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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 computationTue, 13 Dec 2016 22:35:47 +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/13/t1481665009ojn5yxspm0sku0l.htm/, Retrieved Sat, 04 May 2024 23:13:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299242, Retrieved Sat, 04 May 2024 23:13:30 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-13 21:35:47] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
4766
4815
4920
4936
4947
4904
4877
4899
4896
4937
5155
5119
5119
5147
5136
5135
5119
5153
5111
5109
5032
4989
4929
4919
4883
4850
4857
4850
4831
4793
4782
4809
4725
4698
4639
4528
4459
4405
4314
4252
4245
4177
4122
4034
3955
3928
3884
3826
3713
3672
3682
3615
3529
3529
3479
3446
3385
3296
3234
3188
3078
3018
2983




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299242&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299242&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
147664766000
248154812.474791801172.963518651126562.525208198830940.66228095632841
349204917.219956789558.435753311871142.780043210452972.36761309858669
449364933.202488628899.00570290474632.797511371113590.173492102286239
549474944.198314027979.192270393844452.801685972034640.0452883495110937
649044901.295738399863.541728310814412.70426160014145-1.17557184943955
748774874.34591835138-0.1175521371489082.65408164862322-0.683448887094256
848994896.314255018212.728301050802862.685744981788360.49244004354805
948964893.321345726471.953019596458392.67865427352718-0.127049444367695
1049374934.279793252537.431409756800292.720206747470670.863545267586828
1151555152.0879702666837.74338327718222.912029733322734.64694178988766
1251195116.1452990481826.9311479427742.85470095181959-1.62487211678341
1351195148.1883072629527.6271835438476-29.18830726295460.132530189007543
1451475145.0486122858423.01237010146551.95138771415881-0.574404618860977
1551365134.0407262094917.87840451201251.95927379051491-0.747532267109693
1651355133.0370156481215.01491211061591.96298435187953-0.414734107926954
1751195117.0318475257410.29410898741971.96815247426318-0.681144629214107
1851535151.0351949546313.91142525524761.964805045374020.520508150209135
1951115109.028506767775.364539782030071.97149323223457-1.22744424019454
2051095107.027760652934.237317298453781.97223934706549-0.161657759305843
2150325030.02079124729-8.208356920543961.97920875271254-1.78307847684908
2249894987.01826402464-13.54199472141481.98173597536298-0.763596567180153
2349294927.01540695749-20.667470076761.98459304251255-1.01960287216095
2449194917.01596233216-19.03079912687321.984037667838940.234109284488027
2548834903.65295730663-18.174854447558-20.65295730663170.135308509321211
2648504848.65826198676-23.7463027767461.34173801324382-0.734059575949581
2748574855.6679199415-19.02400466607841.332080058502230.674696191271131
2848504848.6711184484-17.17735644122091.328881551599980.263855949005025
2948314829.67070806568-17.45726648795061.32929193432385-0.0399964235866372
3047934791.66679301756-20.61199409343611.33320698243742-0.45079473541769
3147824780.668343567-19.13592142871651.331656433002350.210928347560877
3248094807.67464306281-12.0511358217821.325356937185131.01242127827636
3347254723.66632761043-23.09972016361931.33367238957486-1.57887026275587
3446984696.66594605847-23.69864870137111.33405394152649-0.085589124483574
3546394637.66302294508-29.11950749289961.336977054921-0.77466577762437
3645284526.65728400722-41.69298582410191.34271599278088-1.79681617150488
3744594475.10846075109-43.1936079838888-16.1084607510888-0.228991152415669
3844054403.83686271901-47.45382828898851.16313728098952-0.575364988694938
3943144312.82600162039-54.14359978589821.17399837960824-0.955556434842946
4042524250.82434413381-55.35038716702641.17565586618633-0.172399026472438
4142454243.83297801702-47.92415755952681.167021982979431.06099828490723
4241774175.82994367297-51.00744799635841.17005632702469-0.440545757157532
4341224120.82943289747-51.62060451561541.17056710252988-0.0876132176438894
4440344032.82549353465-57.20739001222581.17450646535053-0.798317812429812
4539553953.82349609979-60.55400349245371.17650390021341-0.47822306010139
4639283926.82609926617-55.40132149719631.173900733830730.736319456649976
4738843882.82684796633-53.6505117882971.173152033668350.250194407986933
4838263824.82660620506-54.31842211372991.17339379493808-0.0954466972872589
4937133730.00159608837-60.5006152255524-17.0015960883715-0.928175967412237
5036723670.44636591157-60.35683705759181.553634088433240.0196681990195506
5136823680.46041638889-49.54914419783291.539583611112131.54388765173355
5236153613.45746536687-52.22954146152761.54253463313463-0.382939515717491
5335293527.45263171147-57.41620002274161.54736828852531-0.741059861028827
5435293527.4595877232-48.59835602407111.540412276799681.2599486399044
5534793477.45944399114-48.81360911169951.54055600886357-0.0307579642993947
5634463444.46081657583-46.38514883950941.539183424169280.347017943678023
5733853383.4597428429-48.62947534411181.54025715709659-0.320712648160025
5832963294.45723233798-54.82888083909741.54276766202092-0.885903929499196
5932343232.45685487079-55.93008614948391.54314512921367-0.157365513415991
6031883186.45729729759-54.40522149168031.54270270240560.21790937702848
6130783097.73175996294-59.6499112414886-19.7317599629357-0.779811462826668
6230183016.3592327916-62.95901358943951.64076720840338-0.456306884787994
6329832981.3638614219-58.66441946403381.636138578104030.613526728057378

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 4766 & 4766 & 0 & 0 & 0 \tabularnewline
2 & 4815 & 4812.47479180117 & 2.96351865112656 & 2.52520819883094 & 0.66228095632841 \tabularnewline
3 & 4920 & 4917.21995678955 & 8.43575331187114 & 2.78004321045297 & 2.36761309858669 \tabularnewline
4 & 4936 & 4933.20248862889 & 9.0057029047463 & 2.79751137111359 & 0.173492102286239 \tabularnewline
5 & 4947 & 4944.19831402797 & 9.19227039384445 & 2.80168597203464 & 0.0452883495110937 \tabularnewline
6 & 4904 & 4901.29573839986 & 3.54172831081441 & 2.70426160014145 & -1.17557184943955 \tabularnewline
7 & 4877 & 4874.34591835138 & -0.117552137148908 & 2.65408164862322 & -0.683448887094256 \tabularnewline
8 & 4899 & 4896.31425501821 & 2.72830105080286 & 2.68574498178836 & 0.49244004354805 \tabularnewline
9 & 4896 & 4893.32134572647 & 1.95301959645839 & 2.67865427352718 & -0.127049444367695 \tabularnewline
10 & 4937 & 4934.27979325253 & 7.43140975680029 & 2.72020674747067 & 0.863545267586828 \tabularnewline
11 & 5155 & 5152.08797026668 & 37.7433832771822 & 2.91202973332273 & 4.64694178988766 \tabularnewline
12 & 5119 & 5116.14529904818 & 26.931147942774 & 2.85470095181959 & -1.62487211678341 \tabularnewline
13 & 5119 & 5148.18830726295 & 27.6271835438476 & -29.1883072629546 & 0.132530189007543 \tabularnewline
14 & 5147 & 5145.04861228584 & 23.0123701014655 & 1.95138771415881 & -0.574404618860977 \tabularnewline
15 & 5136 & 5134.04072620949 & 17.8784045120125 & 1.95927379051491 & -0.747532267109693 \tabularnewline
16 & 5135 & 5133.03701564812 & 15.0149121106159 & 1.96298435187953 & -0.414734107926954 \tabularnewline
17 & 5119 & 5117.03184752574 & 10.2941089874197 & 1.96815247426318 & -0.681144629214107 \tabularnewline
18 & 5153 & 5151.03519495463 & 13.9114252552476 & 1.96480504537402 & 0.520508150209135 \tabularnewline
19 & 5111 & 5109.02850676777 & 5.36453978203007 & 1.97149323223457 & -1.22744424019454 \tabularnewline
20 & 5109 & 5107.02776065293 & 4.23731729845378 & 1.97223934706549 & -0.161657759305843 \tabularnewline
21 & 5032 & 5030.02079124729 & -8.20835692054396 & 1.97920875271254 & -1.78307847684908 \tabularnewline
22 & 4989 & 4987.01826402464 & -13.5419947214148 & 1.98173597536298 & -0.763596567180153 \tabularnewline
23 & 4929 & 4927.01540695749 & -20.66747007676 & 1.98459304251255 & -1.01960287216095 \tabularnewline
24 & 4919 & 4917.01596233216 & -19.0307991268732 & 1.98403766783894 & 0.234109284488027 \tabularnewline
25 & 4883 & 4903.65295730663 & -18.174854447558 & -20.6529573066317 & 0.135308509321211 \tabularnewline
26 & 4850 & 4848.65826198676 & -23.746302776746 & 1.34173801324382 & -0.734059575949581 \tabularnewline
27 & 4857 & 4855.6679199415 & -19.0240046660784 & 1.33208005850223 & 0.674696191271131 \tabularnewline
28 & 4850 & 4848.6711184484 & -17.1773564412209 & 1.32888155159998 & 0.263855949005025 \tabularnewline
29 & 4831 & 4829.67070806568 & -17.4572664879506 & 1.32929193432385 & -0.0399964235866372 \tabularnewline
30 & 4793 & 4791.66679301756 & -20.6119940934361 & 1.33320698243742 & -0.45079473541769 \tabularnewline
31 & 4782 & 4780.668343567 & -19.1359214287165 & 1.33165643300235 & 0.210928347560877 \tabularnewline
32 & 4809 & 4807.67464306281 & -12.051135821782 & 1.32535693718513 & 1.01242127827636 \tabularnewline
33 & 4725 & 4723.66632761043 & -23.0997201636193 & 1.33367238957486 & -1.57887026275587 \tabularnewline
34 & 4698 & 4696.66594605847 & -23.6986487013711 & 1.33405394152649 & -0.085589124483574 \tabularnewline
35 & 4639 & 4637.66302294508 & -29.1195074928996 & 1.336977054921 & -0.77466577762437 \tabularnewline
36 & 4528 & 4526.65728400722 & -41.6929858241019 & 1.34271599278088 & -1.79681617150488 \tabularnewline
37 & 4459 & 4475.10846075109 & -43.1936079838888 & -16.1084607510888 & -0.228991152415669 \tabularnewline
38 & 4405 & 4403.83686271901 & -47.4538282889885 & 1.16313728098952 & -0.575364988694938 \tabularnewline
39 & 4314 & 4312.82600162039 & -54.1435997858982 & 1.17399837960824 & -0.955556434842946 \tabularnewline
40 & 4252 & 4250.82434413381 & -55.3503871670264 & 1.17565586618633 & -0.172399026472438 \tabularnewline
41 & 4245 & 4243.83297801702 & -47.9241575595268 & 1.16702198297943 & 1.06099828490723 \tabularnewline
42 & 4177 & 4175.82994367297 & -51.0074479963584 & 1.17005632702469 & -0.440545757157532 \tabularnewline
43 & 4122 & 4120.82943289747 & -51.6206045156154 & 1.17056710252988 & -0.0876132176438894 \tabularnewline
44 & 4034 & 4032.82549353465 & -57.2073900122258 & 1.17450646535053 & -0.798317812429812 \tabularnewline
45 & 3955 & 3953.82349609979 & -60.5540034924537 & 1.17650390021341 & -0.47822306010139 \tabularnewline
46 & 3928 & 3926.82609926617 & -55.4013214971963 & 1.17390073383073 & 0.736319456649976 \tabularnewline
47 & 3884 & 3882.82684796633 & -53.650511788297 & 1.17315203366835 & 0.250194407986933 \tabularnewline
48 & 3826 & 3824.82660620506 & -54.3184221137299 & 1.17339379493808 & -0.0954466972872589 \tabularnewline
49 & 3713 & 3730.00159608837 & -60.5006152255524 & -17.0015960883715 & -0.928175967412237 \tabularnewline
50 & 3672 & 3670.44636591157 & -60.3568370575918 & 1.55363408843324 & 0.0196681990195506 \tabularnewline
51 & 3682 & 3680.46041638889 & -49.5491441978329 & 1.53958361111213 & 1.54388765173355 \tabularnewline
52 & 3615 & 3613.45746536687 & -52.2295414615276 & 1.54253463313463 & -0.382939515717491 \tabularnewline
53 & 3529 & 3527.45263171147 & -57.4162000227416 & 1.54736828852531 & -0.741059861028827 \tabularnewline
54 & 3529 & 3527.4595877232 & -48.5983560240711 & 1.54041227679968 & 1.2599486399044 \tabularnewline
55 & 3479 & 3477.45944399114 & -48.8136091116995 & 1.54055600886357 & -0.0307579642993947 \tabularnewline
56 & 3446 & 3444.46081657583 & -46.3851488395094 & 1.53918342416928 & 0.347017943678023 \tabularnewline
57 & 3385 & 3383.4597428429 & -48.6294753441118 & 1.54025715709659 & -0.320712648160025 \tabularnewline
58 & 3296 & 3294.45723233798 & -54.8288808390974 & 1.54276766202092 & -0.885903929499196 \tabularnewline
59 & 3234 & 3232.45685487079 & -55.9300861494839 & 1.54314512921367 & -0.157365513415991 \tabularnewline
60 & 3188 & 3186.45729729759 & -54.4052214916803 & 1.5427027024056 & 0.21790937702848 \tabularnewline
61 & 3078 & 3097.73175996294 & -59.6499112414886 & -19.7317599629357 & -0.779811462826668 \tabularnewline
62 & 3018 & 3016.3592327916 & -62.9590135894395 & 1.64076720840338 & -0.456306884787994 \tabularnewline
63 & 2983 & 2981.3638614219 & -58.6644194640338 & 1.63613857810403 & 0.613526728057378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299242&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]4766[/C][C]4766[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]4815[/C][C]4812.47479180117[/C][C]2.96351865112656[/C][C]2.52520819883094[/C][C]0.66228095632841[/C][/ROW]
[ROW][C]3[/C][C]4920[/C][C]4917.21995678955[/C][C]8.43575331187114[/C][C]2.78004321045297[/C][C]2.36761309858669[/C][/ROW]
[ROW][C]4[/C][C]4936[/C][C]4933.20248862889[/C][C]9.0057029047463[/C][C]2.79751137111359[/C][C]0.173492102286239[/C][/ROW]
[ROW][C]5[/C][C]4947[/C][C]4944.19831402797[/C][C]9.19227039384445[/C][C]2.80168597203464[/C][C]0.0452883495110937[/C][/ROW]
[ROW][C]6[/C][C]4904[/C][C]4901.29573839986[/C][C]3.54172831081441[/C][C]2.70426160014145[/C][C]-1.17557184943955[/C][/ROW]
[ROW][C]7[/C][C]4877[/C][C]4874.34591835138[/C][C]-0.117552137148908[/C][C]2.65408164862322[/C][C]-0.683448887094256[/C][/ROW]
[ROW][C]8[/C][C]4899[/C][C]4896.31425501821[/C][C]2.72830105080286[/C][C]2.68574498178836[/C][C]0.49244004354805[/C][/ROW]
[ROW][C]9[/C][C]4896[/C][C]4893.32134572647[/C][C]1.95301959645839[/C][C]2.67865427352718[/C][C]-0.127049444367695[/C][/ROW]
[ROW][C]10[/C][C]4937[/C][C]4934.27979325253[/C][C]7.43140975680029[/C][C]2.72020674747067[/C][C]0.863545267586828[/C][/ROW]
[ROW][C]11[/C][C]5155[/C][C]5152.08797026668[/C][C]37.7433832771822[/C][C]2.91202973332273[/C][C]4.64694178988766[/C][/ROW]
[ROW][C]12[/C][C]5119[/C][C]5116.14529904818[/C][C]26.931147942774[/C][C]2.85470095181959[/C][C]-1.62487211678341[/C][/ROW]
[ROW][C]13[/C][C]5119[/C][C]5148.18830726295[/C][C]27.6271835438476[/C][C]-29.1883072629546[/C][C]0.132530189007543[/C][/ROW]
[ROW][C]14[/C][C]5147[/C][C]5145.04861228584[/C][C]23.0123701014655[/C][C]1.95138771415881[/C][C]-0.574404618860977[/C][/ROW]
[ROW][C]15[/C][C]5136[/C][C]5134.04072620949[/C][C]17.8784045120125[/C][C]1.95927379051491[/C][C]-0.747532267109693[/C][/ROW]
[ROW][C]16[/C][C]5135[/C][C]5133.03701564812[/C][C]15.0149121106159[/C][C]1.96298435187953[/C][C]-0.414734107926954[/C][/ROW]
[ROW][C]17[/C][C]5119[/C][C]5117.03184752574[/C][C]10.2941089874197[/C][C]1.96815247426318[/C][C]-0.681144629214107[/C][/ROW]
[ROW][C]18[/C][C]5153[/C][C]5151.03519495463[/C][C]13.9114252552476[/C][C]1.96480504537402[/C][C]0.520508150209135[/C][/ROW]
[ROW][C]19[/C][C]5111[/C][C]5109.02850676777[/C][C]5.36453978203007[/C][C]1.97149323223457[/C][C]-1.22744424019454[/C][/ROW]
[ROW][C]20[/C][C]5109[/C][C]5107.02776065293[/C][C]4.23731729845378[/C][C]1.97223934706549[/C][C]-0.161657759305843[/C][/ROW]
[ROW][C]21[/C][C]5032[/C][C]5030.02079124729[/C][C]-8.20835692054396[/C][C]1.97920875271254[/C][C]-1.78307847684908[/C][/ROW]
[ROW][C]22[/C][C]4989[/C][C]4987.01826402464[/C][C]-13.5419947214148[/C][C]1.98173597536298[/C][C]-0.763596567180153[/C][/ROW]
[ROW][C]23[/C][C]4929[/C][C]4927.01540695749[/C][C]-20.66747007676[/C][C]1.98459304251255[/C][C]-1.01960287216095[/C][/ROW]
[ROW][C]24[/C][C]4919[/C][C]4917.01596233216[/C][C]-19.0307991268732[/C][C]1.98403766783894[/C][C]0.234109284488027[/C][/ROW]
[ROW][C]25[/C][C]4883[/C][C]4903.65295730663[/C][C]-18.174854447558[/C][C]-20.6529573066317[/C][C]0.135308509321211[/C][/ROW]
[ROW][C]26[/C][C]4850[/C][C]4848.65826198676[/C][C]-23.746302776746[/C][C]1.34173801324382[/C][C]-0.734059575949581[/C][/ROW]
[ROW][C]27[/C][C]4857[/C][C]4855.6679199415[/C][C]-19.0240046660784[/C][C]1.33208005850223[/C][C]0.674696191271131[/C][/ROW]
[ROW][C]28[/C][C]4850[/C][C]4848.6711184484[/C][C]-17.1773564412209[/C][C]1.32888155159998[/C][C]0.263855949005025[/C][/ROW]
[ROW][C]29[/C][C]4831[/C][C]4829.67070806568[/C][C]-17.4572664879506[/C][C]1.32929193432385[/C][C]-0.0399964235866372[/C][/ROW]
[ROW][C]30[/C][C]4793[/C][C]4791.66679301756[/C][C]-20.6119940934361[/C][C]1.33320698243742[/C][C]-0.45079473541769[/C][/ROW]
[ROW][C]31[/C][C]4782[/C][C]4780.668343567[/C][C]-19.1359214287165[/C][C]1.33165643300235[/C][C]0.210928347560877[/C][/ROW]
[ROW][C]32[/C][C]4809[/C][C]4807.67464306281[/C][C]-12.051135821782[/C][C]1.32535693718513[/C][C]1.01242127827636[/C][/ROW]
[ROW][C]33[/C][C]4725[/C][C]4723.66632761043[/C][C]-23.0997201636193[/C][C]1.33367238957486[/C][C]-1.57887026275587[/C][/ROW]
[ROW][C]34[/C][C]4698[/C][C]4696.66594605847[/C][C]-23.6986487013711[/C][C]1.33405394152649[/C][C]-0.085589124483574[/C][/ROW]
[ROW][C]35[/C][C]4639[/C][C]4637.66302294508[/C][C]-29.1195074928996[/C][C]1.336977054921[/C][C]-0.77466577762437[/C][/ROW]
[ROW][C]36[/C][C]4528[/C][C]4526.65728400722[/C][C]-41.6929858241019[/C][C]1.34271599278088[/C][C]-1.79681617150488[/C][/ROW]
[ROW][C]37[/C][C]4459[/C][C]4475.10846075109[/C][C]-43.1936079838888[/C][C]-16.1084607510888[/C][C]-0.228991152415669[/C][/ROW]
[ROW][C]38[/C][C]4405[/C][C]4403.83686271901[/C][C]-47.4538282889885[/C][C]1.16313728098952[/C][C]-0.575364988694938[/C][/ROW]
[ROW][C]39[/C][C]4314[/C][C]4312.82600162039[/C][C]-54.1435997858982[/C][C]1.17399837960824[/C][C]-0.955556434842946[/C][/ROW]
[ROW][C]40[/C][C]4252[/C][C]4250.82434413381[/C][C]-55.3503871670264[/C][C]1.17565586618633[/C][C]-0.172399026472438[/C][/ROW]
[ROW][C]41[/C][C]4245[/C][C]4243.83297801702[/C][C]-47.9241575595268[/C][C]1.16702198297943[/C][C]1.06099828490723[/C][/ROW]
[ROW][C]42[/C][C]4177[/C][C]4175.82994367297[/C][C]-51.0074479963584[/C][C]1.17005632702469[/C][C]-0.440545757157532[/C][/ROW]
[ROW][C]43[/C][C]4122[/C][C]4120.82943289747[/C][C]-51.6206045156154[/C][C]1.17056710252988[/C][C]-0.0876132176438894[/C][/ROW]
[ROW][C]44[/C][C]4034[/C][C]4032.82549353465[/C][C]-57.2073900122258[/C][C]1.17450646535053[/C][C]-0.798317812429812[/C][/ROW]
[ROW][C]45[/C][C]3955[/C][C]3953.82349609979[/C][C]-60.5540034924537[/C][C]1.17650390021341[/C][C]-0.47822306010139[/C][/ROW]
[ROW][C]46[/C][C]3928[/C][C]3926.82609926617[/C][C]-55.4013214971963[/C][C]1.17390073383073[/C][C]0.736319456649976[/C][/ROW]
[ROW][C]47[/C][C]3884[/C][C]3882.82684796633[/C][C]-53.650511788297[/C][C]1.17315203366835[/C][C]0.250194407986933[/C][/ROW]
[ROW][C]48[/C][C]3826[/C][C]3824.82660620506[/C][C]-54.3184221137299[/C][C]1.17339379493808[/C][C]-0.0954466972872589[/C][/ROW]
[ROW][C]49[/C][C]3713[/C][C]3730.00159608837[/C][C]-60.5006152255524[/C][C]-17.0015960883715[/C][C]-0.928175967412237[/C][/ROW]
[ROW][C]50[/C][C]3672[/C][C]3670.44636591157[/C][C]-60.3568370575918[/C][C]1.55363408843324[/C][C]0.0196681990195506[/C][/ROW]
[ROW][C]51[/C][C]3682[/C][C]3680.46041638889[/C][C]-49.5491441978329[/C][C]1.53958361111213[/C][C]1.54388765173355[/C][/ROW]
[ROW][C]52[/C][C]3615[/C][C]3613.45746536687[/C][C]-52.2295414615276[/C][C]1.54253463313463[/C][C]-0.382939515717491[/C][/ROW]
[ROW][C]53[/C][C]3529[/C][C]3527.45263171147[/C][C]-57.4162000227416[/C][C]1.54736828852531[/C][C]-0.741059861028827[/C][/ROW]
[ROW][C]54[/C][C]3529[/C][C]3527.4595877232[/C][C]-48.5983560240711[/C][C]1.54041227679968[/C][C]1.2599486399044[/C][/ROW]
[ROW][C]55[/C][C]3479[/C][C]3477.45944399114[/C][C]-48.8136091116995[/C][C]1.54055600886357[/C][C]-0.0307579642993947[/C][/ROW]
[ROW][C]56[/C][C]3446[/C][C]3444.46081657583[/C][C]-46.3851488395094[/C][C]1.53918342416928[/C][C]0.347017943678023[/C][/ROW]
[ROW][C]57[/C][C]3385[/C][C]3383.4597428429[/C][C]-48.6294753441118[/C][C]1.54025715709659[/C][C]-0.320712648160025[/C][/ROW]
[ROW][C]58[/C][C]3296[/C][C]3294.45723233798[/C][C]-54.8288808390974[/C][C]1.54276766202092[/C][C]-0.885903929499196[/C][/ROW]
[ROW][C]59[/C][C]3234[/C][C]3232.45685487079[/C][C]-55.9300861494839[/C][C]1.54314512921367[/C][C]-0.157365513415991[/C][/ROW]
[ROW][C]60[/C][C]3188[/C][C]3186.45729729759[/C][C]-54.4052214916803[/C][C]1.5427027024056[/C][C]0.21790937702848[/C][/ROW]
[ROW][C]61[/C][C]3078[/C][C]3097.73175996294[/C][C]-59.6499112414886[/C][C]-19.7317599629357[/C][C]-0.779811462826668[/C][/ROW]
[ROW][C]62[/C][C]3018[/C][C]3016.3592327916[/C][C]-62.9590135894395[/C][C]1.64076720840338[/C][C]-0.456306884787994[/C][/ROW]
[ROW][C]63[/C][C]2983[/C][C]2981.3638614219[/C][C]-58.6644194640338[/C][C]1.63613857810403[/C][C]0.613526728057378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299242&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
147664766000
248154812.474791801172.963518651126562.525208198830940.66228095632841
349204917.219956789558.435753311871142.780043210452972.36761309858669
449364933.202488628899.00570290474632.797511371113590.173492102286239
549474944.198314027979.192270393844452.801685972034640.0452883495110937
649044901.295738399863.541728310814412.70426160014145-1.17557184943955
748774874.34591835138-0.1175521371489082.65408164862322-0.683448887094256
848994896.314255018212.728301050802862.685744981788360.49244004354805
948964893.321345726471.953019596458392.67865427352718-0.127049444367695
1049374934.279793252537.431409756800292.720206747470670.863545267586828
1151555152.0879702666837.74338327718222.912029733322734.64694178988766
1251195116.1452990481826.9311479427742.85470095181959-1.62487211678341
1351195148.1883072629527.6271835438476-29.18830726295460.132530189007543
1451475145.0486122858423.01237010146551.95138771415881-0.574404618860977
1551365134.0407262094917.87840451201251.95927379051491-0.747532267109693
1651355133.0370156481215.01491211061591.96298435187953-0.414734107926954
1751195117.0318475257410.29410898741971.96815247426318-0.681144629214107
1851535151.0351949546313.91142525524761.964805045374020.520508150209135
1951115109.028506767775.364539782030071.97149323223457-1.22744424019454
2051095107.027760652934.237317298453781.97223934706549-0.161657759305843
2150325030.02079124729-8.208356920543961.97920875271254-1.78307847684908
2249894987.01826402464-13.54199472141481.98173597536298-0.763596567180153
2349294927.01540695749-20.667470076761.98459304251255-1.01960287216095
2449194917.01596233216-19.03079912687321.984037667838940.234109284488027
2548834903.65295730663-18.174854447558-20.65295730663170.135308509321211
2648504848.65826198676-23.7463027767461.34173801324382-0.734059575949581
2748574855.6679199415-19.02400466607841.332080058502230.674696191271131
2848504848.6711184484-17.17735644122091.328881551599980.263855949005025
2948314829.67070806568-17.45726648795061.32929193432385-0.0399964235866372
3047934791.66679301756-20.61199409343611.33320698243742-0.45079473541769
3147824780.668343567-19.13592142871651.331656433002350.210928347560877
3248094807.67464306281-12.0511358217821.325356937185131.01242127827636
3347254723.66632761043-23.09972016361931.33367238957486-1.57887026275587
3446984696.66594605847-23.69864870137111.33405394152649-0.085589124483574
3546394637.66302294508-29.11950749289961.336977054921-0.77466577762437
3645284526.65728400722-41.69298582410191.34271599278088-1.79681617150488
3744594475.10846075109-43.1936079838888-16.1084607510888-0.228991152415669
3844054403.83686271901-47.45382828898851.16313728098952-0.575364988694938
3943144312.82600162039-54.14359978589821.17399837960824-0.955556434842946
4042524250.82434413381-55.35038716702641.17565586618633-0.172399026472438
4142454243.83297801702-47.92415755952681.167021982979431.06099828490723
4241774175.82994367297-51.00744799635841.17005632702469-0.440545757157532
4341224120.82943289747-51.62060451561541.17056710252988-0.0876132176438894
4440344032.82549353465-57.20739001222581.17450646535053-0.798317812429812
4539553953.82349609979-60.55400349245371.17650390021341-0.47822306010139
4639283926.82609926617-55.40132149719631.173900733830730.736319456649976
4738843882.82684796633-53.6505117882971.173152033668350.250194407986933
4838263824.82660620506-54.31842211372991.17339379493808-0.0954466972872589
4937133730.00159608837-60.5006152255524-17.0015960883715-0.928175967412237
5036723670.44636591157-60.35683705759181.553634088433240.0196681990195506
5136823680.46041638889-49.54914419783291.539583611112131.54388765173355
5236153613.45746536687-52.22954146152761.54253463313463-0.382939515717491
5335293527.45263171147-57.41620002274161.54736828852531-0.741059861028827
5435293527.4595877232-48.59835602407111.540412276799681.2599486399044
5534793477.45944399114-48.81360911169951.54055600886357-0.0307579642993947
5634463444.46081657583-46.38514883950941.539183424169280.347017943678023
5733853383.4597428429-48.62947534411181.54025715709659-0.320712648160025
5832963294.45723233798-54.82888083909741.54276766202092-0.885903929499196
5932343232.45685487079-55.93008614948391.54314512921367-0.157365513415991
6031883186.45729729759-54.40522149168031.54270270240560.21790937702848
6130783097.73175996294-59.6499112414886-19.7317599629357-0.779811462826668
6230183016.3592327916-62.95901358943951.64076720840338-0.456306884787994
6329832981.3638614219-58.66441946403381.636138578104030.613526728057378







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
12914.332435919492907.988149227036.34428669246032
22849.52332558232842.621690557726.90163502458122
32786.821328367612777.255231888419.56609647919938
42711.826446498922711.8887732191-0.0623267201753066
52660.738674106352646.5223145497914.2163595565644
62565.358021171182581.15585588048-15.7978347092991
72503.484473547682515.78939721117-12.3049236634887
82470.918032508552450.4229385418620.4950939666953
92389.258712997572385.056479872554.20223312501962
102294.604528872352319.69002120324-25.0854923308853
112237.329160651392254.32356253393-16.9944018825327
122197.476378326482188.957103864628.51927446186102

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 2914.33243591949 & 2907.98814922703 & 6.34428669246032 \tabularnewline
2 & 2849.5233255823 & 2842.62169055772 & 6.90163502458122 \tabularnewline
3 & 2786.82132836761 & 2777.25523188841 & 9.56609647919938 \tabularnewline
4 & 2711.82644649892 & 2711.8887732191 & -0.0623267201753066 \tabularnewline
5 & 2660.73867410635 & 2646.52231454979 & 14.2163595565644 \tabularnewline
6 & 2565.35802117118 & 2581.15585588048 & -15.7978347092991 \tabularnewline
7 & 2503.48447354768 & 2515.78939721117 & -12.3049236634887 \tabularnewline
8 & 2470.91803250855 & 2450.42293854186 & 20.4950939666953 \tabularnewline
9 & 2389.25871299757 & 2385.05647987255 & 4.20223312501962 \tabularnewline
10 & 2294.60452887235 & 2319.69002120324 & -25.0854923308853 \tabularnewline
11 & 2237.32916065139 & 2254.32356253393 & -16.9944018825327 \tabularnewline
12 & 2197.47637832648 & 2188.95710386462 & 8.51927446186102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299242&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]2914.33243591949[/C][C]2907.98814922703[/C][C]6.34428669246032[/C][/ROW]
[ROW][C]2[/C][C]2849.5233255823[/C][C]2842.62169055772[/C][C]6.90163502458122[/C][/ROW]
[ROW][C]3[/C][C]2786.82132836761[/C][C]2777.25523188841[/C][C]9.56609647919938[/C][/ROW]
[ROW][C]4[/C][C]2711.82644649892[/C][C]2711.8887732191[/C][C]-0.0623267201753066[/C][/ROW]
[ROW][C]5[/C][C]2660.73867410635[/C][C]2646.52231454979[/C][C]14.2163595565644[/C][/ROW]
[ROW][C]6[/C][C]2565.35802117118[/C][C]2581.15585588048[/C][C]-15.7978347092991[/C][/ROW]
[ROW][C]7[/C][C]2503.48447354768[/C][C]2515.78939721117[/C][C]-12.3049236634887[/C][/ROW]
[ROW][C]8[/C][C]2470.91803250855[/C][C]2450.42293854186[/C][C]20.4950939666953[/C][/ROW]
[ROW][C]9[/C][C]2389.25871299757[/C][C]2385.05647987255[/C][C]4.20223312501962[/C][/ROW]
[ROW][C]10[/C][C]2294.60452887235[/C][C]2319.69002120324[/C][C]-25.0854923308853[/C][/ROW]
[ROW][C]11[/C][C]2237.32916065139[/C][C]2254.32356253393[/C][C]-16.9944018825327[/C][/ROW]
[ROW][C]12[/C][C]2197.47637832648[/C][C]2188.95710386462[/C][C]8.51927446186102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299242&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299242&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
12914.332435919492907.988149227036.34428669246032
22849.52332558232842.621690557726.90163502458122
32786.821328367612777.255231888419.56609647919938
42711.826446498922711.8887732191-0.0623267201753066
52660.738674106352646.5223145497914.2163595565644
62565.358021171182581.15585588048-15.7978347092991
72503.484473547682515.78939721117-12.3049236634887
82470.918032508552450.4229385418620.4950939666953
92389.258712997572385.056479872554.20223312501962
102294.604528872352319.69002120324-25.0854923308853
112237.329160651392254.32356253393-16.9944018825327
122197.476378326482188.957103864628.51927446186102



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')