Manipulate a time series¶

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 $(\vect{x}_0, \dots, \vect{x}_{N-1})$ of the time series are defined by:

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

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 otv

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. Be careful that 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

class=TimeSeries name=Unnamed derived from=class=FieldImplementation name=Unnamed mesh=class=Mesh name=Unnamed dimension=1 vertices=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=100 dimension=1 description=[t] data=[[0],[0.1],[0.2],[0.3],[0.4],[0.5],[0.6],[0.7],[0.8],[0.9],[1],[1.1],[1.2],[1.3],[1.4],[1.5],[1.6],[1.7],[1.8],[1.9],[2],[2.1],[2.2],[2.3],[2.4],[2.5],[2.6],[2.7],[2.8],[2.9],[3],[3.1],[3.2],[3.3],[3.4],[3.5],[3.6],[3.7],[3.8],[3.9],[4],[4.1],[4.2],[4.3],[4.4],[4.5],[4.6],[4.7],[4.8],[4.9],[5],[5.1],[5.2],[5.3],[5.4],[5.5],[5.6],[5.7],[5.8],[5.9],[6],[6.1],[6.2],[6.3],[6.4],[6.5],[6.6],[6.7],[6.8],[6.9],[7],[7.1],[7.2],[7.3],[7.4],[7.5],[7.6],[7.7],[7.8],[7.9],[8],[8.1],[8.2],[8.3],[8.4],[8.5],[8.6],[8.7],[8.8],[8.9],[9],[9.1],[9.2],[9.3],[9.4],[9.5],[9.6],[9.7],[9.8],[9.9]] simplices=[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25],[25,26],[26,27],[27,28],[28,29],[29,30],[30,31],[31,32],[32,33],[33,34],[34,35],[35,36],[36,37],[37,38],[38,39],[39,40],[40,41],[41,42],[42,43],[43,44],[44,45],[45,46],[46,47],[47,48],[48,49],[49,50],[50,51],[51,52],[52,53],[53,54],[54,55],[55,56],[56,57],[57,58],[58,59],[59,60],[60,61],[61,62],[62,63],[63,64],[64,65],[65,66],[66,67],[67,68],[68,69],[69,70],[70,71],[71,72],[72,73],[73,74],[74,75],[75,76],[76,77],[77,78],[78,79],[79,80],[80,81],[81,82],[82,83],[83,84],[84,85],[85,86],[86,87],[87,88],[88,89],[89,90],[90,91],[91,92],[92,93],[93,94],[94,95],[95,96],[96,97],[97,98],[98,99]] values=class=Sample name=Normal implementation=class=SampleImplementation name=Normal size=100 dimension=3 description=[X0,X1,X2] data=[[0.608202,-1.26617,-0.438266],[1.20548,-2.18139,0.350042],[-0.355007,1.43725,0.810668],[0.793156,-0.470526,0.261018],[-2.29006,-1.28289,-1.31178],[-0.0907838,0.995793,-0.139453],[-0.560206,0.44549,0.322925],[0.445785,-1.03808,-0.856712],[0.473617,-0.125498,0.351418],[1.78236,0.0702074,-0.781366],[-0.721533,-0.241223,-1.78796],[0.40136,1.36783,1.00434],[0.741548,-0.0436123,0.539345],[0.29995,0.407717,-0.485112],[-0.382992,-0.752817,0.257926],[1.96876,-0.671291,1.85579],[0.0521593,0.790446,0.716353],[-0.743622,0.184356,-1.53073],[0.655027,0.538071,1.73821],[-0.958722,0.377922,-0.181004],[1.67297,-1.03896,-0.353552],[1.21381,-0.777033,-1.36853],[0.103474,-0.89182,0.905602],[0.334794,-0.483642,0.677958],[1.70938,1.07062,-0.506925],[-1.66086,2.24623,0.759602],[-0.510764,-0.633066,-0.957072],[0.544047,0.814561,-0.734708],[-0.111461,0.994482,-0.160625],[-0.938771,-1.96869,-0.657603],[0.338751,1.01556,0.637167],[-0.0899071,-0.855886,1.27128],[-0.238253,1.3263,2.11968],[-0.901581,-1.51696,-1.29938],[0.230372,-3.09737,0.01323],[-1.25743,1.02776,-0.766431],[0.217512,1.04533,0.331569],[-0.488205,-0.465482,0.332084],[-0.167726,3.01263,0.94204],[0.61189,0.611715,-1.5375],[-2.4067,0.662936,-0.65616],[-0.751611,0.438177,-0.455335],[1.86038,0.219721,1.72546],[-0.543405,-0.736749,-0.508206],[-2.25867,-0.5964,-0.31468],[-1.78274,-0.684734,0.0611157],[0.87372,-1.46295,-0.318786],[1.26314,-0.426726,-1.89234],[-0.514391,0.647229,0.00370249],[0.729688,-0.247234,0.479191],[-0.0336098,-0.0367271,0.110256],[-0.37687,-0.0955894,0.109122],[-0.198754,0.47362,0.161637],[0.384483,0.116468,-0.10008],[1.49156,1.22301,0.526646],[-0.656923,-0.131228,-1.45347],[1.17414,0.929395,-0.337113],[0.578688,-0.582459,-1.38886],[-0.499748,-1.55516,0.483083],[0.205004,-0.0972525,0.592563],[-0.602044,-1.21009,-0.886698],[-0.141114,0.441983,0.519162],[-1.51455,-0.676917,0.667678],[-1.40585,-0.0295335,-0.631829],[-0.342157,2.05339,1.1587],[-1.45717,-0.844367,-0.28861],[0.419271,-0.836064,0.858269],[-0.906566,-0.91681,1.16322],[0.301918,0.490331,0.475425],[-0.788704,-0.669449,-0.137928],[-0.971531,-1.18784,1.4282],[-0.58923,-1.73218,0.824993],[3.02799,1.6948,-1.64827],[-0.996469,0.773121,-0.519476],[-0.0351973,-0.439866,-0.259332],[-0.875419,-2.53986,-0.0566709],[-0.0217279,0.59922,0.146868],[-0.74536,-0.521596,0.59202],[-0.470039,-2.17211,-0.432617],[0.26775,-0.36799,1.14842],[-0.0343283,0.461082,-0.622424],[-1.62506,-0.543099,-0.269535],[0.0208818,0.623854,0.767137],[0.888798,1.48031,0.661002],[1.40895,0.576125,1.89326],[0.858611,-0.907348,-0.537503],[-0.638434,1.34856,-2.26608],[0.423232,-0.996141,-1.08751],[0.11108,0.677663,-1.05502],[-0.00409659,0.562833,-0.029616],[0.0702065,-0.23527,-1.29031],[-1.01864,-1.71131,0.943326],[-0.542319,-0.999111,-1.40457],[1.94606,0.779572,1.13848],[0.711148,-0.453386,0.618319],[0.722044,0.660021,0.465919],[-0.40773,1.45919,-0.411565],[0.549439,1.45019,-0.327249],[-1.39796,1.30115,-0.485259],[-0.272407,-0.338823,-0.790757]] start=0 timeStep=0.1 n=100

Case 2: Get a time series from a Process

myProcess = ot.WhiteNoise(ot.Normal(3), myTimeGrid)
myTimeSeries2 = myProcess.getRealization()
myTimeSeries2

	t	X0	X1	X2
0	0	1.739449	0.9359392	1.275114
1	0.1	-0.5950037	-0.0230083	1.853373
2	0.2	0.3561882	-1.317651	-1.194996
3	0.3	-0.4436842	-0.8262043	-0.7488164
4	0.4	0.4340344	-0.6442085	-0.559902
5	0.5	0.05466818	-0.05647917	0.7575347
6	0.6	-0.6631575	0.6836458	0.5910434
7	0.7	-2.208718	-0.7790315	-0.7030859
8	0.8	-0.05669555	0.5881009	0.7388395
9	0.9	0.7271276	-1.183102	0.8531994
10	1	1.031982	0.1044672	0.5155103
11	1.1	-1.732508	0.3692314	0.6671036
12	1.2	-0.5128099	-0.4777539	1.262641
13	1.3	1.578458	1.890055	0.3902966
14	1.4	0.2357594	0.2449476	0.5716903
15	1.5	-0.4205421	0.5532545	-2.19382
16	1.6	0.4212794	0.7537578	-0.5124193
17	1.7	-0.3062254	-1.211032	0.01748019
18	1.8	-1.165014	0.06438942	0.7176094
19	1.9	-0.3042681	-0.3913752	0.2582147
20	2	-1.490777	1.061818	0.3749687
21	2.1	-0.1654673	0.3578707	0.8851181
22	2.2	1.737898	-0.7131956	1.706424
23	2.3	0.4286364	-0.2775952	0.4112949
24	2.4	0.3704449	0.1878542	1.432656
25	2.5	-0.4161282	-0.1228684	0.950488
26	2.6	-0.4111282	-0.9804902	0.564196
27	2.7	-1.556663	0.6248883	1.057974
28	2.8	-0.7695287	1.542366	0.3748018
29	2.9	0.5061052	0.4197679	1.58128
30	3	0.009563751	-0.3830202	0.1636987
31	3.1	1.256104	0.006203967	0.2720044
32	3.2	-0.1537841	-0.404166	2.092243
33	3.3	0.6750433	-0.3832085	-0.3552394
34	3.4	-1.305296	-1.515767	0.172158
35	3.5	0.5776802	-0.1730494	0.6621723
36	3.6	0.6978382	0.7895777	0.4793068
37	3.7	-0.4494332	1.765705	0.281658
38	3.8	0.1279809	-0.7479662	0.5128914
39	3.9	1.08613	-0.5519517	1.578906
40	4	-0.2223936	0.2055034	1.338509
41	4.1	0.04525299	2.156495	1.009849
42	4.2	1.188981	1.287652	-0.2798472
43	4.3	-0.5673421	0.07894311	-0.3740983
44	4.4	0.36891	-0.2162491	-0.9644931
45	4.5	1.142547	0.2719525	-0.6267599
46	4.6	-1.245543	-0.7938689	0.8086521
47	4.7	0.551898	1.262139	-0.3987307
48	4.8	-2.13505	0.4206717	-0.1649563
49	4.9	-1.277891	-0.748335	0.447628
50	5	1.606495	-1.238318	-0.8571127
51	5.1	-0.7960124	2.555329	-1.409656
52	5.2	0.1617572	1.071526	-0.07561517
53	5.3	-0.3858102	-0.6958986	-0.2401711
54	5.4	0.01403395	-1.327828	-0.4218051
55	5.5	-1.31457	-0.314242	0.8700968
56	5.6	-1.050287	-0.6617487	-0.3989571
57	5.7	-0.3068693	2.240972	-1.842254
58	5.8	-1.126287	-0.343091	1.357067
59	5.9	-1.141444	0.7199106	0.6912884
60	6	0.01574154	0.8978544	-0.02689165
61	6.1	-1.172528	-1.223227	1.337288
62	6.2	-0.4120875	1.405077	0.8399413
63	6.3	-0.1718261	-0.6121364	0.4331895
64	6.4	1.259888	-2.151353	0.6383845
65	6.5	1.198597	0.5760515	-2.721058
66	6.6	-0.4566343	0.8344516	0.1897228
67	6.7	-1.559897	0.141706	-0.3128766
68	6.8	-1.096692	1.306282	-0.6035431
69	6.9	0.08447148	-1.011566	-0.4541302
70	7	0.184323	1.111031	0.03326554
71	7.1	-0.4027267	0.8121354	0.1379583
72	7.2	-0.5523964	0.7122982	0.6577979
73	7.3	-0.2971004	0.2881424	-0.843501
74	7.4	1.481402	0.9048591	0.9005403
75	7.5	0.2113785	0.408217	-0.2907085
76	7.6	-1.037685	0.4036742	-0.03612466
77	7.7	-0.04399572	1.578567	1.445033
78	7.8	-0.9083433	-1.329003	-0.4762143
79	7.9	1.022384	-1.197875	2.596026
80	8	0.1498547	-0.390626	-0.3116555
81	8.1	-0.4514491	0.2370956	0.6243862
82	8.2	-0.5553002	0.7656447	0.5092548
83	8.3	0.4161323	-1.428256	-0.1552423
84	8.4	1.198645	-0.1898108	-1.099809
85	8.5	0.7271951	0.5664686	-1.437003
86	8.6	-0.2535926	0.8982354	0.7326738
87	8.7	-0.1095485	-0.4859692	-0.3567203
88	8.8	-1.259387	0.03497645	-0.4096377
89	8.9	0.7955166	-2.108143	-0.9148845
90	9	1.095021	-0.06328519	2.003632
91	9.1	-0.1248814	0.06040856	-0.4496756
92	9.2	0.15909	-2.043173	1.061442
93	9.3	-1.444155	0.7511011	0.8440584
94	9.4	-1.239076	0.743606	1.434637
95	9.5	0.07700021	-2.187386	0.2376129
96	9.6	0.8050322	0.7841974	1.021327
97	9.7	-0.3590296	-1.166527	1.017866
98	9.8	0.2758391	0.907344	0.359928
99	9.9	1.178278	1.578528	2.0749

Get the number of values of the time series

myTimeSeries.getSize()

Get the dimension of the values observed at each time

myTimeSeries.getMesh().getDimension()

Get the value $X_i$ at index $i$

i = 37
print("Xi = ", myTimeSeries.getValueAtIndex(i))

Xi =  [-0.488205,-0.465482,0.332084]

Get the time series at index $i$ : $X_i$

i = 37
print("Xi = ", myTimeSeries[i])

Xi =  [-0.488205,-0.465482,0.332084]

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 =  -0.4882047479037244

Get all the values $(X_1, \dots, X_n)$ of the time series

myTimeSeries.getValues()

	X0	X1	X2
0	0.6082017	-1.266173	-0.4382656
1	1.205478	-2.181385	0.3500421
2	-0.355007	1.437249	0.810668
3	0.793156	-0.4705256	0.2610179
4	-2.290062	-1.282885	-1.311781
5	-0.09078383	0.9957932	-0.1394528
6	-0.5602056	0.4454897	0.322925
7	0.4457853	-1.038077	-0.8567123
8	0.4736169	-0.1254977	0.3514178
9	1.782359	0.07020736	-0.7813665
10	-0.7215334	-0.2412235	-1.787964
11	0.4013597	1.367826	1.004343
12	0.7415484	-0.04361234	0.5393447
13	0.2999504	0.4077172	-0.485112
14	-0.382992	-0.7528166	0.2579264
15	1.96876	-0.6712905	1.855792
16	0.05215933	0.7904458	0.7163526
17	-0.743622	0.184356	-1.530734
18	0.6550275	0.5380715	1.738213
19	-0.9587223	0.3779221	-0.1810042
20	1.672965	-1.038958	-0.3535524
21	1.213814	-0.7770331	-1.368531
22	0.1034744	-0.8918195	0.9056017
23	0.3347945	-0.4836416	0.6779583
24	1.709379	1.07062	-0.5069247
25	-1.660864	2.246229	0.7596015
26	-0.5107638	-0.6330662	-0.9570722
27	0.5440466	0.8145607	-0.7347084
28	-0.1114608	0.9944819	-0.1606253
29	-0.9387706	-1.968692	-0.6576035
30	0.3387511	1.015558	0.6371672
31	-0.08990712	-0.8558864	1.271283
32	-0.2382526	1.326299	2.119676
33	-0.9015814	-1.516965	-1.29938
34	0.2303724	-3.097374	0.01323
35	-1.25743	1.02776	-0.7664307
36	0.2175121	1.045333	0.3315688
37	-0.4882047	-0.4654821	0.3320839
38	-0.1677258	3.012627	0.9420405
39	0.6118901	0.6117152	-1.537497
40	-2.406702	0.662936	-0.6561602
41	-0.7516115	0.438177	-0.4553346
42	1.860378	0.2197212	1.725463
43	-0.5434055	-0.7367488	-0.5082064
44	-2.258672	-0.5963998	-0.31468
45	-1.782738	-0.6847338	0.06111571
46	0.8737197	-1.462953	-0.3187856
47	1.263142	-0.4267256	-1.892343
48	-0.5143905	0.6472294	0.003702486
49	0.7296878	-0.2472338	0.479191
50	-0.03360983	-0.03672706	0.1102562
51	-0.3768704	-0.09558941	0.1091224
52	-0.1987541	0.4736195	0.1616373
53	0.3844829	0.1164676	-0.1000805
54	1.491564	1.223005	0.5266463
55	-0.6569234	-0.1312282	-1.453471
56	1.174145	0.9293947	-0.3371135
57	0.5786883	-0.5824589	-1.388861
58	-0.4997483	-1.555158	0.483083
59	0.2050042	-0.09725248	0.5925631
60	-0.6020445	-1.210086	-0.8866979
61	-0.1411137	0.4419834	0.519162
62	-1.514551	-0.6769174	0.6676776
63	-1.405845	-0.02953347	-0.6318287
64	-0.3421569	2.053386	1.158703
65	-1.45717	-0.8443667	-0.2886103
66	0.4192711	-0.8360644	0.8582686
67	-0.9065659	-0.9168099	1.163221
68	0.3019183	0.4903313	0.4754246
69	-0.7887043	-0.6694492	-0.137928
70	-0.9715312	-1.187838	1.428203
71	-0.5892299	-1.732176	0.8249934
72	3.02799	1.694797	-1.648267
73	-0.9964693	0.7731214	-0.5194758
74	-0.03519734	-0.4398656	-0.2593322
75	-0.875419	-2.539863	-0.05667093
76	-0.02172791	0.5992195	0.1468679
77	-0.7453604	-0.521596	0.5920202
78	-0.4700387	-2.172109	-0.4326173
79	0.2677502	-0.3679897	1.148417
80	-0.0343283	0.4610818	-0.6224244
81	-1.625056	-0.5430992	-0.2695349
82	0.0208818	0.6238537	0.7671373
83	0.8887984	1.480306	0.6610018
84	1.408952	0.5761247	1.893265
85	0.8586112	-0.9073479	-0.5375027
86	-0.6384336	1.348564	-2.266083
87	0.4232324	-0.9961412	-1.087506
88	0.11108	0.6776631	-1.055018
89	-0.004096592	0.5628333	-0.02961597
90	0.07020646	-0.2352699	-1.290308
91	-1.01864	-1.711309	0.943326
92	-0.5423195	-0.9991113	-1.40457
93	1.946062	0.7795719	1.138475
94	0.7111476	-0.4533858	0.6183194
95	0.7220435	0.6600207	0.4659188
96	-0.4077298	1.45919	-0.4115654
97	0.5494387	1.450193	-0.3272495
98	-1.397957	1.301151	-0.4852593
99	-0.2724066	-0.3388229	-0.7907566

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

myTimeSeries.getInputMean()

class=Point name=Unnamed dimension=3 values=[-0.025392,-0.027327,-0.0146978]

Draw the marginal $i$ of the time series using linear interpolation

graph = myTimeSeries.drawMarginal(0)
view = otv.View(graph)

With no interpolation

graph = myTimeSeries.drawMarginal(0, False)
view = otv.View(graph)

Display all figures

otv.View.ShowAll()

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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Manipulate a time series¶