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 $(\underline{x}_0, \dots, \underline{x}_{N-1})$ 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

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=[[1.01189,-0.608942,0.259667],[0.324782,0.541045,0.124925],[0.63389,0.71797,0.204209],[-0.230565,-0.441029,0.218173],[0.358047,0.389048,0.0223299],[1.65473,0.718066,1.20039],[-0.0428541,0.299168,-1.95814],[0.342204,-0.822006,0.414328],[-0.336382,1.84368,-0.637582],[0.411799,-0.176888,-1.10384],[-0.414421,0.266101,-0.340295],[0.716981,-0.624488,1.48763],[-0.235484,0.22803,-0.8464],[-0.0506129,0.963482,-0.266606],[0.718303,-1.35427,-0.399967],[0.827442,-1.60123,-0.789026],[-0.470555,-1.17375,-1.17225],[1.44633,-0.0109896,-0.392194],[0.423681,-0.215168,-1.36186],[0.653895,1.87561,-0.402469],[0.623307,-0.207295,1.17231],[0.2915,-2.07544,-0.229841],[0.93204,-2.89787,-0.485802],[-0.315465,0.563317,-1.54763],[1.74913,-0.711751,0.120468],[0.85627,0.591214,-1.07519],[-0.751024,-0.550295,-1.29029],[0.776951,0.556825,-0.989392],[2.2382,-0.015504,0.87992],[1.10091,-1.08794,1.28143],[0.770213,-1.11943,0.361488],[-1.43777,0.192138,-1.69362],[1.48814,-0.979175,-1.66438],[2.75891,-0.0568873,-0.517364],[0.0644103,-0.497525,-1.67019],[-0.527852,1.15265,0.156536],[-0.790078,0.119299,-1.69795],[-0.4429,-0.541246,-1.35629],[-0.549982,-1.22042,-0.177045],[1.70917,-0.636661,0.218454],[0.448041,1.22407,-0.239304],[-0.437019,-0.533459,0.430689],[-0.549999,-0.920782,-2.35124],[-0.956058,0.943051,0.725423],[0.103282,0.516111,2.00502],[1.63507,-1.43977,0.529791],[1.03687,-0.444105,-0.753347],[0.100154,-0.550234,1.41372],[0.464214,0.447407,-1.05761],[1.35995,-0.710775,-0.164241],[-1.28354,0.556653,0.548566],[1.68737,0.79344,-0.540027],[-0.848387,-0.103264,0.958601],[-1.02522,-0.354939,-0.869302],[0.266897,0.296524,-2.24114],[-1.5607,-2.272,0.722451],[-2.16128,-0.32861,1.06975],[-1.77994,-0.832708,-0.245372],[-0.0205006,-0.170101,0.529296],[-0.725104,-1.16247,0.199523],[0.727148,-0.260688,-0.136772],[0.52023,-0.659133,-0.180673],[-1.04885,0.512371,0.20648],[-0.960832,0.414682,-1.22871],[2.57497,-0.00804901,-1.8859],[0.830757,-0.378346,0.479046],[1.60938,-0.570841,0.269096],[0.803503,0.583218,0.449756],[-0.693556,1.89666,0.0270818],[-0.258272,-0.37012,0.0456596],[-0.343048,-0.392484,-2.41093],[1.93921,-0.590044,0.22705],[-0.141765,0.855507,0.286761],[0.564812,-0.509701,1.40334],[-1.37852,0.434035,0.0342518],[0.896116,-0.870577,1.36995],[0.272597,0.579223,-1.5321],[0.957065,0.427663,-0.36668],[0.648699,-0.00464944,0.171548],[-0.0795761,0.455389,-2.14009],[0.933245,0.818686,-1.54826],[0.370246,-0.773089,-0.0129833],[0.187309,-2.13145,-1.19768],[-0.00500185,-0.125673,-1.89201],[3.40565,-0.103576,0.415448],[0.727255,0.978855,1.15808],[0.295275,0.283934,1.29426],[0.200773,0.342265,0.164085],[-0.608383,0.144346,0.537733],[0.696557,1.18791,2.18097],[-0.194809,0.628316,0.230866],[-0.648071,-0.0280203,0.871005],[1.24473,-0.106358,-0.234489],[-2.0102,0.121701,-1.33163],[-0.825457,-1.21658,-1.02579],[-1.22486,-0.735057,0.267431],[-0.313967,0.328403,-1.18542],[0.272577,-0.537997,-0.154628],[0.0348939,0.357208,0.87381],[-1.4897,-1.60323,0.276884]] 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	-0.2052791	0.3135911	1.520626
1	0.1	2.127892	0.1574096	0.05643199
2	0.2	1.05201	-1.069286	0.03896958
3	0.3	0.1088619	1.560223	0.8978581
4	0.4	0.07131786	0.3290581	0.7683447
5	0.5	-0.2017215	0.1483074	0.4988259
6	0.6	-0.5406089	0.202215	1.52964
7	0.7	-1.192179	0.5249542	-0.1271758
8	0.8	1.001217	0.2995675	-0.07324792
9	0.9	-0.5928008	0.509773	1.568079
10	1	0.3693428	0.6873462	0.2602205
11	1.1	1.560101	0.6838802	-0.2604079
12	1.2	0.1696515	-1.016573	0.8102853
13	1.3	-0.9345477	0.4402335	0.1026545
14	1.4	0.1625502	0.9776058	-0.6851276
15	1.5	-0.04119683	-0.1615313	0.009488993
16	1.6	-0.6992373	0.8356431	0.9612086
17	1.7	-0.3953424	0.2505092	-1.712787
18	1.8	-0.3033722	1.713433	0.2879968
19	1.9	-0.3462038	-1.243077	-0.6619336
20	2	-0.5396257	0.7891796	0.525199
21	2.1	0.2655049	-0.6153533	0.6677281
22	2.2	-0.3206562	-0.00603524	-1.440427
23	2.3	0.07065125	0.4005165	-0.5370034
24	2.4	-2.130432	0.1862285	-1.326288
25	2.5	0.2426011	-0.8973327	-0.9573643
26	2.6	1.588237	-0.2380769	-0.6543979
27	2.7	1.498919	-0.7131357	-1.335157
28	2.8	0.5676285	0.640198	-0.259729
29	2.9	0.1922855	-1.402221	0.5600177
30	3	-1.356244	1.034522	-0.3787931
31	3.1	-0.1257271	-0.5878356	1.078941
32	3.2	-1.669386	1.708344	-0.8459409
33	3.3	-0.1786205	-0.1958844	1.811325
34	3.4	0.4000363	1.108118	-0.4552358
35	3.5	-0.7934174	2.283829	0.351885
36	3.6	-0.06082214	1.182574	2.057236
37	3.7	2.083603	-1.109457	0.6461174
38	3.8	0.3140881	-1.259195	2.51347
39	3.9	1.106768	-1.237082	-0.4050629
40	4	1.244775	0.2588656	-0.1137998
41	4.1	0.3814998	0.1557911	0.4024124
42	4.2	1.332716	-0.8056192	0.3854209
43	4.3	-1.61086	-0.6874292	-0.02107395
44	4.4	-1.405266	-0.6029087	-0.07453712
45	4.5	-0.287633	-0.4026233	-0.4894317
46	4.6	-0.5803388	1.196489	1.004556
47	4.7	0.5372572	-0.08770909	1.423935
48	4.8	0.6820146	2.884055	0.2796988
49	4.9	-1.178997	-0.143892	0.6813079
50	5	0.01437919	0.5099701	-1.060234
51	5.1	0.04483657	0.2499197	1.24773
52	5.2	-0.3856004	-0.2880728	-0.5890517
53	5.3	0.4995753	1.132313	-0.8437811
54	5.4	1.43619	-0.1876503	0.940522
55	5.5	0.7151117	-1.439318	-0.1429401
56	5.6	-0.1765888	0.9054335	0.6688361
57	5.7	-0.1848348	-0.2056171	0.8539061
58	5.8	1.082717	0.7860448	-1.839514
59	5.9	-0.4807376	-0.7431111	0.2583894
60	6	0.06498678	0.8220976	-0.2202976
61	6.1	-1.267407	0.06548754	-2.506485
62	6.2	0.2182682	-0.3734256	-0.3483342
63	6.3	-1.020392	-0.9373684	0.793814
64	6.4	-0.983334	-0.4151898	0.1049272
65	6.5	-0.4991656	0.3643877	-0.1627931
66	6.6	0.4925782	0.3548167	-0.8811936
67	6.7	-0.819895	-2.106536	0.1773956
68	6.8	-0.04881701	-0.9867962	-0.8862132
69	6.9	1.219161	0.266691	0.188304
70	7	0.8090514	1.619885	-0.5646788
71	7.1	-0.9921044	0.7245245	0.3057475
72	7.2	-0.4119946	2.759856	0.4088039
73	7.3	1.121707	-0.6501654	-1.034288
74	7.4	1.150379	0.5587453	1.332409
75	7.5	-0.3225148	0.4750779	-0.1536095
76	7.6	1.035535	1.381175	1.225896
77	7.7	-0.1056646	0.3069166	0.4924758
78	7.8	0.4262604	-0.5698308	-0.4156163
79	7.9	-2.609303	-2.173168	-1.324497
80	8	-1.45585	0.1801837	1.421198
81	8.1	1.866039	-0.1742316	-1.55547
82	8.2	1.4884	1.303924	-1.061323
83	8.3	-1.305955	-1.629615	-0.2962869
84	8.4	0.8739792	0.1051378	-0.02998592
85	8.5	-1.516032	1.474471	-1.03669
86	8.6	-1.534651	0.8259901	0.457382
87	8.7	-0.3865615	1.28411	-0.3259461
88	8.8	1.637177	-0.8420178	-0.2924097
89	8.9	0.3615991	0.4570965	0.237978
90	9	1.020826	1.699262	-0.5438809
91	9.1	0.4973056	-1.469904	-2.294773
92	9.2	-0.2623551	-1.554523	-2.82731
93	9.3	0.5825531	0.4139608	-0.9302437
94	9.4	0.549059	-0.69065	-0.6021352
95	9.5	-0.7677184	1.285077	-0.22259
96	9.6	1.221741	0.4439343	-0.7078664
97	9.7	-1.056912	0.5648551	0.2980986
98	9.8	1.342418	1.085837	0.8239627
99	9.9	-0.6283856	-0.8834576	0.8607533

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 Xi at index i

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

Xi =  [-0.4429,-0.541246,-1.35629]

Get the time series at index i : Xi

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

Xi =  [-0.4429,-0.541246,-1.35629]

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 =  -0.44290028916853585

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

myTimeSeries.getValues()

	X0	X1	X2
0	1.011887	-0.6089418	0.259667
1	0.3247816	0.5410446	0.124925
2	0.6338902	0.7179695	0.2042093
3	-0.2305653	-0.4410291	0.2181727
4	0.3580472	0.3890482	0.02232993
5	1.654732	0.7180658	1.200392
6	-0.04285412	0.2991685	-1.958143
7	0.3422039	-0.8220064	0.4143278
8	-0.3363815	1.84368	-0.637582
9	0.4117993	-0.1768882	-1.10384
10	-0.4144207	0.2661011	-0.3402945
11	0.7169809	-0.6244882	1.487634
12	-0.2354843	0.2280304	-0.8464
13	-0.05061286	0.9634821	-0.2666059
14	0.7183027	-1.35427	-0.3999666
15	0.8274424	-1.601233	-0.7890261
16	-0.470555	-1.173748	-1.172249
17	1.446331	-0.01098964	-0.3921936
18	0.4236814	-0.2151677	-1.361857
19	0.6538955	1.875609	-0.4024692
20	0.6233072	-0.2072951	1.17231
21	0.2915004	-2.075439	-0.2298406
22	0.9320396	-2.897866	-0.485802
23	-0.3154649	0.5633166	-1.547632
24	1.749131	-0.7117512	0.1204685
25	0.8562701	0.5912137	-1.075188
26	-0.751024	-0.5502947	-1.290288
27	0.7769506	0.5568254	-0.9893918
28	2.238198	-0.01550398	0.87992
29	1.100906	-1.087936	1.281433
30	0.7702127	-1.119431	0.3614885
31	-1.437774	0.1921378	-1.693616
32	1.488139	-0.9791753	-1.664384
33	2.758905	-0.05688733	-0.5173643
34	0.06441027	-0.4975254	-1.670192
35	-0.5278518	1.152648	0.1565362
36	-0.790078	0.1192994	-1.69795
37	-0.4429003	-0.5412464	-1.356292
38	-0.5499819	-1.220419	-0.1770449
39	1.709167	-0.6366608	0.2184536
40	0.4480405	1.224067	-0.2393039
41	-0.4370185	-0.5334587	0.4306893
42	-0.5499989	-0.9207816	-2.351244
43	-0.9560584	0.943051	0.7254229
44	0.1032824	0.5161109	2.005021
45	1.635069	-1.439767	0.5297914
46	1.036868	-0.4441049	-0.7533471
47	0.1001542	-0.5502341	1.41372
48	0.464214	0.4474071	-1.057613
49	1.359945	-0.710775	-0.1642414
50	-1.283544	0.5566532	0.5485656
51	1.687374	0.7934399	-0.5400267
52	-0.848387	-0.1032642	0.9586013
53	-1.025222	-0.3549386	-0.8693017
54	0.266897	0.296524	-2.241144
55	-1.560704	-2.271998	0.7224505
56	-2.161275	-0.3286104	1.069747
57	-1.779941	-0.8327076	-0.2453716
58	-0.0205006	-0.1701006	0.5292955
59	-0.7251038	-1.162473	0.1995235
60	0.7271477	-0.2606875	-0.1367718
61	0.5202298	-0.6591333	-0.1806734
62	-1.048847	0.5123711	0.2064803
63	-0.960832	0.4146824	-1.228714
64	2.57497	-0.008049008	-1.885899
65	0.830757	-0.3783459	0.4790463
66	1.609382	-0.5708413	0.2690964
67	0.8035033	0.5832181	0.4497564
68	-0.6935559	1.896662	0.02708176
69	-0.258272	-0.37012	0.04565963
70	-0.3430478	-0.3924844	-2.410929
71	1.939206	-0.5900438	0.2270499
72	-0.1417654	0.8555065	0.286761
73	0.5648119	-0.5097008	1.403344
74	-1.378522	0.4340351	0.03425181
75	0.8961165	-0.8705775	1.369953
76	0.2725969	0.5792226	-1.532103
77	0.957065	0.4276634	-0.3666802
78	0.6486989	-0.004649441	0.1715484
79	-0.07957611	0.4553892	-2.140093
80	0.9332446	0.8186856	-1.548256
81	0.370246	-0.773089	-0.01298333
82	0.1873089	-2.131449	-1.197682
83	-0.005001849	-0.1256726	-1.892007
84	3.40565	-0.1035762	0.4154477
85	0.7272545	0.9788553	1.158081
86	0.2952752	0.2839339	1.294258
87	0.2007735	0.342265	0.1640854
88	-0.6083832	0.1443463	0.5377329
89	0.6965567	1.187906	2.180975
90	-0.1948093	0.6283156	0.2308662
91	-0.6480712	-0.02802031	0.8710046
92	1.244731	-0.1063582	-0.2344887
93	-2.010204	0.1217012	-1.331632
94	-0.8254575	-1.216578	-1.025789
95	-1.224865	-0.7350567	0.2674311
96	-0.3139666	0.3284034	-1.185418
97	0.2725766	-0.5379969	-0.1546276
98	0.03489387	0.3572081	0.8738098
99	-1.489697	-1.603233	0.2768838

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=[0.153322,-0.0887119,-0.139828]

Draw the marginal i of the time series using linear interpolation

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

with no interpolation

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

OpenTURNS

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

Previous topic

Next topic

This Page

Manipulate a time series¶