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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationTue, 20 Dec 2016 17:01:06 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/20/t1482249948nft7xf44qwsma26.htm/, Retrieved Sun, 28 Apr 2024 14:37:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301731, Retrieved Sun, 28 Apr 2024 14:37:45 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-20 16:01:06] [672675941468e072e71d9fb024f2b817] [Current]
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Dataseries X:
5133
5155
5174
5201
5221
5205
5235
5255
5272
5299
5318
5340
5385
5430
5454
5493
5536
5565
5586
5594
5576
5544
5530
5536
5544
5564
5596
5596
5599
5591
5566
5532
5498
5484
5442
5447
5490
5544
5583
5628
5679
5691
5707
5724
5726
5745
5767
5789
5785
5785
5806
5827
5856
5896
5914
5938




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301731&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301731&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301731&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
151335133000
251555155.0000005456122.0000004364862-5.45607700177061e-071.19935435374009
351745173.9999999252418.99999917769087.47553502998034e-08-0.163548386518671
452015200.9999998940727.00000000000011.05932941696098e-070.436128906298529
552215220.9999998940719.99999999999961.05932941696097e-07-0.381612745606061
652055204.99999989407-15.99999999999991.05932941696097e-07-1.9625798345453
752355234.9999998940729.99999999999961.05932941696098e-072.50774089969678
852555254.9999998940719.99999999999921.05932941696098e-07-0.545161065151505
952725271.9999998940717.00000000000051.05932941696097e-07-0.16354831954537
1052995298.9999998940727.00000000000011.05932941696097e-070.545161065151455
1153185317.9999998940719.00000000000051.05932941696097e-07-0.436128852121159
1253405339.9999998940722.00000000000011.05932941696097e-070.163548319545419
135385538545.0000001140822-1.10371682047971e-221.2538704558456
1454305430.0000011408245.000001140816-1.14081632833179e-065.5973531515458e-08
1554545453.9999997296823.99999702643722.70323911341175e-07-1.14483845685915
1654935492.9999996712238.99999999999993.28781914126941e-070.817741777362243
1755365535.9999996712243.00000000000033.28781914126941e-070.218064426060615
1855655564.9999996712229.00000000000073.28781914126941e-07-0.763225491212048
1955865585.9999996712221.00000000000023.28781914126942e-07-0.43612885212121
2055945593.999999671228.000000000000673.28781914126942e-07-0.7087093846969
2155765575.99999967122-17.99999999999983.28781914126942e-07-1.41741876939387
2255445543.99999967122-31.99999999999943.28781914126942e-07-0.763225491212048
2355305529.99999967122-13.99999999999993.28781914126941e-070.981289917272636
2455365535.999999671226.000000000000533.28781914126942e-071.09032213030298
25554455448.00000032949054-4.31697982370632e-220.109032230973494
2655645564.0000036775420.0000036775389-3.67753918942339e-060.654193449231486
2755965595.9999997215331.99999693680062.7847266421112e-070.654192908269333
2855965595.99999984624-2.8421709430404e-131.53762266473986e-07-1.74451527888403
2955995598.999999846242.999999999999351.53762266473986e-070.163548319545424
3055915590.99999984624-8.00000000000011.53762266473986e-07-0.599677171666598
3155665565.99999984624-25.00000000000051.53762266473986e-07-0.926773810757535
3255325531.99999984624-33.99999999999991.53762266473986e-07-0.490644958636302
3354985497.99999984624-34.00000000000031.53762266473986e-07-1.9827952214294e-14
3454845483.99999984624-14.00000000000061.53762266473986e-071.09032213030294
3554425441.99999984624-42.00000000000011.53762266473985e-07-1.52645098242411
3654475446.999999846244.999999999999541.53762266473987e-072.56225700621193
375490549043.0000001672254-5.58039336204805e-222.07161205632515
3855445544.00000202354.0000020230016-2.02300130662203e-060.599677262319537
3955835582.999999686138.99999654708013.13901827970877e-07-0.817741893211091
4056285627.9999996627145.00000000000063.37285048576863e-070.327096834341864
4156795678.9999996627150.99999999999993.37285048576862e-070.327096639090846
4256915690.99999966271123.37285048576862e-07-2.12612815409076
4357075706.9999996627116.00000000000023.37285048576863e-070.2180644260606
4457245723.9999996627117.00000000000033.37285048576863e-070.0545161065151562
4557265725.999999662712.000000000000463.37285048576863e-07-0.817741597727211
4657455744.9999996627118.99999999999973.37285048576862e-070.926773810757474
4757675766.9999996627121.99999999999993.37285048576861e-070.163548319545452
4857895788.99999966271223.37285048576863e-078.29085994196534e-15
4957855785-3.999999671926362.12719189601963e-22-1.41741875125746
5057855785.000003408283.40827948708267e-06-3.40827968652679e-060.218064590157135
5158065805.9999998154120.99999796955791.84585654274495e-071.14483793606132
5258275826.9999998154121.00000000000021.84585662187541e-071.10691811490092e-07
5358565855.9999998154129.00000000000011.84585662187536e-070.43612885212118
5458965895.99999981541401.84585662187539e-070.599677171666624
5559145913.99999981541181.84585662187539e-07-1.19935434333326
5659385937.9999998154123.99999999999991.84585662187539e-070.327096639090884

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 5133 & 5133 & 0 & 0 & 0 \tabularnewline
2 & 5155 & 5155.00000054561 & 22.0000004364862 & -5.45607700177061e-07 & 1.19935435374009 \tabularnewline
3 & 5174 & 5173.99999992524 & 18.9999991776908 & 7.47553502998034e-08 & -0.163548386518671 \tabularnewline
4 & 5201 & 5200.99999989407 & 27.0000000000001 & 1.05932941696098e-07 & 0.436128906298529 \tabularnewline
5 & 5221 & 5220.99999989407 & 19.9999999999996 & 1.05932941696097e-07 & -0.381612745606061 \tabularnewline
6 & 5205 & 5204.99999989407 & -15.9999999999999 & 1.05932941696097e-07 & -1.9625798345453 \tabularnewline
7 & 5235 & 5234.99999989407 & 29.9999999999996 & 1.05932941696098e-07 & 2.50774089969678 \tabularnewline
8 & 5255 & 5254.99999989407 & 19.9999999999992 & 1.05932941696098e-07 & -0.545161065151505 \tabularnewline
9 & 5272 & 5271.99999989407 & 17.0000000000005 & 1.05932941696097e-07 & -0.16354831954537 \tabularnewline
10 & 5299 & 5298.99999989407 & 27.0000000000001 & 1.05932941696097e-07 & 0.545161065151455 \tabularnewline
11 & 5318 & 5317.99999989407 & 19.0000000000005 & 1.05932941696097e-07 & -0.436128852121159 \tabularnewline
12 & 5340 & 5339.99999989407 & 22.0000000000001 & 1.05932941696097e-07 & 0.163548319545419 \tabularnewline
13 & 5385 & 5385 & 45.0000001140822 & -1.10371682047971e-22 & 1.2538704558456 \tabularnewline
14 & 5430 & 5430.00000114082 & 45.000001140816 & -1.14081632833179e-06 & 5.5973531515458e-08 \tabularnewline
15 & 5454 & 5453.99999972968 & 23.9999970264372 & 2.70323911341175e-07 & -1.14483845685915 \tabularnewline
16 & 5493 & 5492.99999967122 & 38.9999999999999 & 3.28781914126941e-07 & 0.817741777362243 \tabularnewline
17 & 5536 & 5535.99999967122 & 43.0000000000003 & 3.28781914126941e-07 & 0.218064426060615 \tabularnewline
18 & 5565 & 5564.99999967122 & 29.0000000000007 & 3.28781914126941e-07 & -0.763225491212048 \tabularnewline
19 & 5586 & 5585.99999967122 & 21.0000000000002 & 3.28781914126942e-07 & -0.43612885212121 \tabularnewline
20 & 5594 & 5593.99999967122 & 8.00000000000067 & 3.28781914126942e-07 & -0.7087093846969 \tabularnewline
21 & 5576 & 5575.99999967122 & -17.9999999999998 & 3.28781914126942e-07 & -1.41741876939387 \tabularnewline
22 & 5544 & 5543.99999967122 & -31.9999999999994 & 3.28781914126942e-07 & -0.763225491212048 \tabularnewline
23 & 5530 & 5529.99999967122 & -13.9999999999999 & 3.28781914126941e-07 & 0.981289917272636 \tabularnewline
24 & 5536 & 5535.99999967122 & 6.00000000000053 & 3.28781914126942e-07 & 1.09032213030298 \tabularnewline
25 & 5544 & 5544 & 8.00000032949054 & -4.31697982370632e-22 & 0.109032230973494 \tabularnewline
26 & 5564 & 5564.00000367754 & 20.0000036775389 & -3.67753918942339e-06 & 0.654193449231486 \tabularnewline
27 & 5596 & 5595.99999972153 & 31.9999969368006 & 2.7847266421112e-07 & 0.654192908269333 \tabularnewline
28 & 5596 & 5595.99999984624 & -2.8421709430404e-13 & 1.53762266473986e-07 & -1.74451527888403 \tabularnewline
29 & 5599 & 5598.99999984624 & 2.99999999999935 & 1.53762266473986e-07 & 0.163548319545424 \tabularnewline
30 & 5591 & 5590.99999984624 & -8.0000000000001 & 1.53762266473986e-07 & -0.599677171666598 \tabularnewline
31 & 5566 & 5565.99999984624 & -25.0000000000005 & 1.53762266473986e-07 & -0.926773810757535 \tabularnewline
32 & 5532 & 5531.99999984624 & -33.9999999999999 & 1.53762266473986e-07 & -0.490644958636302 \tabularnewline
33 & 5498 & 5497.99999984624 & -34.0000000000003 & 1.53762266473986e-07 & -1.9827952214294e-14 \tabularnewline
34 & 5484 & 5483.99999984624 & -14.0000000000006 & 1.53762266473986e-07 & 1.09032213030294 \tabularnewline
35 & 5442 & 5441.99999984624 & -42.0000000000001 & 1.53762266473985e-07 & -1.52645098242411 \tabularnewline
36 & 5447 & 5446.99999984624 & 4.99999999999954 & 1.53762266473987e-07 & 2.56225700621193 \tabularnewline
37 & 5490 & 5490 & 43.0000001672254 & -5.58039336204805e-22 & 2.07161205632515 \tabularnewline
38 & 5544 & 5544.000002023 & 54.0000020230016 & -2.02300130662203e-06 & 0.599677262319537 \tabularnewline
39 & 5583 & 5582.9999996861 & 38.9999965470801 & 3.13901827970877e-07 & -0.817741893211091 \tabularnewline
40 & 5628 & 5627.99999966271 & 45.0000000000006 & 3.37285048576863e-07 & 0.327096834341864 \tabularnewline
41 & 5679 & 5678.99999966271 & 50.9999999999999 & 3.37285048576862e-07 & 0.327096639090846 \tabularnewline
42 & 5691 & 5690.99999966271 & 12 & 3.37285048576862e-07 & -2.12612815409076 \tabularnewline
43 & 5707 & 5706.99999966271 & 16.0000000000002 & 3.37285048576863e-07 & 0.2180644260606 \tabularnewline
44 & 5724 & 5723.99999966271 & 17.0000000000003 & 3.37285048576863e-07 & 0.0545161065151562 \tabularnewline
45 & 5726 & 5725.99999966271 & 2.00000000000046 & 3.37285048576863e-07 & -0.817741597727211 \tabularnewline
46 & 5745 & 5744.99999966271 & 18.9999999999997 & 3.37285048576862e-07 & 0.926773810757474 \tabularnewline
47 & 5767 & 5766.99999966271 & 21.9999999999999 & 3.37285048576861e-07 & 0.163548319545452 \tabularnewline
48 & 5789 & 5788.99999966271 & 22 & 3.37285048576863e-07 & 8.29085994196534e-15 \tabularnewline
49 & 5785 & 5785 & -3.99999967192636 & 2.12719189601963e-22 & -1.41741875125746 \tabularnewline
50 & 5785 & 5785.00000340828 & 3.40827948708267e-06 & -3.40827968652679e-06 & 0.218064590157135 \tabularnewline
51 & 5806 & 5805.99999981541 & 20.9999979695579 & 1.84585654274495e-07 & 1.14483793606132 \tabularnewline
52 & 5827 & 5826.99999981541 & 21.0000000000002 & 1.84585662187541e-07 & 1.10691811490092e-07 \tabularnewline
53 & 5856 & 5855.99999981541 & 29.0000000000001 & 1.84585662187536e-07 & 0.43612885212118 \tabularnewline
54 & 5896 & 5895.99999981541 & 40 & 1.84585662187539e-07 & 0.599677171666624 \tabularnewline
55 & 5914 & 5913.99999981541 & 18 & 1.84585662187539e-07 & -1.19935434333326 \tabularnewline
56 & 5938 & 5937.99999981541 & 23.9999999999999 & 1.84585662187539e-07 & 0.327096639090884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301731&T=1

[TABLE]
[ROW][C]Structural Time Series Model -- Interpolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Slope[/C][C]Seasonal[/C][C]Stand. Residuals[/C][/ROW]
[ROW][C]1[/C][C]5133[/C][C]5133[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]5155[/C][C]5155.00000054561[/C][C]22.0000004364862[/C][C]-5.45607700177061e-07[/C][C]1.19935435374009[/C][/ROW]
[ROW][C]3[/C][C]5174[/C][C]5173.99999992524[/C][C]18.9999991776908[/C][C]7.47553502998034e-08[/C][C]-0.163548386518671[/C][/ROW]
[ROW][C]4[/C][C]5201[/C][C]5200.99999989407[/C][C]27.0000000000001[/C][C]1.05932941696098e-07[/C][C]0.436128906298529[/C][/ROW]
[ROW][C]5[/C][C]5221[/C][C]5220.99999989407[/C][C]19.9999999999996[/C][C]1.05932941696097e-07[/C][C]-0.381612745606061[/C][/ROW]
[ROW][C]6[/C][C]5205[/C][C]5204.99999989407[/C][C]-15.9999999999999[/C][C]1.05932941696097e-07[/C][C]-1.9625798345453[/C][/ROW]
[ROW][C]7[/C][C]5235[/C][C]5234.99999989407[/C][C]29.9999999999996[/C][C]1.05932941696098e-07[/C][C]2.50774089969678[/C][/ROW]
[ROW][C]8[/C][C]5255[/C][C]5254.99999989407[/C][C]19.9999999999992[/C][C]1.05932941696098e-07[/C][C]-0.545161065151505[/C][/ROW]
[ROW][C]9[/C][C]5272[/C][C]5271.99999989407[/C][C]17.0000000000005[/C][C]1.05932941696097e-07[/C][C]-0.16354831954537[/C][/ROW]
[ROW][C]10[/C][C]5299[/C][C]5298.99999989407[/C][C]27.0000000000001[/C][C]1.05932941696097e-07[/C][C]0.545161065151455[/C][/ROW]
[ROW][C]11[/C][C]5318[/C][C]5317.99999989407[/C][C]19.0000000000005[/C][C]1.05932941696097e-07[/C][C]-0.436128852121159[/C][/ROW]
[ROW][C]12[/C][C]5340[/C][C]5339.99999989407[/C][C]22.0000000000001[/C][C]1.05932941696097e-07[/C][C]0.163548319545419[/C][/ROW]
[ROW][C]13[/C][C]5385[/C][C]5385[/C][C]45.0000001140822[/C][C]-1.10371682047971e-22[/C][C]1.2538704558456[/C][/ROW]
[ROW][C]14[/C][C]5430[/C][C]5430.00000114082[/C][C]45.000001140816[/C][C]-1.14081632833179e-06[/C][C]5.5973531515458e-08[/C][/ROW]
[ROW][C]15[/C][C]5454[/C][C]5453.99999972968[/C][C]23.9999970264372[/C][C]2.70323911341175e-07[/C][C]-1.14483845685915[/C][/ROW]
[ROW][C]16[/C][C]5493[/C][C]5492.99999967122[/C][C]38.9999999999999[/C][C]3.28781914126941e-07[/C][C]0.817741777362243[/C][/ROW]
[ROW][C]17[/C][C]5536[/C][C]5535.99999967122[/C][C]43.0000000000003[/C][C]3.28781914126941e-07[/C][C]0.218064426060615[/C][/ROW]
[ROW][C]18[/C][C]5565[/C][C]5564.99999967122[/C][C]29.0000000000007[/C][C]3.28781914126941e-07[/C][C]-0.763225491212048[/C][/ROW]
[ROW][C]19[/C][C]5586[/C][C]5585.99999967122[/C][C]21.0000000000002[/C][C]3.28781914126942e-07[/C][C]-0.43612885212121[/C][/ROW]
[ROW][C]20[/C][C]5594[/C][C]5593.99999967122[/C][C]8.00000000000067[/C][C]3.28781914126942e-07[/C][C]-0.7087093846969[/C][/ROW]
[ROW][C]21[/C][C]5576[/C][C]5575.99999967122[/C][C]-17.9999999999998[/C][C]3.28781914126942e-07[/C][C]-1.41741876939387[/C][/ROW]
[ROW][C]22[/C][C]5544[/C][C]5543.99999967122[/C][C]-31.9999999999994[/C][C]3.28781914126942e-07[/C][C]-0.763225491212048[/C][/ROW]
[ROW][C]23[/C][C]5530[/C][C]5529.99999967122[/C][C]-13.9999999999999[/C][C]3.28781914126941e-07[/C][C]0.981289917272636[/C][/ROW]
[ROW][C]24[/C][C]5536[/C][C]5535.99999967122[/C][C]6.00000000000053[/C][C]3.28781914126942e-07[/C][C]1.09032213030298[/C][/ROW]
[ROW][C]25[/C][C]5544[/C][C]5544[/C][C]8.00000032949054[/C][C]-4.31697982370632e-22[/C][C]0.109032230973494[/C][/ROW]
[ROW][C]26[/C][C]5564[/C][C]5564.00000367754[/C][C]20.0000036775389[/C][C]-3.67753918942339e-06[/C][C]0.654193449231486[/C][/ROW]
[ROW][C]27[/C][C]5596[/C][C]5595.99999972153[/C][C]31.9999969368006[/C][C]2.7847266421112e-07[/C][C]0.654192908269333[/C][/ROW]
[ROW][C]28[/C][C]5596[/C][C]5595.99999984624[/C][C]-2.8421709430404e-13[/C][C]1.53762266473986e-07[/C][C]-1.74451527888403[/C][/ROW]
[ROW][C]29[/C][C]5599[/C][C]5598.99999984624[/C][C]2.99999999999935[/C][C]1.53762266473986e-07[/C][C]0.163548319545424[/C][/ROW]
[ROW][C]30[/C][C]5591[/C][C]5590.99999984624[/C][C]-8.0000000000001[/C][C]1.53762266473986e-07[/C][C]-0.599677171666598[/C][/ROW]
[ROW][C]31[/C][C]5566[/C][C]5565.99999984624[/C][C]-25.0000000000005[/C][C]1.53762266473986e-07[/C][C]-0.926773810757535[/C][/ROW]
[ROW][C]32[/C][C]5532[/C][C]5531.99999984624[/C][C]-33.9999999999999[/C][C]1.53762266473986e-07[/C][C]-0.490644958636302[/C][/ROW]
[ROW][C]33[/C][C]5498[/C][C]5497.99999984624[/C][C]-34.0000000000003[/C][C]1.53762266473986e-07[/C][C]-1.9827952214294e-14[/C][/ROW]
[ROW][C]34[/C][C]5484[/C][C]5483.99999984624[/C][C]-14.0000000000006[/C][C]1.53762266473986e-07[/C][C]1.09032213030294[/C][/ROW]
[ROW][C]35[/C][C]5442[/C][C]5441.99999984624[/C][C]-42.0000000000001[/C][C]1.53762266473985e-07[/C][C]-1.52645098242411[/C][/ROW]
[ROW][C]36[/C][C]5447[/C][C]5446.99999984624[/C][C]4.99999999999954[/C][C]1.53762266473987e-07[/C][C]2.56225700621193[/C][/ROW]
[ROW][C]37[/C][C]5490[/C][C]5490[/C][C]43.0000001672254[/C][C]-5.58039336204805e-22[/C][C]2.07161205632515[/C][/ROW]
[ROW][C]38[/C][C]5544[/C][C]5544.000002023[/C][C]54.0000020230016[/C][C]-2.02300130662203e-06[/C][C]0.599677262319537[/C][/ROW]
[ROW][C]39[/C][C]5583[/C][C]5582.9999996861[/C][C]38.9999965470801[/C][C]3.13901827970877e-07[/C][C]-0.817741893211091[/C][/ROW]
[ROW][C]40[/C][C]5628[/C][C]5627.99999966271[/C][C]45.0000000000006[/C][C]3.37285048576863e-07[/C][C]0.327096834341864[/C][/ROW]
[ROW][C]41[/C][C]5679[/C][C]5678.99999966271[/C][C]50.9999999999999[/C][C]3.37285048576862e-07[/C][C]0.327096639090846[/C][/ROW]
[ROW][C]42[/C][C]5691[/C][C]5690.99999966271[/C][C]12[/C][C]3.37285048576862e-07[/C][C]-2.12612815409076[/C][/ROW]
[ROW][C]43[/C][C]5707[/C][C]5706.99999966271[/C][C]16.0000000000002[/C][C]3.37285048576863e-07[/C][C]0.2180644260606[/C][/ROW]
[ROW][C]44[/C][C]5724[/C][C]5723.99999966271[/C][C]17.0000000000003[/C][C]3.37285048576863e-07[/C][C]0.0545161065151562[/C][/ROW]
[ROW][C]45[/C][C]5726[/C][C]5725.99999966271[/C][C]2.00000000000046[/C][C]3.37285048576863e-07[/C][C]-0.817741597727211[/C][/ROW]
[ROW][C]46[/C][C]5745[/C][C]5744.99999966271[/C][C]18.9999999999997[/C][C]3.37285048576862e-07[/C][C]0.926773810757474[/C][/ROW]
[ROW][C]47[/C][C]5767[/C][C]5766.99999966271[/C][C]21.9999999999999[/C][C]3.37285048576861e-07[/C][C]0.163548319545452[/C][/ROW]
[ROW][C]48[/C][C]5789[/C][C]5788.99999966271[/C][C]22[/C][C]3.37285048576863e-07[/C][C]8.29085994196534e-15[/C][/ROW]
[ROW][C]49[/C][C]5785[/C][C]5785[/C][C]-3.99999967192636[/C][C]2.12719189601963e-22[/C][C]-1.41741875125746[/C][/ROW]
[ROW][C]50[/C][C]5785[/C][C]5785.00000340828[/C][C]3.40827948708267e-06[/C][C]-3.40827968652679e-06[/C][C]0.218064590157135[/C][/ROW]
[ROW][C]51[/C][C]5806[/C][C]5805.99999981541[/C][C]20.9999979695579[/C][C]1.84585654274495e-07[/C][C]1.14483793606132[/C][/ROW]
[ROW][C]52[/C][C]5827[/C][C]5826.99999981541[/C][C]21.0000000000002[/C][C]1.84585662187541e-07[/C][C]1.10691811490092e-07[/C][/ROW]
[ROW][C]53[/C][C]5856[/C][C]5855.99999981541[/C][C]29.0000000000001[/C][C]1.84585662187536e-07[/C][C]0.43612885212118[/C][/ROW]
[ROW][C]54[/C][C]5896[/C][C]5895.99999981541[/C][C]40[/C][C]1.84585662187539e-07[/C][C]0.599677171666624[/C][/ROW]
[ROW][C]55[/C][C]5914[/C][C]5913.99999981541[/C][C]18[/C][C]1.84585662187539e-07[/C][C]-1.19935434333326[/C][/ROW]
[ROW][C]56[/C][C]5938[/C][C]5937.99999981541[/C][C]23.9999999999999[/C][C]1.84585662187539e-07[/C][C]0.327096639090884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301731&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301731&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
151335133000
251555155.0000005456122.0000004364862-5.45607700177061e-071.19935435374009
351745173.9999999252418.99999917769087.47553502998034e-08-0.163548386518671
452015200.9999998940727.00000000000011.05932941696098e-070.436128906298529
552215220.9999998940719.99999999999961.05932941696097e-07-0.381612745606061
652055204.99999989407-15.99999999999991.05932941696097e-07-1.9625798345453
752355234.9999998940729.99999999999961.05932941696098e-072.50774089969678
852555254.9999998940719.99999999999921.05932941696098e-07-0.545161065151505
952725271.9999998940717.00000000000051.05932941696097e-07-0.16354831954537
1052995298.9999998940727.00000000000011.05932941696097e-070.545161065151455
1153185317.9999998940719.00000000000051.05932941696097e-07-0.436128852121159
1253405339.9999998940722.00000000000011.05932941696097e-070.163548319545419
135385538545.0000001140822-1.10371682047971e-221.2538704558456
1454305430.0000011408245.000001140816-1.14081632833179e-065.5973531515458e-08
1554545453.9999997296823.99999702643722.70323911341175e-07-1.14483845685915
1654935492.9999996712238.99999999999993.28781914126941e-070.817741777362243
1755365535.9999996712243.00000000000033.28781914126941e-070.218064426060615
1855655564.9999996712229.00000000000073.28781914126941e-07-0.763225491212048
1955865585.9999996712221.00000000000023.28781914126942e-07-0.43612885212121
2055945593.999999671228.000000000000673.28781914126942e-07-0.7087093846969
2155765575.99999967122-17.99999999999983.28781914126942e-07-1.41741876939387
2255445543.99999967122-31.99999999999943.28781914126942e-07-0.763225491212048
2355305529.99999967122-13.99999999999993.28781914126941e-070.981289917272636
2455365535.999999671226.000000000000533.28781914126942e-071.09032213030298
25554455448.00000032949054-4.31697982370632e-220.109032230973494
2655645564.0000036775420.0000036775389-3.67753918942339e-060.654193449231486
2755965595.9999997215331.99999693680062.7847266421112e-070.654192908269333
2855965595.99999984624-2.8421709430404e-131.53762266473986e-07-1.74451527888403
2955995598.999999846242.999999999999351.53762266473986e-070.163548319545424
3055915590.99999984624-8.00000000000011.53762266473986e-07-0.599677171666598
3155665565.99999984624-25.00000000000051.53762266473986e-07-0.926773810757535
3255325531.99999984624-33.99999999999991.53762266473986e-07-0.490644958636302
3354985497.99999984624-34.00000000000031.53762266473986e-07-1.9827952214294e-14
3454845483.99999984624-14.00000000000061.53762266473986e-071.09032213030294
3554425441.99999984624-42.00000000000011.53762266473985e-07-1.52645098242411
3654475446.999999846244.999999999999541.53762266473987e-072.56225700621193
375490549043.0000001672254-5.58039336204805e-222.07161205632515
3855445544.00000202354.0000020230016-2.02300130662203e-060.599677262319537
3955835582.999999686138.99999654708013.13901827970877e-07-0.817741893211091
4056285627.9999996627145.00000000000063.37285048576863e-070.327096834341864
4156795678.9999996627150.99999999999993.37285048576862e-070.327096639090846
4256915690.99999966271123.37285048576862e-07-2.12612815409076
4357075706.9999996627116.00000000000023.37285048576863e-070.2180644260606
4457245723.9999996627117.00000000000033.37285048576863e-070.0545161065151562
4557265725.999999662712.000000000000463.37285048576863e-07-0.817741597727211
4657455744.9999996627118.99999999999973.37285048576862e-070.926773810757474
4757675766.9999996627121.99999999999993.37285048576861e-070.163548319545452
4857895788.99999966271223.37285048576863e-078.29085994196534e-15
4957855785-3.999999671926362.12719189601963e-22-1.41741875125746
5057855785.000003408283.40827948708267e-06-3.40827968652679e-060.218064590157135
5158065805.9999998154120.99999796955791.84585654274495e-071.14483793606132
5258275826.9999998154121.00000000000021.84585662187541e-071.10691811490092e-07
5358565855.9999998154129.00000000000011.84585662187536e-070.43612885212118
5458965895.99999981541401.84585662187539e-070.599677171666624
5559145913.99999981541181.84585662187539e-07-1.19935434333326
5659385937.9999998154123.99999999999991.84585662187539e-070.327096639090884







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15940.086850123165943.96239217312-3.87554204996144
25953.79388770695970.61955616383-16.8256684569315
35963.348924150425997.27672015454-33.9277960041148
45990.001951125066023.93388414525-33.9319330201899
56025.653126453066050.59104813596-24.9379216828965
66067.391491929756077.24821212666-9.85672019691286
76107.608255316756103.905376117373.70287919938268
86146.903424195536130.5625401080816.3408840874488
96188.677002133066157.2197040987931.4572980342708
106212.328995325756183.8768680894928.4521272362527
116236.259401371436210.534032080225.725369291232
126254.868219633336237.1911960709117.6770235624199

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5940.08685012316 & 5943.96239217312 & -3.87554204996144 \tabularnewline
2 & 5953.7938877069 & 5970.61955616383 & -16.8256684569315 \tabularnewline
3 & 5963.34892415042 & 5997.27672015454 & -33.9277960041148 \tabularnewline
4 & 5990.00195112506 & 6023.93388414525 & -33.9319330201899 \tabularnewline
5 & 6025.65312645306 & 6050.59104813596 & -24.9379216828965 \tabularnewline
6 & 6067.39149192975 & 6077.24821212666 & -9.85672019691286 \tabularnewline
7 & 6107.60825531675 & 6103.90537611737 & 3.70287919938268 \tabularnewline
8 & 6146.90342419553 & 6130.56254010808 & 16.3408840874488 \tabularnewline
9 & 6188.67700213306 & 6157.21970409879 & 31.4572980342708 \tabularnewline
10 & 6212.32899532575 & 6183.87686808949 & 28.4521272362527 \tabularnewline
11 & 6236.25940137143 & 6210.5340320802 & 25.725369291232 \tabularnewline
12 & 6254.86821963333 & 6237.19119607091 & 17.6770235624199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301731&T=2

[TABLE]
[ROW][C]Structural Time Series Model -- Extrapolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Seasonal[/C][/ROW]
[ROW][C]1[/C][C]5940.08685012316[/C][C]5943.96239217312[/C][C]-3.87554204996144[/C][/ROW]
[ROW][C]2[/C][C]5953.7938877069[/C][C]5970.61955616383[/C][C]-16.8256684569315[/C][/ROW]
[ROW][C]3[/C][C]5963.34892415042[/C][C]5997.27672015454[/C][C]-33.9277960041148[/C][/ROW]
[ROW][C]4[/C][C]5990.00195112506[/C][C]6023.93388414525[/C][C]-33.9319330201899[/C][/ROW]
[ROW][C]5[/C][C]6025.65312645306[/C][C]6050.59104813596[/C][C]-24.9379216828965[/C][/ROW]
[ROW][C]6[/C][C]6067.39149192975[/C][C]6077.24821212666[/C][C]-9.85672019691286[/C][/ROW]
[ROW][C]7[/C][C]6107.60825531675[/C][C]6103.90537611737[/C][C]3.70287919938268[/C][/ROW]
[ROW][C]8[/C][C]6146.90342419553[/C][C]6130.56254010808[/C][C]16.3408840874488[/C][/ROW]
[ROW][C]9[/C][C]6188.67700213306[/C][C]6157.21970409879[/C][C]31.4572980342708[/C][/ROW]
[ROW][C]10[/C][C]6212.32899532575[/C][C]6183.87686808949[/C][C]28.4521272362527[/C][/ROW]
[ROW][C]11[/C][C]6236.25940137143[/C][C]6210.5340320802[/C][C]25.725369291232[/C][/ROW]
[ROW][C]12[/C][C]6254.86821963333[/C][C]6237.19119607091[/C][C]17.6770235624199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301731&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301731&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15940.086850123165943.96239217312-3.87554204996144
25953.79388770695970.61955616383-16.8256684569315
35963.348924150425997.27672015454-33.9277960041148
45990.001951125066023.93388414525-33.9319330201899
56025.653126453066050.59104813596-24.9379216828965
66067.391491929756077.24821212666-9.85672019691286
76107.608255316756103.905376117373.70287919938268
86146.903424195536130.5625401080816.3408840874488
96188.677002133066157.2197040987931.4572980342708
106212.328995325756183.8768680894928.4521272362527
116236.259401371436210.534032080225.725369291232
126254.868219633336237.1911960709117.6770235624199



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
R code (references can be found in the software module):
require('stsm')
require('stsm.class')
require('KFKSDS')
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
print(m$coef)
print(m$fitted)
print(m$resid)
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mm <- stsm.model(model = 'BSM', y = x, transPars = 'StructTS')
fit2 <- stsmFit(mm, stsm.method = 'maxlik.td.optim', method = par3, KF.args = list(P0cov = TRUE))
(fit2.comps <- tsSmooth(fit2, P0cov = FALSE)$states)
m2 <- set.pars(mm, pmax(fit2$par, .Machine$double.eps))
(ss <- char2numeric(m2))
(pred <- predict(ss, x, n.ahead = par2))
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')
grid()
dev.off()
bitmap(file='test5.png')
op <- par(mfrow = c(2,2))
hist(m$resid,main='Residual Histogram')
plot(density(m$resid),main='Residual Kernel Density')
qqnorm(m$resid,main='Residual Normal QQ Plot')
qqline(m$resid)
plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')
par(op)
dev.off()
bitmap(file='test6.png')
par(mfrow = c(3,1), mar = c(3,3,3,3))
plot(cbind(x, pred$pred), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred + 2 * pred$se, rev(pred$pred)), col = 'gray85', border = NA)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred - 2 * pred$se, rev(pred$pred)), col = ' gray85', border = NA)
lines(pred$pred, col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the observed series', side = 3, adj = 0)
plot(cbind(x, pred$a[,1]), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] + 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] - 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = ' gray85', border = NA)
lines(pred$a[,1], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the level component', side = 3, adj = 0)
plot(cbind(fit2.comps[,3], pred$a[,3]), type = 'n', plot.type = 'single', ylab = '')
lines(fit2.comps[,3])
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] + 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] - 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = ' gray85', border = NA)
lines(pred$a[,3], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the seasonal component', side = 3, adj = 0)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Interpolation',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Slope',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Stand. Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,mylevel[i])
a<-table.element(a,myslope[i])
a<-table.element(a,myseas[i])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Extrapolation',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.row.end(a)
for (i in 1:par2) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,pred$pred[i])
a<-table.element(a,pred$a[i,1])
a<-table.element(a,pred$a[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')