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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationWed, 07 Dec 2016 11:20:51 +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/07/t1481106134g698gsigj6eonql.htm/, Retrieved Tue, 07 May 2024 16:37:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297970, Retrieved Tue, 07 May 2024 16:37:47 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [Voorbeeld Structu...] [2016-12-07 10:20:51] [fc6d28d208bad0c833791fcb11cb4db1] [Current]
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Dataseries X:
2157.07
2267.88
2375.38
2803.62
2367.53
2439.08
2533.76
2956.28
2484.24
2588.49
2668.42
3085.62
2595.93
2686.64
2779.43
3221.13
2752.7
2886.58
2958.05
3444.61
2939.78
3088.73
3161.34
3672.39
3092.36
3228.05
3311.16
3801.93
3246.26
3309.22
3458.64
4005.04
3477.65
3524.42
3699.5
4247.68
3697.6
3746.72
3950.67
4566.86
3967.9
4059.35
4215.38
4856.13




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 time7 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297970&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]7 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297970&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297970&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 time7 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
12157.072157.07000
22267.882190.81164453096-0.55682491841332177.06835546903710.939660058787899
32375.382296.997977219137.4800640224999978.38202278087151.57696373666142
42803.622518.8953655930725.7768946590251284.724634406933.6168190821253
52367.532526.7276503431524.3363136268087-159.197650343154-0.3572958663918
62439.082501.7567443361720.7222985200143-62.6767443361703-1.04637957919325
72533.762504.410340884119.458029719497229.3496591159014-0.386865629203782
82956.282657.3620820550328.8751020277655298.9179179449742.83622943503365
92484.242653.741660401626.4885050493864-169.501660401596-0.683300692929796
102588.492631.2811627389322.7117328803605-42.7911627389329-1.01948807532144
112668.422636.3517618965821.287388442668632.0682381034209-0.364454713156057
123085.622793.1502435696232.6407455393263292.4697564303752.7811204297425
132595.932834.8804699345333.2961135899446-238.9504699345260.189960566809903
142686.642843.5753627972731.3852014672066-156.935362797274-0.520975372842783
152779.432854.919838477429.6321246147877-75.4898384773975-0.398448994636375
163221.132886.6407815323429.8262661738688334.4892184676570.0397002992821105
172752.72906.0834411844828.8443699500043-153.383441184478-0.198810152240927
182886.582944.5219320410229.7496515520046-57.94193204101590.188200507625629
192958.052983.4339698902530.607373280584-25.38396989025070.182260879357475
203444.613047.8632257175133.7499957234271396.7467742824880.673828099949084
212939.783092.4691330165634.753343302048-152.6891330165560.215352777888678
223088.733143.0193310280236.2078566530562-54.28933102802240.311738937915798
233161.343196.8167617492937.8219953321365-35.47676174928880.345890806794951
243672.393287.9659319260842.7008122961089384.4240680739241.04936602766713
253092.363336.9863532451943.2787442602335-244.626353245190.125138811087061
263228.053378.1186770550343.0811399631919-150.068677055028-0.0426344449186236
273311.163407.8917793521841.8441831544403-96.7317793521753-0.26198983223366
283801.933451.3362535876741.9938980649647350.5937464123260.0311268155542663
293246.263465.7660037807939.4093363473895-219.506003780793-0.534572210616193
303309.223456.7635814304134.8704757616577-147.543581430415-0.944416086703372
313458.643486.6983590320234.4081175412166-28.058359032016-0.0969219191083301
324005.043556.5679890786437.7262227320536448.4720109213630.697654739767283
333477.653625.2376433352940.6171400207475-147.5876433352860.607163996358766
343524.423654.9691276701139.602029358619-130.549127670113-0.212763803940607
353699.53718.4644773209341.8261627465289-18.9644773209310.466095196064516
364247.683802.6950923812345.7692382527557444.984907618770.828324955413254
373697.63888.6103920013949.503013008709-191.0103920013870.786701527345595
383746.723928.0666194272448.5673907039435-181.346619427235-0.197159031090405
393950.673991.5104091493849.9548513849808-40.84040914937830.291263764189424
404566.864093.2074337225154.7843629237439473.6525662774881.00912692344004
413967.94165.0743660606756.3787608289865-197.1743660606670.332584903335799
424059.354224.5321167797256.6660498398518-165.1821167797230.0600358294533894
434215.384280.0637941219456.5602208914439-64.683794121941-0.022176316526142
444856.134368.1810866952659.504262692675487.9489133047420.617610568134301

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 2157.07 & 2157.07 & 0 & 0 & 0 \tabularnewline
2 & 2267.88 & 2190.81164453096 & -0.556824918413321 & 77.0683554690371 & 0.939660058787899 \tabularnewline
3 & 2375.38 & 2296.99797721913 & 7.48006402249999 & 78.3820227808715 & 1.57696373666142 \tabularnewline
4 & 2803.62 & 2518.89536559307 & 25.7768946590251 & 284.72463440693 & 3.6168190821253 \tabularnewline
5 & 2367.53 & 2526.72765034315 & 24.3363136268087 & -159.197650343154 & -0.3572958663918 \tabularnewline
6 & 2439.08 & 2501.75674433617 & 20.7222985200143 & -62.6767443361703 & -1.04637957919325 \tabularnewline
7 & 2533.76 & 2504.4103408841 & 19.4580297194972 & 29.3496591159014 & -0.386865629203782 \tabularnewline
8 & 2956.28 & 2657.36208205503 & 28.8751020277655 & 298.917917944974 & 2.83622943503365 \tabularnewline
9 & 2484.24 & 2653.7416604016 & 26.4885050493864 & -169.501660401596 & -0.683300692929796 \tabularnewline
10 & 2588.49 & 2631.28116273893 & 22.7117328803605 & -42.7911627389329 & -1.01948807532144 \tabularnewline
11 & 2668.42 & 2636.35176189658 & 21.2873884426686 & 32.0682381034209 & -0.364454713156057 \tabularnewline
12 & 3085.62 & 2793.15024356962 & 32.6407455393263 & 292.469756430375 & 2.7811204297425 \tabularnewline
13 & 2595.93 & 2834.88046993453 & 33.2961135899446 & -238.950469934526 & 0.189960566809903 \tabularnewline
14 & 2686.64 & 2843.57536279727 & 31.3852014672066 & -156.935362797274 & -0.520975372842783 \tabularnewline
15 & 2779.43 & 2854.9198384774 & 29.6321246147877 & -75.4898384773975 & -0.398448994636375 \tabularnewline
16 & 3221.13 & 2886.64078153234 & 29.8262661738688 & 334.489218467657 & 0.0397002992821105 \tabularnewline
17 & 2752.7 & 2906.08344118448 & 28.8443699500043 & -153.383441184478 & -0.198810152240927 \tabularnewline
18 & 2886.58 & 2944.52193204102 & 29.7496515520046 & -57.9419320410159 & 0.188200507625629 \tabularnewline
19 & 2958.05 & 2983.43396989025 & 30.607373280584 & -25.3839698902507 & 0.182260879357475 \tabularnewline
20 & 3444.61 & 3047.86322571751 & 33.7499957234271 & 396.746774282488 & 0.673828099949084 \tabularnewline
21 & 2939.78 & 3092.46913301656 & 34.753343302048 & -152.689133016556 & 0.215352777888678 \tabularnewline
22 & 3088.73 & 3143.01933102802 & 36.2078566530562 & -54.2893310280224 & 0.311738937915798 \tabularnewline
23 & 3161.34 & 3196.81676174929 & 37.8219953321365 & -35.4767617492888 & 0.345890806794951 \tabularnewline
24 & 3672.39 & 3287.96593192608 & 42.7008122961089 & 384.424068073924 & 1.04936602766713 \tabularnewline
25 & 3092.36 & 3336.98635324519 & 43.2787442602335 & -244.62635324519 & 0.125138811087061 \tabularnewline
26 & 3228.05 & 3378.11867705503 & 43.0811399631919 & -150.068677055028 & -0.0426344449186236 \tabularnewline
27 & 3311.16 & 3407.89177935218 & 41.8441831544403 & -96.7317793521753 & -0.26198983223366 \tabularnewline
28 & 3801.93 & 3451.33625358767 & 41.9938980649647 & 350.593746412326 & 0.0311268155542663 \tabularnewline
29 & 3246.26 & 3465.76600378079 & 39.4093363473895 & -219.506003780793 & -0.534572210616193 \tabularnewline
30 & 3309.22 & 3456.76358143041 & 34.8704757616577 & -147.543581430415 & -0.944416086703372 \tabularnewline
31 & 3458.64 & 3486.69835903202 & 34.4081175412166 & -28.058359032016 & -0.0969219191083301 \tabularnewline
32 & 4005.04 & 3556.56798907864 & 37.7262227320536 & 448.472010921363 & 0.697654739767283 \tabularnewline
33 & 3477.65 & 3625.23764333529 & 40.6171400207475 & -147.587643335286 & 0.607163996358766 \tabularnewline
34 & 3524.42 & 3654.96912767011 & 39.602029358619 & -130.549127670113 & -0.212763803940607 \tabularnewline
35 & 3699.5 & 3718.46447732093 & 41.8261627465289 & -18.964477320931 & 0.466095196064516 \tabularnewline
36 & 4247.68 & 3802.69509238123 & 45.7692382527557 & 444.98490761877 & 0.828324955413254 \tabularnewline
37 & 3697.6 & 3888.61039200139 & 49.503013008709 & -191.010392001387 & 0.786701527345595 \tabularnewline
38 & 3746.72 & 3928.06661942724 & 48.5673907039435 & -181.346619427235 & -0.197159031090405 \tabularnewline
39 & 3950.67 & 3991.51040914938 & 49.9548513849808 & -40.8404091493783 & 0.291263764189424 \tabularnewline
40 & 4566.86 & 4093.20743372251 & 54.7843629237439 & 473.652566277488 & 1.00912692344004 \tabularnewline
41 & 3967.9 & 4165.07436606067 & 56.3787608289865 & -197.174366060667 & 0.332584903335799 \tabularnewline
42 & 4059.35 & 4224.53211677972 & 56.6660498398518 & -165.182116779723 & 0.0600358294533894 \tabularnewline
43 & 4215.38 & 4280.06379412194 & 56.5602208914439 & -64.683794121941 & -0.022176316526142 \tabularnewline
44 & 4856.13 & 4368.18108669526 & 59.504262692675 & 487.948913304742 & 0.617610568134301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297970&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]2157.07[/C][C]2157.07[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]2267.88[/C][C]2190.81164453096[/C][C]-0.556824918413321[/C][C]77.0683554690371[/C][C]0.939660058787899[/C][/ROW]
[ROW][C]3[/C][C]2375.38[/C][C]2296.99797721913[/C][C]7.48006402249999[/C][C]78.3820227808715[/C][C]1.57696373666142[/C][/ROW]
[ROW][C]4[/C][C]2803.62[/C][C]2518.89536559307[/C][C]25.7768946590251[/C][C]284.72463440693[/C][C]3.6168190821253[/C][/ROW]
[ROW][C]5[/C][C]2367.53[/C][C]2526.72765034315[/C][C]24.3363136268087[/C][C]-159.197650343154[/C][C]-0.3572958663918[/C][/ROW]
[ROW][C]6[/C][C]2439.08[/C][C]2501.75674433617[/C][C]20.7222985200143[/C][C]-62.6767443361703[/C][C]-1.04637957919325[/C][/ROW]
[ROW][C]7[/C][C]2533.76[/C][C]2504.4103408841[/C][C]19.4580297194972[/C][C]29.3496591159014[/C][C]-0.386865629203782[/C][/ROW]
[ROW][C]8[/C][C]2956.28[/C][C]2657.36208205503[/C][C]28.8751020277655[/C][C]298.917917944974[/C][C]2.83622943503365[/C][/ROW]
[ROW][C]9[/C][C]2484.24[/C][C]2653.7416604016[/C][C]26.4885050493864[/C][C]-169.501660401596[/C][C]-0.683300692929796[/C][/ROW]
[ROW][C]10[/C][C]2588.49[/C][C]2631.28116273893[/C][C]22.7117328803605[/C][C]-42.7911627389329[/C][C]-1.01948807532144[/C][/ROW]
[ROW][C]11[/C][C]2668.42[/C][C]2636.35176189658[/C][C]21.2873884426686[/C][C]32.0682381034209[/C][C]-0.364454713156057[/C][/ROW]
[ROW][C]12[/C][C]3085.62[/C][C]2793.15024356962[/C][C]32.6407455393263[/C][C]292.469756430375[/C][C]2.7811204297425[/C][/ROW]
[ROW][C]13[/C][C]2595.93[/C][C]2834.88046993453[/C][C]33.2961135899446[/C][C]-238.950469934526[/C][C]0.189960566809903[/C][/ROW]
[ROW][C]14[/C][C]2686.64[/C][C]2843.57536279727[/C][C]31.3852014672066[/C][C]-156.935362797274[/C][C]-0.520975372842783[/C][/ROW]
[ROW][C]15[/C][C]2779.43[/C][C]2854.9198384774[/C][C]29.6321246147877[/C][C]-75.4898384773975[/C][C]-0.398448994636375[/C][/ROW]
[ROW][C]16[/C][C]3221.13[/C][C]2886.64078153234[/C][C]29.8262661738688[/C][C]334.489218467657[/C][C]0.0397002992821105[/C][/ROW]
[ROW][C]17[/C][C]2752.7[/C][C]2906.08344118448[/C][C]28.8443699500043[/C][C]-153.383441184478[/C][C]-0.198810152240927[/C][/ROW]
[ROW][C]18[/C][C]2886.58[/C][C]2944.52193204102[/C][C]29.7496515520046[/C][C]-57.9419320410159[/C][C]0.188200507625629[/C][/ROW]
[ROW][C]19[/C][C]2958.05[/C][C]2983.43396989025[/C][C]30.607373280584[/C][C]-25.3839698902507[/C][C]0.182260879357475[/C][/ROW]
[ROW][C]20[/C][C]3444.61[/C][C]3047.86322571751[/C][C]33.7499957234271[/C][C]396.746774282488[/C][C]0.673828099949084[/C][/ROW]
[ROW][C]21[/C][C]2939.78[/C][C]3092.46913301656[/C][C]34.753343302048[/C][C]-152.689133016556[/C][C]0.215352777888678[/C][/ROW]
[ROW][C]22[/C][C]3088.73[/C][C]3143.01933102802[/C][C]36.2078566530562[/C][C]-54.2893310280224[/C][C]0.311738937915798[/C][/ROW]
[ROW][C]23[/C][C]3161.34[/C][C]3196.81676174929[/C][C]37.8219953321365[/C][C]-35.4767617492888[/C][C]0.345890806794951[/C][/ROW]
[ROW][C]24[/C][C]3672.39[/C][C]3287.96593192608[/C][C]42.7008122961089[/C][C]384.424068073924[/C][C]1.04936602766713[/C][/ROW]
[ROW][C]25[/C][C]3092.36[/C][C]3336.98635324519[/C][C]43.2787442602335[/C][C]-244.62635324519[/C][C]0.125138811087061[/C][/ROW]
[ROW][C]26[/C][C]3228.05[/C][C]3378.11867705503[/C][C]43.0811399631919[/C][C]-150.068677055028[/C][C]-0.0426344449186236[/C][/ROW]
[ROW][C]27[/C][C]3311.16[/C][C]3407.89177935218[/C][C]41.8441831544403[/C][C]-96.7317793521753[/C][C]-0.26198983223366[/C][/ROW]
[ROW][C]28[/C][C]3801.93[/C][C]3451.33625358767[/C][C]41.9938980649647[/C][C]350.593746412326[/C][C]0.0311268155542663[/C][/ROW]
[ROW][C]29[/C][C]3246.26[/C][C]3465.76600378079[/C][C]39.4093363473895[/C][C]-219.506003780793[/C][C]-0.534572210616193[/C][/ROW]
[ROW][C]30[/C][C]3309.22[/C][C]3456.76358143041[/C][C]34.8704757616577[/C][C]-147.543581430415[/C][C]-0.944416086703372[/C][/ROW]
[ROW][C]31[/C][C]3458.64[/C][C]3486.69835903202[/C][C]34.4081175412166[/C][C]-28.058359032016[/C][C]-0.0969219191083301[/C][/ROW]
[ROW][C]32[/C][C]4005.04[/C][C]3556.56798907864[/C][C]37.7262227320536[/C][C]448.472010921363[/C][C]0.697654739767283[/C][/ROW]
[ROW][C]33[/C][C]3477.65[/C][C]3625.23764333529[/C][C]40.6171400207475[/C][C]-147.587643335286[/C][C]0.607163996358766[/C][/ROW]
[ROW][C]34[/C][C]3524.42[/C][C]3654.96912767011[/C][C]39.602029358619[/C][C]-130.549127670113[/C][C]-0.212763803940607[/C][/ROW]
[ROW][C]35[/C][C]3699.5[/C][C]3718.46447732093[/C][C]41.8261627465289[/C][C]-18.964477320931[/C][C]0.466095196064516[/C][/ROW]
[ROW][C]36[/C][C]4247.68[/C][C]3802.69509238123[/C][C]45.7692382527557[/C][C]444.98490761877[/C][C]0.828324955413254[/C][/ROW]
[ROW][C]37[/C][C]3697.6[/C][C]3888.61039200139[/C][C]49.503013008709[/C][C]-191.010392001387[/C][C]0.786701527345595[/C][/ROW]
[ROW][C]38[/C][C]3746.72[/C][C]3928.06661942724[/C][C]48.5673907039435[/C][C]-181.346619427235[/C][C]-0.197159031090405[/C][/ROW]
[ROW][C]39[/C][C]3950.67[/C][C]3991.51040914938[/C][C]49.9548513849808[/C][C]-40.8404091493783[/C][C]0.291263764189424[/C][/ROW]
[ROW][C]40[/C][C]4566.86[/C][C]4093.20743372251[/C][C]54.7843629237439[/C][C]473.652566277488[/C][C]1.00912692344004[/C][/ROW]
[ROW][C]41[/C][C]3967.9[/C][C]4165.07436606067[/C][C]56.3787608289865[/C][C]-197.174366060667[/C][C]0.332584903335799[/C][/ROW]
[ROW][C]42[/C][C]4059.35[/C][C]4224.53211677972[/C][C]56.6660498398518[/C][C]-165.182116779723[/C][C]0.0600358294533894[/C][/ROW]
[ROW][C]43[/C][C]4215.38[/C][C]4280.06379412194[/C][C]56.5602208914439[/C][C]-64.683794121941[/C][C]-0.022176316526142[/C][/ROW]
[ROW][C]44[/C][C]4856.13[/C][C]4368.18108669526[/C][C]59.504262692675[/C][C]487.948913304742[/C][C]0.617610568134301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297970&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297970&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
12157.072157.07000
22267.882190.81164453096-0.55682491841332177.06835546903710.939660058787899
32375.382296.997977219137.4800640224999978.38202278087151.57696373666142
42803.622518.8953655930725.7768946590251284.724634406933.6168190821253
52367.532526.7276503431524.3363136268087-159.197650343154-0.3572958663918
62439.082501.7567443361720.7222985200143-62.6767443361703-1.04637957919325
72533.762504.410340884119.458029719497229.3496591159014-0.386865629203782
82956.282657.3620820550328.8751020277655298.9179179449742.83622943503365
92484.242653.741660401626.4885050493864-169.501660401596-0.683300692929796
102588.492631.2811627389322.7117328803605-42.7911627389329-1.01948807532144
112668.422636.3517618965821.287388442668632.0682381034209-0.364454713156057
123085.622793.1502435696232.6407455393263292.4697564303752.7811204297425
132595.932834.8804699345333.2961135899446-238.9504699345260.189960566809903
142686.642843.5753627972731.3852014672066-156.935362797274-0.520975372842783
152779.432854.919838477429.6321246147877-75.4898384773975-0.398448994636375
163221.132886.6407815323429.8262661738688334.4892184676570.0397002992821105
172752.72906.0834411844828.8443699500043-153.383441184478-0.198810152240927
182886.582944.5219320410229.7496515520046-57.94193204101590.188200507625629
192958.052983.4339698902530.607373280584-25.38396989025070.182260879357475
203444.613047.8632257175133.7499957234271396.7467742824880.673828099949084
212939.783092.4691330165634.753343302048-152.6891330165560.215352777888678
223088.733143.0193310280236.2078566530562-54.28933102802240.311738937915798
233161.343196.8167617492937.8219953321365-35.47676174928880.345890806794951
243672.393287.9659319260842.7008122961089384.4240680739241.04936602766713
253092.363336.9863532451943.2787442602335-244.626353245190.125138811087061
263228.053378.1186770550343.0811399631919-150.068677055028-0.0426344449186236
273311.163407.8917793521841.8441831544403-96.7317793521753-0.26198983223366
283801.933451.3362535876741.9938980649647350.5937464123260.0311268155542663
293246.263465.7660037807939.4093363473895-219.506003780793-0.534572210616193
303309.223456.7635814304134.8704757616577-147.543581430415-0.944416086703372
313458.643486.6983590320234.4081175412166-28.058359032016-0.0969219191083301
324005.043556.5679890786437.7262227320536448.4720109213630.697654739767283
333477.653625.2376433352940.6171400207475-147.5876433352860.607163996358766
343524.423654.9691276701139.602029358619-130.549127670113-0.212763803940607
353699.53718.4644773209341.8261627465289-18.9644773209310.466095196064516
364247.683802.6950923812345.7692382527557444.984907618770.828324955413254
373697.63888.6103920013949.503013008709-191.0103920013870.786701527345595
383746.723928.0666194272448.5673907039435-181.346619427235-0.197159031090405
393950.673991.5104091493849.9548513849808-40.84040914937830.291263764189424
404566.864093.2074337225154.7843629237439473.6525662774881.00912692344004
413967.94165.0743660606756.3787608289865-197.1743660606670.332584903335799
424059.354224.5321167797256.6660498398518-165.1821167797230.0600358294533894
434215.384280.0637941219456.5602208914439-64.683794121941-0.022176316526142
444856.134368.1810866952659.504262692675487.9489133047420.617610568134301







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14250.066907176084436.76018906841-186.693281892329
24330.799493320594495.43841947316-164.63892615257
34500.188669854344554.11664987792-53.9279800235767
45039.739471783514612.79488028267426.944591500838
54483.632894103594671.47311068743-187.840216583835
64526.476829828044730.15134109219-203.674511264148
74710.822108043634788.82957149694-78.0074634533074
85305.745682289454847.5078019017458.237880387758
94696.840259535174906.18603230645-209.345772771281
104780.944555100934964.86426271121-183.919707610277
114928.359839642345023.54249311596-95.1826534736213
125560.268764857075082.22072352072478.048041336349
134954.205672033145140.89895392547-186.693281892329
145034.938258177665199.57718433023-164.63892615257
155204.327434711415258.25541473499-53.9279800235767
165743.878236640585316.93364513974426.944591500838
175187.771658960665375.6118755445-187.840216583835
185230.61559468515434.29010594925-203.674511264148

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4250.06690717608 & 4436.76018906841 & -186.693281892329 \tabularnewline
2 & 4330.79949332059 & 4495.43841947316 & -164.63892615257 \tabularnewline
3 & 4500.18866985434 & 4554.11664987792 & -53.9279800235767 \tabularnewline
4 & 5039.73947178351 & 4612.79488028267 & 426.944591500838 \tabularnewline
5 & 4483.63289410359 & 4671.47311068743 & -187.840216583835 \tabularnewline
6 & 4526.47682982804 & 4730.15134109219 & -203.674511264148 \tabularnewline
7 & 4710.82210804363 & 4788.82957149694 & -78.0074634533074 \tabularnewline
8 & 5305.74568228945 & 4847.5078019017 & 458.237880387758 \tabularnewline
9 & 4696.84025953517 & 4906.18603230645 & -209.345772771281 \tabularnewline
10 & 4780.94455510093 & 4964.86426271121 & -183.919707610277 \tabularnewline
11 & 4928.35983964234 & 5023.54249311596 & -95.1826534736213 \tabularnewline
12 & 5560.26876485707 & 5082.22072352072 & 478.048041336349 \tabularnewline
13 & 4954.20567203314 & 5140.89895392547 & -186.693281892329 \tabularnewline
14 & 5034.93825817766 & 5199.57718433023 & -164.63892615257 \tabularnewline
15 & 5204.32743471141 & 5258.25541473499 & -53.9279800235767 \tabularnewline
16 & 5743.87823664058 & 5316.93364513974 & 426.944591500838 \tabularnewline
17 & 5187.77165896066 & 5375.6118755445 & -187.840216583835 \tabularnewline
18 & 5230.6155946851 & 5434.29010594925 & -203.674511264148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297970&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]4250.06690717608[/C][C]4436.76018906841[/C][C]-186.693281892329[/C][/ROW]
[ROW][C]2[/C][C]4330.79949332059[/C][C]4495.43841947316[/C][C]-164.63892615257[/C][/ROW]
[ROW][C]3[/C][C]4500.18866985434[/C][C]4554.11664987792[/C][C]-53.9279800235767[/C][/ROW]
[ROW][C]4[/C][C]5039.73947178351[/C][C]4612.79488028267[/C][C]426.944591500838[/C][/ROW]
[ROW][C]5[/C][C]4483.63289410359[/C][C]4671.47311068743[/C][C]-187.840216583835[/C][/ROW]
[ROW][C]6[/C][C]4526.47682982804[/C][C]4730.15134109219[/C][C]-203.674511264148[/C][/ROW]
[ROW][C]7[/C][C]4710.82210804363[/C][C]4788.82957149694[/C][C]-78.0074634533074[/C][/ROW]
[ROW][C]8[/C][C]5305.74568228945[/C][C]4847.5078019017[/C][C]458.237880387758[/C][/ROW]
[ROW][C]9[/C][C]4696.84025953517[/C][C]4906.18603230645[/C][C]-209.345772771281[/C][/ROW]
[ROW][C]10[/C][C]4780.94455510093[/C][C]4964.86426271121[/C][C]-183.919707610277[/C][/ROW]
[ROW][C]11[/C][C]4928.35983964234[/C][C]5023.54249311596[/C][C]-95.1826534736213[/C][/ROW]
[ROW][C]12[/C][C]5560.26876485707[/C][C]5082.22072352072[/C][C]478.048041336349[/C][/ROW]
[ROW][C]13[/C][C]4954.20567203314[/C][C]5140.89895392547[/C][C]-186.693281892329[/C][/ROW]
[ROW][C]14[/C][C]5034.93825817766[/C][C]5199.57718433023[/C][C]-164.63892615257[/C][/ROW]
[ROW][C]15[/C][C]5204.32743471141[/C][C]5258.25541473499[/C][C]-53.9279800235767[/C][/ROW]
[ROW][C]16[/C][C]5743.87823664058[/C][C]5316.93364513974[/C][C]426.944591500838[/C][/ROW]
[ROW][C]17[/C][C]5187.77165896066[/C][C]5375.6118755445[/C][C]-187.840216583835[/C][/ROW]
[ROW][C]18[/C][C]5230.6155946851[/C][C]5434.29010594925[/C][C]-203.674511264148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297970&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297970&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
14250.066907176084436.76018906841-186.693281892329
24330.799493320594495.43841947316-164.63892615257
34500.188669854344554.11664987792-53.9279800235767
45039.739471783514612.79488028267426.944591500838
54483.632894103594671.47311068743-187.840216583835
64526.476829828044730.15134109219-203.674511264148
74710.822108043634788.82957149694-78.0074634533074
85305.745682289454847.5078019017458.237880387758
94696.840259535174906.18603230645-209.345772771281
104780.944555100934964.86426271121-183.919707610277
114928.359839642345023.54249311596-95.1826534736213
125560.268764857075082.22072352072478.048041336349
134954.205672033145140.89895392547-186.693281892329
145034.938258177665199.57718433023-164.63892615257
155204.327434711415258.25541473499-53.9279800235767
165743.878236640585316.93364513974426.944591500838
175187.771658960665375.6118755445-187.840216583835
185230.61559468515434.29010594925-203.674511264148



Parameters (Session):
par1 = 12 ; par2 = 18 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = 18 ; 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')