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

[ t X0 X1 X2 ]
0 : [ 0 -0.304826 -1.00361 0.483947 ]
1 : [ 0.1 0.624004 0.0395438 0.66043 ]
2 : [ 0.2 1.10081 0.585758 0.328136 ]
3 : [ 0.3 -0.178412 0.0833079 0.897776 ]
4 : [ 0.4 -1.40973 0.711103 -1.75418 ]
5 : [ 0.5 -1.33661 0.269893 1.41368 ]
6 : [ 0.6 0.499241 1.15854 -0.098967 ]
7 : [ 0.7 -0.650467 1.46114 0.61372 ]
8 : [ 0.8 2.14201 -1.66772 -0.151473 ]
9 : [ 0.9 2.4158 0.137289 -0.969704 ]
10 : [ 1 -0.292688 -1.02522 -0.354939 ]
11 : [ 1.1 -0.869302 0.266897 0.296524 ]
12 : [ 1.2 -2.24114 -1.5607 -2.272 ]
13 : [ 1.3 0.722451 -2.16128 -0.32861 ]
14 : [ 1.4 1.06975 -1.77994 -0.832708 ]
15 : [ 1.5 -0.245372 -0.0205006 -0.170101 ]
16 : [ 1.6 0.529296 -0.725104 -1.16247 ]
17 : [ 1.7 0.199523 0.727148 -0.260688 ]
18 : [ 1.8 -0.136772 0.52023 -0.659133 ]
19 : [ 1.9 -0.180673 -1.04885 0.512371 ]
20 : [ 2 0.20648 -0.960832 0.414682 ]
21 : [ 2.1 -1.22871 2.57497 -0.00804901 ]
22 : [ 2.2 -1.8859 0.830757 -0.378346 ]
23 : [ 2.3 0.479046 1.60938 -0.570841 ]
24 : [ 2.4 0.269096 0.803503 0.583218 ]
25 : [ 2.5 0.449756 -0.693556 1.89666 ]
26 : [ 2.6 0.0270818 -0.258272 -0.37012 ]
27 : [ 2.7 0.0456596 -0.343048 -0.392484 ]
28 : [ 2.8 -2.41093 1.93921 -0.590044 ]
29 : [ 2.9 0.22705 -0.141765 0.855507 ]
30 : [ 3 0.286761 0.564812 -0.509701 ]
31 : [ 3.1 1.40334 -1.37852 0.434035 ]
32 : [ 3.2 0.0342518 0.896116 -0.870577 ]
33 : [ 3.3 1.36995 0.272597 0.579223 ]
34 : [ 3.4 -1.5321 0.957065 0.427663 ]
35 : [ 3.5 -0.36668 0.648699 -0.00464944 ]
36 : [ 3.6 0.171548 -0.0795761 0.455389 ]
37 : [ 3.7 -2.14009 0.933245 0.818686 ]
38 : [ 3.8 -1.54826 0.370246 -0.773089 ]
39 : [ 3.9 -0.0129833 0.187309 -2.13145 ]
40 : [ 4 -1.19768 -0.00500185 -0.125673 ]
41 : [ 4.1 -1.89201 3.40565 -0.103576 ]
42 : [ 4.2 0.415448 0.727255 0.978855 ]
43 : [ 4.3 1.15808 0.295275 0.283934 ]
44 : [ 4.4 1.29426 0.200773 0.342265 ]
45 : [ 4.5 0.164085 -0.608383 0.144346 ]
46 : [ 4.6 0.537733 0.696557 1.18791 ]
47 : [ 4.7 2.18097 -0.194809 0.628316 ]
48 : [ 4.8 0.230866 -0.648071 -0.0280203 ]
49 : [ 4.9 0.871005 1.24473 -0.106358 ]
50 : [ 5 -0.234489 -2.0102 0.121701 ]
51 : [ 5.1 -1.33163 -0.825457 -1.21658 ]
52 : [ 5.2 -1.02579 -1.22486 -0.735057 ]
53 : [ 5.3 0.267431 -0.313967 0.328403 ]
54 : [ 5.4 -1.18542 0.272577 -0.537997 ]
55 : [ 5.5 -0.154628 0.0348939 0.357208 ]
56 : [ 5.6 0.87381 -1.4897 -1.60323 ]
57 : [ 5.7 0.276884 -0.205279 0.313591 ]
58 : [ 5.8 1.52063 2.12789 0.15741 ]
59 : [ 5.9 0.056432 1.05201 -1.06929 ]
60 : [ 6 0.0389696 0.108862 1.56022 ]
61 : [ 6.1 0.897858 0.0713179 0.329058 ]
62 : [ 6.2 0.768345 -0.201722 0.148307 ]
63 : [ 6.3 0.498826 -0.540609 0.202215 ]
64 : [ 6.4 1.52964 -1.19218 0.524954 ]
65 : [ 6.5 -0.127176 1.00122 0.299567 ]
66 : [ 6.6 -0.0732479 -0.592801 0.509773 ]
67 : [ 6.7 1.56808 0.369343 0.687346 ]
68 : [ 6.8 0.26022 1.5601 0.68388 ]
69 : [ 6.9 -0.260408 0.169652 -1.01657 ]
70 : [ 7 0.810285 -0.934548 0.440233 ]
71 : [ 7.1 0.102655 0.16255 0.977606 ]
72 : [ 7.2 -0.685128 -0.0411968 -0.161531 ]
73 : [ 7.3 0.00948899 -0.699237 0.835643 ]
74 : [ 7.4 0.961209 -0.395342 0.250509 ]
75 : [ 7.5 -1.71279 -0.303372 1.71343 ]
76 : [ 7.6 0.287997 -0.346204 -1.24308 ]
77 : [ 7.7 -0.661934 -0.539626 0.78918 ]
78 : [ 7.8 0.525199 0.265505 -0.615353 ]
79 : [ 7.9 0.667728 -0.320656 -0.00603524 ]
80 : [ 8 -1.44043 0.0706512 0.400517 ]
81 : [ 8.1 -0.537003 -2.13043 0.186229 ]
82 : [ 8.2 -1.32629 0.242601 -0.897333 ]
83 : [ 8.3 -0.957364 1.58824 -0.238077 ]
84 : [ 8.4 -0.654398 1.49892 -0.713136 ]
85 : [ 8.5 -1.33516 0.567629 0.640198 ]
86 : [ 8.6 -0.259729 0.192286 -1.40222 ]
87 : [ 8.7 0.560018 -1.35624 1.03452 ]
88 : [ 8.8 -0.378793 -0.125727 -0.587836 ]
89 : [ 8.9 1.07894 -1.66939 1.70834 ]
90 : [ 9 -0.845941 -0.178621 -0.195884 ]
91 : [ 9.1 1.81133 0.400036 1.10812 ]
92 : [ 9.2 -0.455236 -0.793417 2.28383 ]
93 : [ 9.3 0.351885 -0.0608221 1.18257 ]
94 : [ 9.4 2.05724 2.0836 -1.10946 ]
95 : [ 9.5 0.646117 0.314088 -1.25919 ]
96 : [ 9.6 2.51347 1.10677 -1.23708 ]
97 : [ 9.7 -0.405063 1.24478 0.258866 ]
98 : [ 9.8 -0.1138 0.3815 0.155791 ]
99 : [ 9.9 0.402412 1.33272 -0.805619 ]

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	0.3854209	-1.61086	-0.6874292
1	0.1	-0.02107395	-1.405266	-0.6029087
2	0.2	-0.07453712	-0.287633	-0.4026233
3	0.3	-0.4894317	-0.5803388	1.196489
4	0.4	1.004556	0.5372572	-0.08770909
5	0.5	1.423935	0.6820146	2.884055
6	0.6	0.2796988	-1.178997	-0.143892
7	0.7	0.6813079	0.01437919	0.5099701
8	0.8	-1.060234	0.04483657	0.2499197
9	0.9	1.24773	-0.3856004	-0.2880728
10	1	-0.5890517	0.4995753	1.132313
11	1.1	-0.8437811	1.43619	-0.1876503
12	1.2	0.940522	0.7151117	-1.439318
13	1.3	-0.1429401	-0.1765888	0.9054335
14	1.4	0.6688361	-0.1848348	-0.2056171
15	1.5	0.8539061	1.082717	0.7860448
16	1.6	-1.839514	-0.4807376	-0.7431111
17	1.7	0.2583894	0.06498678	0.8220976
18	1.8	-0.2202976	-1.267407	0.06548754
19	1.9	-2.506485	0.2182682	-0.3734256
20	2	-0.3483342	-1.020392	-0.9373684
21	2.1	0.793814	-0.983334	-0.4151898
22	2.2	0.1049272	-0.4991656	0.3643877
23	2.3	-0.1627931	0.4925782	0.3548167
24	2.4	-0.8811936	-0.819895	-2.106536
25	2.5	0.1773956	-0.04881701	-0.9867962
26	2.6	-0.8862132	1.219161	0.266691
27	2.7	0.188304	0.8090514	1.619885
28	2.8	-0.5646788	-0.9921044	0.7245245
29	2.9	0.3057475	-0.4119946	2.759856
30	3	0.4088039	1.121707	-0.6501654
31	3.1	-1.034288	1.150379	0.5587453
32	3.2	1.332409	-0.3225148	0.4750779
33	3.3	-0.1536095	1.035535	1.381175
34	3.4	1.225896	-0.1056646	0.3069166
35	3.5	0.4924758	0.4262604	-0.5698308
36	3.6	-0.4156163	-2.609303	-2.173168
37	3.7	-1.324497	-1.45585	0.1801837
38	3.8	1.421198	1.866039	-0.1742316
39	3.9	-1.55547	1.4884	1.303924
40	4	-1.061323	-1.305955	-1.629615
41	4.1	-0.2962869	0.8739792	0.1051378
42	4.2	-0.02998592	-1.516032	1.474471
43	4.3	-1.03669	-1.534651	0.8259901
44	4.4	0.457382	-0.3865615	1.28411
45	4.5	-0.3259461	1.637177	-0.8420178
46	4.6	-0.2924097	0.3615991	0.4570965
47	4.7	0.237978	1.020826	1.699262
48	4.8	-0.5438809	0.4973056	-1.469904
49	4.9	-2.294773	-0.2623551	-1.554523
50	5	-2.82731	0.5825531	0.4139608
51	5.1	-0.9302437	0.549059	-0.69065
52	5.2	-0.6021352	-0.7677184	1.285077
53	5.3	-0.22259	1.221741	0.4439343
54	5.4	-0.7078664	-1.056912	0.5648551
55	5.5	0.2980986	1.342418	1.085837
56	5.6	0.8239627	-0.6283856	-0.8834576
57	5.7	0.8607533	1.456264	0.1421699
58	5.8	-0.3323323	0.8952978	0.1655028
59	5.9	0.02714461	0.1645807	0.2626963
60	6	1.638611	0.1818056	-0.1240066
61	6.1	1.56386	-0.5471615	0.4136208
62	6.2	-0.5009097	-1.561814	-2.157897
63	6.3	-0.8845609	-0.03278067	-0.4371368
64	6.4	0.9263022	0.3640217	1.127778
65	6.5	-0.2958129	0.521623	-0.5048369
66	6.6	-1.126024	-0.1538759	0.9138794
67	6.7	-2.058274	1.093646	0.353957
68	6.8	-0.5708488	1.521397	0.2852253
69	6.9	-1.835236	-0.3044852	0.9165636
70	7	0.9140664	0.1075705	0.06927429
71	7.1	-0.6650488	1.951216	0.7997068
72	7.2	-0.8125796	-0.5797791	0.1117721
73	7.3	-0.2133026	-1.116885	-0.872058
74	7.4	1.629164	3.399959	-0.9405087
75	7.5	0.8080016	-0.5450092	1.626903
76	7.6	-0.06128802	0.308256	-0.9618253
77	7.7	-1.255094	0.4358796	-0.7273887
78	7.8	-0.3513546	-1.318261	-0.47417
79	7.9	-0.1005602	1.643525	-0.4139103
80	8	0.8686027	-0.4322521	1.012874
81	8.1	-1.114927	0.469528	0.9161205
82	8.2	-0.356955	1.022334	-2.00257
83	8.3	-1.71516	0.6274581	-1.352094
84	8.4	-0.03491598	-0.03793251	0.05596954
85	8.5	-0.2810947	0.144073	-2.171863
86	8.6	-0.3389453	0.5843859	-0.8390798
87	8.7	-1.04138	0.3519497	1.069267
88	8.8	-2.866462	1.182504	0.2067203
89	8.9	-0.6907754	-0.7425984	1.164752
90	9	-0.09003073	-1.209451	0.7730654
91	9.1	-0.8069562	-1.046643	0.1396704
92	9.2	1.067365	0.1232827	-0.776005
93	9.3	-0.882326	-0.0145659	0.2200673
94	9.4	0.4727389	-0.3159074	1.723677
95	9.5	0.5338985	0.4875888	-0.5419431
96	9.6	0.7959215	-0.9714537	-0.3666259
97	9.7	0.1363355	1.229809	-0.4606246
98	9.8	0.5330227	-0.9875807	0.2573491
99	9.9	0.415046	-0.7534109	0.07963906

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 =  [-2.14009,0.933245,0.818686]

Get the time series at index i : Xi

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

Xi =  [-2.14009,0.933245,0.818686]

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 =  -2.1400929826096444

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

myTimeSeries.getValues()

	X0	X1	X2
0	-0.3048259	-1.003608	0.4839469
1	0.624004	0.03954378	0.6604305
2	1.100812	0.5857581	0.3281357
3	-0.1784119	0.08330789	0.8977757
4	-1.409734	0.7111029	-1.754176
5	-1.336608	0.2698927	1.413675
6	0.4992414	1.158536	-0.09896703
7	-0.6504669	1.461145	0.6137203
8	2.142012	-1.667722	-0.1514732
9	2.4158	0.1372886	-0.9697043
10	-0.292688	-1.025222	-0.3549386
11	-0.8693017	0.266897	0.296524
12	-2.241144	-1.560704	-2.271998
13	0.7224505	-2.161275	-0.3286104
14	1.069747	-1.779941	-0.8327076
15	-0.2453716	-0.0205006	-0.1701006
16	0.5292955	-0.7251038	-1.162473
17	0.1995235	0.7271477	-0.2606875
18	-0.1367718	0.5202298	-0.6591333
19	-0.1806734	-1.048847	0.5123711
20	0.2064803	-0.960832	0.4146824
21	-1.228714	2.57497	-0.008049008
22	-1.885899	0.830757	-0.3783459
23	0.4790463	1.609382	-0.5708413
24	0.2690964	0.8035033	0.5832181
25	0.4497564	-0.6935559	1.896662
26	0.02708176	-0.258272	-0.37012
27	0.04565963	-0.3430478	-0.3924844
28	-2.410929	1.939206	-0.5900438
29	0.2270499	-0.1417654	0.8555065
30	0.286761	0.5648119	-0.5097008
31	1.403344	-1.378522	0.4340351
32	0.03425181	0.8961165	-0.8705775
33	1.369953	0.2725969	0.5792226
34	-1.532103	0.957065	0.4276634
35	-0.3666802	0.6486989	-0.004649441
36	0.1715484	-0.07957611	0.4553892
37	-2.140093	0.9332446	0.8186856
38	-1.548256	0.370246	-0.773089
39	-0.01298333	0.1873089	-2.131449
40	-1.197682	-0.005001849	-0.1256726
41	-1.892007	3.40565	-0.1035762
42	0.4154477	0.7272545	0.9788553
43	1.158081	0.2952752	0.2839339
44	1.294258	0.2007735	0.342265
45	0.1640854	-0.6083832	0.1443463
46	0.5377329	0.6965567	1.187906
47	2.180975	-0.1948093	0.6283156
48	0.2308662	-0.6480712	-0.02802031
49	0.8710046	1.244731	-0.1063582
50	-0.2344887	-2.010204	0.1217012
51	-1.331632	-0.8254575	-1.216578
52	-1.025789	-1.224865	-0.7350567
53	0.2674311	-0.3139666	0.3284034
54	-1.185418	0.2725766	-0.5379969
55	-0.1546276	0.03489387	0.3572081
56	0.8738098	-1.489697	-1.603233
57	0.2768838	-0.2052791	0.3135911
58	1.520626	2.127892	0.1574096
59	0.05643199	1.05201	-1.069286
60	0.03896958	0.1088619	1.560223
61	0.8978581	0.07131786	0.3290581
62	0.7683447	-0.2017215	0.1483074
63	0.4988259	-0.5406089	0.202215
64	1.52964	-1.192179	0.5249542
65	-0.1271758	1.001217	0.2995675
66	-0.07324792	-0.5928008	0.509773
67	1.568079	0.3693428	0.6873462
68	0.2602205	1.560101	0.6838802
69	-0.2604079	0.1696515	-1.016573
70	0.8102853	-0.9345477	0.4402335
71	0.1026545	0.1625502	0.9776058
72	-0.6851276	-0.04119683	-0.1615313
73	0.009488993	-0.6992373	0.8356431
74	0.9612086	-0.3953424	0.2505092
75	-1.712787	-0.3033722	1.713433
76	0.2879968	-0.3462038	-1.243077
77	-0.6619336	-0.5396257	0.7891796
78	0.525199	0.2655049	-0.6153533
79	0.6677281	-0.3206562	-0.00603524
80	-1.440427	0.07065125	0.4005165
81	-0.5370034	-2.130432	0.1862285
82	-1.326288	0.2426011	-0.8973327
83	-0.9573643	1.588237	-0.2380769
84	-0.6543979	1.498919	-0.7131357
85	-1.335157	0.5676285	0.640198
86	-0.259729	0.1922855	-1.402221
87	0.5600177	-1.356244	1.034522
88	-0.3787931	-0.1257271	-0.5878356
89	1.078941	-1.669386	1.708344
90	-0.8459409	-0.1786205	-0.1958844
91	1.811325	0.4000363	1.108118
92	-0.4552358	-0.7934174	2.283829
93	0.351885	-0.06082214	1.182574
94	2.057236	2.083603	-1.109457
95	0.6461174	0.3140881	-1.259195
96	2.51347	1.106768	-1.237082
97	-0.4050629	1.244775	0.2588656
98	-0.1137998	0.3814998	0.1557911
99	0.4024124	1.332716	-0.8056192

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

myTimeSeries.getInputMean()

[0.0282591,0.0564162,0.0199248]

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()

Total running time of the script: ( 0 minutes 0.121 seconds)

OpenTURNS

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

Previous topic

Next topic

This Page

Manipulate a time series¶