242601 -0.897333 ]
79 : [ 7.9 -0.957364 1.58824 -0.238077 ]
80 : [ 8 -0.654398 1.49892 -0.713136 ]
81 : [ 8.1 -1.33516 0.567629 0.640198 ]
82 : [ 8.2 -0.259729 0.192286 -1.40222 ]
83 : [ 8.3 0.560018 -1.35624 1.03452 ]
84 : [ 8.4 -0.378793 -0.125727 -0.587836 ]
85 : [ 8.5 1.07894 -1.66939 1.70834 ]
86 : [ 8.6 -0.845941 -0.178621 -0.195884 ]
87 : [ 8.7 1.81133 0.400036 1.10812 ]
88 : [ 8.8 -0.455236 -0.793417 2.28383 ]
89 : [ 8.9 0.351885 -0.0608221 1.18257 ]
90 : [ 9 2.05724 2.0836 -1.10946 ]
91 : [ 9.1 0.646117 0.314088 -1.25919 ]
92 : [ 9.2 2.51347 1.10677 -1.23708 ]
93 : [ 9.3 -0.405063 1.24478 0.258866 ]
94 : [ 9.4 -0.1138 0.3815 0.155791 ]
95 : [ 9.5 0.402412 1.33272 -0.805619 ]
96 : [ 9.6 0.385421 -1.61086 -0.687429 ]
97 : [ 9.7 -0.021074 -1.40527 -0.602909 ]
98 : [ 9.8 -0.0745371 -0.287633 -0.402623 ]
99 : [ 9.9 -0.489432 -0.580339 1.19649 ]



Case 2: Get a time series from a Process

myProcess = ot.WhiteNoise(ot.Normal(3), myTimeGrid)
myTimeSeries2 = myProcess.getRealization()
myTimeSeries2
tX0X1X2
001.0045560.5372572-0.08770909
10.11.4239350.68201462.884055
20.20.2796988-1.178997-0.143892
30.30.68130790.014379190.5099701
40.4-1.0602340.044836570.2499197
50.51.24773-0.3856004-0.2880728
60.6-0.58905170.49957531.132313
70.7-0.84378111.43619-0.1876503
80.80.9405220.7151117-1.439318
90.9-0.1429401-0.17658880.9054335
1010.6688361-0.1848348-0.2056171
111.10.85390611.0827170.7860448
121.2-1.839514-0.4807376-0.7431111
131.30.25838940.064986780.8220976
141.4-0.2202976-1.2674070.06548754
151.5-2.5064850.2182682-0.3734256
161.6-0.3483342-1.020392-0.9373684
171.70.793814-0.983334-0.4151898
181.80.1049272-0.49916560.3643877
191.9-0.16279310.49257820.3548167
202-0.8811936-0.819895-2.106536
212.10.1773956-0.04881701-0.9867962
222.2-0.88621321.2191610.266691
232.30.1883040.80905141.619885
242.4-0.5646788-0.99210440.7245245
252.50.3057475-0.41199462.759856
262.60.40880391.121707-0.6501654
272.7-1.0342881.1503790.5587453
282.81.332409-0.32251480.4750779
292.9-0.15360951.0355351.381175
3031.225896-0.10566460.3069166
313.10.49247580.4262604-0.5698308
323.2-0.4156163-2.609303-2.173168
333.3-1.324497-1.455850.1801837
343.41.4211981.866039-0.1742316
353.5-1.555471.48841.303924
363.6-1.061323-1.305955-1.629615
373.7-0.29628690.87397920.1051378
383.8-0.02998592-1.5160321.474471
393.9-1.03669-1.5346510.8259901
4040.457382-0.38656151.28411
414.1-0.32594611.637177-0.8420178
424.2-0.29240970.36159910.4570965
434.30.2379781.0208261.699262
444.4-0.54388090.4973056-1.469904
454.5-2.294773-0.2623551-1.554523
464.6-2.827310.58255310.4139608
474.7-0.93024370.549059-0.69065
484.8-0.6021352-0.76771841.285077
494.9-0.222591.2217410.4439343
505-0.7078664-1.0569120.5648551
515.10.29809861.3424181.085837
525.20.8239627-0.6283856-0.8834576
535.30.86075331.4562640.1421699
545.4-0.33233230.89529780.1655028
555.50.027144610.16458070.2626963
565.61.6386110.1818056-0.1240066
575.71.56386-0.54716150.4136208
585.8-0.5009097-1.561814-2.157897
595.9-0.8845609-0.03278067-0.4371368
6060.92630220.36402171.127778
616.1-0.29581290.521623-0.5048369
626.2-1.126024-0.15387590.9138794
636.3-2.0582741.0936460.353957
646.4-0.57084881.5213970.2852253
656.5-1.835236-0.30448520.9165636
666.60.91406640.10757050.06927429
676.7-0.66504881.9512160.7997068
686.8-0.8125796-0.57977910.1117721
696.9-0.2133026-1.116885-0.872058
7071.6291643.399959-0.9405087
717.10.8080016-0.54500921.626903
727.2-0.061288020.308256-0.9618253
737.3-1.2550940.4358796-0.7273887
747.4-0.3513546-1.318261-0.47417
757.5-0.10056021.643525-0.4139103
767.60.8686027-0.43225211.012874
777.7-1.1149270.4695280.9161205
787.8-0.3569551.022334-2.00257
797.9-1.715160.6274581-1.352094
808-0.03491598-0.037932510.05596954
818.1-0.28109470.144073-2.171863
828.2-0.33894530.5843859-0.8390798
838.3-1.041380.35194971.069267
848.4-2.8664621.1825040.2067203
858.5-0.6907754-0.74259841.164752
868.6-0.09003073-1.2094510.7730654
878.7-0.8069562-1.0466430.1396704
888.81.0673650.1232827-0.776005
898.9-0.882326-0.01456590.2200673
9090.4727389-0.31590741.723677
919.10.53389850.4875888-0.5419431
929.20.7959215-0.9714537-0.3666259
939.30.13633551.229809-0.4606246
949.40.5330227-0.98758070.2573491
959.50.415046-0.75341090.07963906
969.60.5442014-1.354907-0.03364811
979.7-0.7464795-0.63558080.7484256
989.8-1.115680.12871660.8080038
999.9-0.5232872-0.029844340.04724269


Get the number of values of the time series

myTimeSeries.getSize()
100

Get the dimension of the values observed at each time

myTimeSeries.getMesh().getDimension()
1

Get the value Xi at index i

i = 37
print("Xi = ", myTimeSeries.getValueAtIndex(i))
Xi =  [-1.89201,3.40565,-0.103576]

Get the time series at index i : Xi

i = 37
print("Xi = ", myTimeSeries[i])
Xi =  [-1.89201,3.40565,-0.103576]

Get a the marginal value at index i of the time series

i = 37
# get the time stamp:
print("ti = ", myTimeSeries.getTimeGrid().getValue(i))
# get the first component of the corresponding value :
print("Xi1 = ", myTimeSeries[i, 0])
ti =  3.7
Xi1 =  -1.892006989486264

Get all the values (X1, .., Xn) of the time series

myTimeSeries.getValues()
X0X1X2
0-1.4097340.7111029-1.754176
1-1.3366080.26989271.413675
20.49924141.158536-0.09896703
3-0.65046691.4611450.6137203
42.142012-1.667722-0.1514732
52.41580.1372886-0.9697043
6-0.292688-1.025222-0.3549386
7-0.86930170.2668970.296524
8-2.241144-1.560704-2.271998
90.7224505-2.161275-0.3286104
101.069747-1.779941-0.8327076
11-0.2453716-0.0205006-0.1701006
120.5292955-0.7251038-1.162473
130.19952350.7271477-0.2606875
14-0.13677180.5202298-0.6591333
15-0.1806734-1.0488470.5123711
160.2064803-0.9608320.4146824
17-1.2287142.57497-0.008049008
18-1.8858990.830757-0.3783459
190.47904631.609382-0.5708413
200.26909640.80350330.5832181
210.4497564-0.69355591.896662
220.02708176-0.258272-0.37012
230.04565963-0.3430478-0.3924844
24-2.4109291.939206-0.5900438
250.2270499-0.14176540.8555065
260.2867610.5648119-0.5097008
271.403344-1.3785220.4340351
280.034251810.8961165-0.8705775
291.3699530.27259690.5792226
30-1.5321030.9570650.4276634
31-0.36668020.6486989-0.004649441
320.1715484-0.079576110.4553892
33-2.1400930.93324460.8186856
34-1.5482560.370246-0.773089
35-0.012983330.1873089-2.131449
36-1.197682-0.005001849-0.1256726
37-1.8920073.40565-0.1035762
380.41544770.72725450.9788553
391.1580810.29527520.2839339
401.2942580.20077350.342265
410.1640854-0.60838320.1443463
420.53773290.69655671.187906
432.180975-0.19480930.6283156
440.2308662-0.6480712-0.02802031
450.87100461.244731-0.1063582
46-0.2344887-2.0102040.1217012
47-1.331632-0.8254575-1.216578
48-1.025789-1.224865-0.7350567
490.2674311-0.31396660.3284034
50-1.1854180.2725766-0.5379969
51-0.15462760.034893870.3572081
520.8738098-1.489697-1.603233
530.2768838-0.20527910.3135911
541.5206262.1278920.1574096
550.056431991.05201-1.069286
560.038969580.10886191.560223
570.89785810.071317860.3290581
580.7683447-0.20172150.1483074
590.4988259-0.54060890.202215
601.52964-1.1921790.5249542
61-0.12717581.0012170.2995675
62-0.07324792-0.59280080.509773
631.5680790.36934280.6873462
640.26022051.5601010.6838802
65-0.26040790.1696515-1.016573
660.8102853-0.93454770.4402335
670.10265450.16255020.9776058
68-0.6851276-0.04119683-0.1615313
690.009488993-0.69923730.8356431
700.9612086-0.39534240.2505092
71-1.712787-0.30337221.713433
720.2879968-0.3462038-1.243077
73-0.6619336-0.53962570.7891796
740.5251990.2655049-0.6153533
750.6677281-0.3206562-0.00603524
76-1.4404270.070651250.4005165
77-0.5370034-2.1304320.1862285
78-1.3262880.2426011-0.8973327
79-0.95736431.588237-0.2380769
80-0.65439791.498919-0.7131357
81-1.3351570.56762850.640198
82-0.2597290.1922855-1.402221
830.5600177-1.3562441.034522
84-0.3787931-0.1257271-0.5878356
851.078941-1.6693861.708344
86-0.8459409-0.1786205-0.1958844
871.8113250.40003631.108118
88-0.4552358-0.79341742.283829
890.351885-0.060822141.182574
902.0572362.083603-1.109457
910.64611740.3140881-1.259195
922.513471.106768-1.237082
93-0.40506291.2447750.2588656
94-0.11379980.38149980.1557911
950.40241241.332716-0.8056192
960.3854209-1.61086-0.6874292
97-0.02107395-1.405266-0.6029087
98-0.07453712-0.287633-0.4026233
99-0.4894317-0.58033881.196489


Compute the temporal Mean It corresponds to the mean of the values of the time series

myTimeSeries.getInputMean()

[0.0252771,0.032915,0.00141464]



Draw the marginal i of the time series using linear interpolation

graph = myTimeSeries.drawMarginal(0)
view = viewer.View(graph)
Unnamed - 0 marginal

with no interpolation

graph = myTimeSeries.drawMarginal(0, False)
view = viewer.View(graph)
plt.show()
Unnamed - 0 marginal