Free Statistics

of Irreproducible Research!

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 computationSat, 24 Dec 2016 04:30:29 +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/24/t1482550294jtvezf788z6ovp0.htm/, Retrieved Sat, 27 Apr 2024 13:15:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=303060, Retrieved Sat, 27 Apr 2024 13:15:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [Structural Time S...] [2016-12-24 03:30:29] [070714f07871aeb0c40d04255feda5cb] [Current]
Feedback Forum

Post a new message
Dataseries X:
434.50
455.00
448.00
425.51
405.00
392.50
394.00
439.98
445.00
440.00
422.00
418.00
420.00
426.34
421.00
429.00
444.44
462.34
455.00
458.00
459.08
510.05
578.00
590.00
745.00
735.00
687.80
685.76
660.00
669.01
658.06
649.00
595.69
583.37
594.80
606.00
627.42
629.00
614.68
610.99
618.26
642.76
657.00
712.00
730.00
729.47
744.90
745.00
773.64
770.00
780.00
890.00




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=303060&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=303060&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303060&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
1434.5434.5000
2455453.8964462338531.116635241354081.103553766146550.38269307526839
3448447.1059397432740.9508336405446010.894060256726317-0.258241069734323
4425.51424.8197657440810.3043939587657090.690234255919308-0.755557676758962
5405404.285257445423-0.4327440808060470.714742554577142-0.674894803447125
6392.5391.726468904945-0.9445921842291210.773531095055445-0.391250168251743
7394393.078118533849-0.833376811442330.9218814661506540.0738327398031367
8439.98438.4468176334371.663091714990061.53318236656341.48087987299935
9445444.1475401614831.90137864884380.8524598385167840.129046363792191
10440439.1283759670551.462574401558870.871624032944608-0.220623746496185
11422421.2802591049340.1641439762658920.719740895065545-0.614228017183005
12418417.060319880505-0.1451972686125350.939680119494883-0.139171146803688
13420425.9722519189910.293344364290719-5.972251918991120.340960177135211
14426.34425.7357138069270.2481956780698660.60428619307319-0.0143333276201587
15421420.549858019194-0.1747453776324840.4501419808057-0.171586677959753
16429428.2991602724350.45159789588470.7008397275647770.249756720319693
17444.44443.6195645316691.651306823841050.820435468330670.468271919871258
18462.34461.4432488122292.977710974576160.896751187771320.508931784866658
19455455.2659701663622.21667852903504-0.265970166362151-0.28790673405144
20458456.9328059369242.170458619424261.06719406307624-0.0172816704580931
21459.08458.6763417859982.134237859714370.403658214001518-0.0134118285697652
22510.05508.2858022155656.193171288274611.764197784435331.49084037419284
23578576.4658659421911.52778699846331.534134057810091.94602357633851
24590589.92696227057211.69481550381630.07303772942828330.0606500343496477
25745723.82955826304221.765445804957221.17044173695844.17035198027123
26735736.79722695413320.9831906538613-1.79722695413314-0.253400232740168
27687.8692.30425954066815.2507375693495-4.50425954066804-2.05369105665708
28685.76687.80557427994713.5215020260728-2.04557427994749-0.618717437049339
29660663.13409857812110.1695206327272-3.13409857812095-1.19659804425196
30669.01670.1533073343859.89252824108363-1.14330733438524-0.0986958629734271
31658.06661.3700172232798.2480359497978-3.31001722327871-0.585048261350475
32649650.504857053386.56298076853356-1.50485705337973-0.598710529376112
33595.69600.0946381207031.53503852927571-4.40463812070337-1.78455741939555
34583.37585.4586926450720.106710639288394-2.08869264507213-0.506504065867329
35594.8594.6602324049890.9106867031922440.139767595011370.284887988798477
36606610.4339390303012.22397883005736-4.433939030301390.465217242001881
37627.42605.5251098599161.6015321568792521.8948901400843-0.23572654093059
38629628.1188952130713.461991865172340.881104786929460.621696653707217
39614.68619.2902748593132.37403740568214-4.61027485931325-0.38495488672143
40610.99611.8535773733131.50558964329563-0.863577373312545-0.3070011104769
41618.26620.8033800459372.16470899476365-2.543380045937030.23297276448202
42642.76642.5908446738333.902494087258250.1691553261670830.614157904923393
43657659.6949432526345.07180957415416-2.694943252634080.413188602222779
44712709.9531183804789.074653476710412.046881619522321.41425415266796
45730733.48699426671910.3556660002933-3.486994266718740.452548019403729
46729.47732.1270680151259.31761315190473-2.65706801512509-0.366688625708124
47744.9744.7262430988099.608413302209390.1737569011906060.102721461982475
48745749.206972595919.15432346042536-4.20697259590977-0.16038056489908
49773.64754.7686302858428.8376239691824418.8713697141578-0.116793378571091
50770768.4910335914019.26964651535121.508966408599410.146919471390606
51780783.7950657350979.80397501148534-3.795065735096470.188847925053805
52890886.76416038406818.05836228970543.23583961593222.9142241580806

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 434.5 & 434.5 & 0 & 0 & 0 \tabularnewline
2 & 455 & 453.896446233853 & 1.11663524135408 & 1.10355376614655 & 0.38269307526839 \tabularnewline
3 & 448 & 447.105939743274 & 0.950833640544601 & 0.894060256726317 & -0.258241069734323 \tabularnewline
4 & 425.51 & 424.819765744081 & 0.304393958765709 & 0.690234255919308 & -0.755557676758962 \tabularnewline
5 & 405 & 404.285257445423 & -0.432744080806047 & 0.714742554577142 & -0.674894803447125 \tabularnewline
6 & 392.5 & 391.726468904945 & -0.944592184229121 & 0.773531095055445 & -0.391250168251743 \tabularnewline
7 & 394 & 393.078118533849 & -0.83337681144233 & 0.921881466150654 & 0.0738327398031367 \tabularnewline
8 & 439.98 & 438.446817633437 & 1.66309171499006 & 1.5331823665634 & 1.48087987299935 \tabularnewline
9 & 445 & 444.147540161483 & 1.9013786488438 & 0.852459838516784 & 0.129046363792191 \tabularnewline
10 & 440 & 439.128375967055 & 1.46257440155887 & 0.871624032944608 & -0.220623746496185 \tabularnewline
11 & 422 & 421.280259104934 & 0.164143976265892 & 0.719740895065545 & -0.614228017183005 \tabularnewline
12 & 418 & 417.060319880505 & -0.145197268612535 & 0.939680119494883 & -0.139171146803688 \tabularnewline
13 & 420 & 425.972251918991 & 0.293344364290719 & -5.97225191899112 & 0.340960177135211 \tabularnewline
14 & 426.34 & 425.735713806927 & 0.248195678069866 & 0.60428619307319 & -0.0143333276201587 \tabularnewline
15 & 421 & 420.549858019194 & -0.174745377632484 & 0.4501419808057 & -0.171586677959753 \tabularnewline
16 & 429 & 428.299160272435 & 0.4515978958847 & 0.700839727564777 & 0.249756720319693 \tabularnewline
17 & 444.44 & 443.619564531669 & 1.65130682384105 & 0.82043546833067 & 0.468271919871258 \tabularnewline
18 & 462.34 & 461.443248812229 & 2.97771097457616 & 0.89675118777132 & 0.508931784866658 \tabularnewline
19 & 455 & 455.265970166362 & 2.21667852903504 & -0.265970166362151 & -0.28790673405144 \tabularnewline
20 & 458 & 456.932805936924 & 2.17045861942426 & 1.06719406307624 & -0.0172816704580931 \tabularnewline
21 & 459.08 & 458.676341785998 & 2.13423785971437 & 0.403658214001518 & -0.0134118285697652 \tabularnewline
22 & 510.05 & 508.285802215565 & 6.19317128827461 & 1.76419778443533 & 1.49084037419284 \tabularnewline
23 & 578 & 576.46586594219 & 11.5277869984633 & 1.53413405781009 & 1.94602357633851 \tabularnewline
24 & 590 & 589.926962270572 & 11.6948155038163 & 0.0730377294282833 & 0.0606500343496477 \tabularnewline
25 & 745 & 723.829558263042 & 21.7654458049572 & 21.1704417369584 & 4.17035198027123 \tabularnewline
26 & 735 & 736.797226954133 & 20.9831906538613 & -1.79722695413314 & -0.253400232740168 \tabularnewline
27 & 687.8 & 692.304259540668 & 15.2507375693495 & -4.50425954066804 & -2.05369105665708 \tabularnewline
28 & 685.76 & 687.805574279947 & 13.5215020260728 & -2.04557427994749 & -0.618717437049339 \tabularnewline
29 & 660 & 663.134098578121 & 10.1695206327272 & -3.13409857812095 & -1.19659804425196 \tabularnewline
30 & 669.01 & 670.153307334385 & 9.89252824108363 & -1.14330733438524 & -0.0986958629734271 \tabularnewline
31 & 658.06 & 661.370017223279 & 8.2480359497978 & -3.31001722327871 & -0.585048261350475 \tabularnewline
32 & 649 & 650.50485705338 & 6.56298076853356 & -1.50485705337973 & -0.598710529376112 \tabularnewline
33 & 595.69 & 600.094638120703 & 1.53503852927571 & -4.40463812070337 & -1.78455741939555 \tabularnewline
34 & 583.37 & 585.458692645072 & 0.106710639288394 & -2.08869264507213 & -0.506504065867329 \tabularnewline
35 & 594.8 & 594.660232404989 & 0.910686703192244 & 0.13976759501137 & 0.284887988798477 \tabularnewline
36 & 606 & 610.433939030301 & 2.22397883005736 & -4.43393903030139 & 0.465217242001881 \tabularnewline
37 & 627.42 & 605.525109859916 & 1.60153215687925 & 21.8948901400843 & -0.23572654093059 \tabularnewline
38 & 629 & 628.118895213071 & 3.46199186517234 & 0.88110478692946 & 0.621696653707217 \tabularnewline
39 & 614.68 & 619.290274859313 & 2.37403740568214 & -4.61027485931325 & -0.38495488672143 \tabularnewline
40 & 610.99 & 611.853577373313 & 1.50558964329563 & -0.863577373312545 & -0.3070011104769 \tabularnewline
41 & 618.26 & 620.803380045937 & 2.16470899476365 & -2.54338004593703 & 0.23297276448202 \tabularnewline
42 & 642.76 & 642.590844673833 & 3.90249408725825 & 0.169155326167083 & 0.614157904923393 \tabularnewline
43 & 657 & 659.694943252634 & 5.07180957415416 & -2.69494325263408 & 0.413188602222779 \tabularnewline
44 & 712 & 709.953118380478 & 9.07465347671041 & 2.04688161952232 & 1.41425415266796 \tabularnewline
45 & 730 & 733.486994266719 & 10.3556660002933 & -3.48699426671874 & 0.452548019403729 \tabularnewline
46 & 729.47 & 732.127068015125 & 9.31761315190473 & -2.65706801512509 & -0.366688625708124 \tabularnewline
47 & 744.9 & 744.726243098809 & 9.60841330220939 & 0.173756901190606 & 0.102721461982475 \tabularnewline
48 & 745 & 749.20697259591 & 9.15432346042536 & -4.20697259590977 & -0.16038056489908 \tabularnewline
49 & 773.64 & 754.768630285842 & 8.83762396918244 & 18.8713697141578 & -0.116793378571091 \tabularnewline
50 & 770 & 768.491033591401 & 9.2696465153512 & 1.50896640859941 & 0.146919471390606 \tabularnewline
51 & 780 & 783.795065735097 & 9.80397501148534 & -3.79506573509647 & 0.188847925053805 \tabularnewline
52 & 890 & 886.764160384068 & 18.0583622897054 & 3.2358396159322 & 2.9142241580806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303060&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]434.5[/C][C]434.5[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]455[/C][C]453.896446233853[/C][C]1.11663524135408[/C][C]1.10355376614655[/C][C]0.38269307526839[/C][/ROW]
[ROW][C]3[/C][C]448[/C][C]447.105939743274[/C][C]0.950833640544601[/C][C]0.894060256726317[/C][C]-0.258241069734323[/C][/ROW]
[ROW][C]4[/C][C]425.51[/C][C]424.819765744081[/C][C]0.304393958765709[/C][C]0.690234255919308[/C][C]-0.755557676758962[/C][/ROW]
[ROW][C]5[/C][C]405[/C][C]404.285257445423[/C][C]-0.432744080806047[/C][C]0.714742554577142[/C][C]-0.674894803447125[/C][/ROW]
[ROW][C]6[/C][C]392.5[/C][C]391.726468904945[/C][C]-0.944592184229121[/C][C]0.773531095055445[/C][C]-0.391250168251743[/C][/ROW]
[ROW][C]7[/C][C]394[/C][C]393.078118533849[/C][C]-0.83337681144233[/C][C]0.921881466150654[/C][C]0.0738327398031367[/C][/ROW]
[ROW][C]8[/C][C]439.98[/C][C]438.446817633437[/C][C]1.66309171499006[/C][C]1.5331823665634[/C][C]1.48087987299935[/C][/ROW]
[ROW][C]9[/C][C]445[/C][C]444.147540161483[/C][C]1.9013786488438[/C][C]0.852459838516784[/C][C]0.129046363792191[/C][/ROW]
[ROW][C]10[/C][C]440[/C][C]439.128375967055[/C][C]1.46257440155887[/C][C]0.871624032944608[/C][C]-0.220623746496185[/C][/ROW]
[ROW][C]11[/C][C]422[/C][C]421.280259104934[/C][C]0.164143976265892[/C][C]0.719740895065545[/C][C]-0.614228017183005[/C][/ROW]
[ROW][C]12[/C][C]418[/C][C]417.060319880505[/C][C]-0.145197268612535[/C][C]0.939680119494883[/C][C]-0.139171146803688[/C][/ROW]
[ROW][C]13[/C][C]420[/C][C]425.972251918991[/C][C]0.293344364290719[/C][C]-5.97225191899112[/C][C]0.340960177135211[/C][/ROW]
[ROW][C]14[/C][C]426.34[/C][C]425.735713806927[/C][C]0.248195678069866[/C][C]0.60428619307319[/C][C]-0.0143333276201587[/C][/ROW]
[ROW][C]15[/C][C]421[/C][C]420.549858019194[/C][C]-0.174745377632484[/C][C]0.4501419808057[/C][C]-0.171586677959753[/C][/ROW]
[ROW][C]16[/C][C]429[/C][C]428.299160272435[/C][C]0.4515978958847[/C][C]0.700839727564777[/C][C]0.249756720319693[/C][/ROW]
[ROW][C]17[/C][C]444.44[/C][C]443.619564531669[/C][C]1.65130682384105[/C][C]0.82043546833067[/C][C]0.468271919871258[/C][/ROW]
[ROW][C]18[/C][C]462.34[/C][C]461.443248812229[/C][C]2.97771097457616[/C][C]0.89675118777132[/C][C]0.508931784866658[/C][/ROW]
[ROW][C]19[/C][C]455[/C][C]455.265970166362[/C][C]2.21667852903504[/C][C]-0.265970166362151[/C][C]-0.28790673405144[/C][/ROW]
[ROW][C]20[/C][C]458[/C][C]456.932805936924[/C][C]2.17045861942426[/C][C]1.06719406307624[/C][C]-0.0172816704580931[/C][/ROW]
[ROW][C]21[/C][C]459.08[/C][C]458.676341785998[/C][C]2.13423785971437[/C][C]0.403658214001518[/C][C]-0.0134118285697652[/C][/ROW]
[ROW][C]22[/C][C]510.05[/C][C]508.285802215565[/C][C]6.19317128827461[/C][C]1.76419778443533[/C][C]1.49084037419284[/C][/ROW]
[ROW][C]23[/C][C]578[/C][C]576.46586594219[/C][C]11.5277869984633[/C][C]1.53413405781009[/C][C]1.94602357633851[/C][/ROW]
[ROW][C]24[/C][C]590[/C][C]589.926962270572[/C][C]11.6948155038163[/C][C]0.0730377294282833[/C][C]0.0606500343496477[/C][/ROW]
[ROW][C]25[/C][C]745[/C][C]723.829558263042[/C][C]21.7654458049572[/C][C]21.1704417369584[/C][C]4.17035198027123[/C][/ROW]
[ROW][C]26[/C][C]735[/C][C]736.797226954133[/C][C]20.9831906538613[/C][C]-1.79722695413314[/C][C]-0.253400232740168[/C][/ROW]
[ROW][C]27[/C][C]687.8[/C][C]692.304259540668[/C][C]15.2507375693495[/C][C]-4.50425954066804[/C][C]-2.05369105665708[/C][/ROW]
[ROW][C]28[/C][C]685.76[/C][C]687.805574279947[/C][C]13.5215020260728[/C][C]-2.04557427994749[/C][C]-0.618717437049339[/C][/ROW]
[ROW][C]29[/C][C]660[/C][C]663.134098578121[/C][C]10.1695206327272[/C][C]-3.13409857812095[/C][C]-1.19659804425196[/C][/ROW]
[ROW][C]30[/C][C]669.01[/C][C]670.153307334385[/C][C]9.89252824108363[/C][C]-1.14330733438524[/C][C]-0.0986958629734271[/C][/ROW]
[ROW][C]31[/C][C]658.06[/C][C]661.370017223279[/C][C]8.2480359497978[/C][C]-3.31001722327871[/C][C]-0.585048261350475[/C][/ROW]
[ROW][C]32[/C][C]649[/C][C]650.50485705338[/C][C]6.56298076853356[/C][C]-1.50485705337973[/C][C]-0.598710529376112[/C][/ROW]
[ROW][C]33[/C][C]595.69[/C][C]600.094638120703[/C][C]1.53503852927571[/C][C]-4.40463812070337[/C][C]-1.78455741939555[/C][/ROW]
[ROW][C]34[/C][C]583.37[/C][C]585.458692645072[/C][C]0.106710639288394[/C][C]-2.08869264507213[/C][C]-0.506504065867329[/C][/ROW]
[ROW][C]35[/C][C]594.8[/C][C]594.660232404989[/C][C]0.910686703192244[/C][C]0.13976759501137[/C][C]0.284887988798477[/C][/ROW]
[ROW][C]36[/C][C]606[/C][C]610.433939030301[/C][C]2.22397883005736[/C][C]-4.43393903030139[/C][C]0.465217242001881[/C][/ROW]
[ROW][C]37[/C][C]627.42[/C][C]605.525109859916[/C][C]1.60153215687925[/C][C]21.8948901400843[/C][C]-0.23572654093059[/C][/ROW]
[ROW][C]38[/C][C]629[/C][C]628.118895213071[/C][C]3.46199186517234[/C][C]0.88110478692946[/C][C]0.621696653707217[/C][/ROW]
[ROW][C]39[/C][C]614.68[/C][C]619.290274859313[/C][C]2.37403740568214[/C][C]-4.61027485931325[/C][C]-0.38495488672143[/C][/ROW]
[ROW][C]40[/C][C]610.99[/C][C]611.853577373313[/C][C]1.50558964329563[/C][C]-0.863577373312545[/C][C]-0.3070011104769[/C][/ROW]
[ROW][C]41[/C][C]618.26[/C][C]620.803380045937[/C][C]2.16470899476365[/C][C]-2.54338004593703[/C][C]0.23297276448202[/C][/ROW]
[ROW][C]42[/C][C]642.76[/C][C]642.590844673833[/C][C]3.90249408725825[/C][C]0.169155326167083[/C][C]0.614157904923393[/C][/ROW]
[ROW][C]43[/C][C]657[/C][C]659.694943252634[/C][C]5.07180957415416[/C][C]-2.69494325263408[/C][C]0.413188602222779[/C][/ROW]
[ROW][C]44[/C][C]712[/C][C]709.953118380478[/C][C]9.07465347671041[/C][C]2.04688161952232[/C][C]1.41425415266796[/C][/ROW]
[ROW][C]45[/C][C]730[/C][C]733.486994266719[/C][C]10.3556660002933[/C][C]-3.48699426671874[/C][C]0.452548019403729[/C][/ROW]
[ROW][C]46[/C][C]729.47[/C][C]732.127068015125[/C][C]9.31761315190473[/C][C]-2.65706801512509[/C][C]-0.366688625708124[/C][/ROW]
[ROW][C]47[/C][C]744.9[/C][C]744.726243098809[/C][C]9.60841330220939[/C][C]0.173756901190606[/C][C]0.102721461982475[/C][/ROW]
[ROW][C]48[/C][C]745[/C][C]749.20697259591[/C][C]9.15432346042536[/C][C]-4.20697259590977[/C][C]-0.16038056489908[/C][/ROW]
[ROW][C]49[/C][C]773.64[/C][C]754.768630285842[/C][C]8.83762396918244[/C][C]18.8713697141578[/C][C]-0.116793378571091[/C][/ROW]
[ROW][C]50[/C][C]770[/C][C]768.491033591401[/C][C]9.2696465153512[/C][C]1.50896640859941[/C][C]0.146919471390606[/C][/ROW]
[ROW][C]51[/C][C]780[/C][C]783.795065735097[/C][C]9.80397501148534[/C][C]-3.79506573509647[/C][C]0.188847925053805[/C][/ROW]
[ROW][C]52[/C][C]890[/C][C]886.764160384068[/C][C]18.0583622897054[/C][C]3.2358396159322[/C][C]2.9142241580806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303060&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303060&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
1434.5434.5000
2455453.8964462338531.116635241354081.103553766146550.38269307526839
3448447.1059397432740.9508336405446010.894060256726317-0.258241069734323
4425.51424.8197657440810.3043939587657090.690234255919308-0.755557676758962
5405404.285257445423-0.4327440808060470.714742554577142-0.674894803447125
6392.5391.726468904945-0.9445921842291210.773531095055445-0.391250168251743
7394393.078118533849-0.833376811442330.9218814661506540.0738327398031367
8439.98438.4468176334371.663091714990061.53318236656341.48087987299935
9445444.1475401614831.90137864884380.8524598385167840.129046363792191
10440439.1283759670551.462574401558870.871624032944608-0.220623746496185
11422421.2802591049340.1641439762658920.719740895065545-0.614228017183005
12418417.060319880505-0.1451972686125350.939680119494883-0.139171146803688
13420425.9722519189910.293344364290719-5.972251918991120.340960177135211
14426.34425.7357138069270.2481956780698660.60428619307319-0.0143333276201587
15421420.549858019194-0.1747453776324840.4501419808057-0.171586677959753
16429428.2991602724350.45159789588470.7008397275647770.249756720319693
17444.44443.6195645316691.651306823841050.820435468330670.468271919871258
18462.34461.4432488122292.977710974576160.896751187771320.508931784866658
19455455.2659701663622.21667852903504-0.265970166362151-0.28790673405144
20458456.9328059369242.170458619424261.06719406307624-0.0172816704580931
21459.08458.6763417859982.134237859714370.403658214001518-0.0134118285697652
22510.05508.2858022155656.193171288274611.764197784435331.49084037419284
23578576.4658659421911.52778699846331.534134057810091.94602357633851
24590589.92696227057211.69481550381630.07303772942828330.0606500343496477
25745723.82955826304221.765445804957221.17044173695844.17035198027123
26735736.79722695413320.9831906538613-1.79722695413314-0.253400232740168
27687.8692.30425954066815.2507375693495-4.50425954066804-2.05369105665708
28685.76687.80557427994713.5215020260728-2.04557427994749-0.618717437049339
29660663.13409857812110.1695206327272-3.13409857812095-1.19659804425196
30669.01670.1533073343859.89252824108363-1.14330733438524-0.0986958629734271
31658.06661.3700172232798.2480359497978-3.31001722327871-0.585048261350475
32649650.504857053386.56298076853356-1.50485705337973-0.598710529376112
33595.69600.0946381207031.53503852927571-4.40463812070337-1.78455741939555
34583.37585.4586926450720.106710639288394-2.08869264507213-0.506504065867329
35594.8594.6602324049890.9106867031922440.139767595011370.284887988798477
36606610.4339390303012.22397883005736-4.433939030301390.465217242001881
37627.42605.5251098599161.6015321568792521.8948901400843-0.23572654093059
38629628.1188952130713.461991865172340.881104786929460.621696653707217
39614.68619.2902748593132.37403740568214-4.61027485931325-0.38495488672143
40610.99611.8535773733131.50558964329563-0.863577373312545-0.3070011104769
41618.26620.8033800459372.16470899476365-2.543380045937030.23297276448202
42642.76642.5908446738333.902494087258250.1691553261670830.614157904923393
43657659.6949432526345.07180957415416-2.694943252634080.413188602222779
44712709.9531183804789.074653476710412.046881619522321.41425415266796
45730733.48699426671910.3556660002933-3.486994266718740.452548019403729
46729.47732.1270680151259.31761315190473-2.65706801512509-0.366688625708124
47744.9744.7262430988099.608413302209390.1737569011906060.102721461982475
48745749.206972595919.15432346042536-4.20697259590977-0.16038056489908
49773.64754.7686302858428.8376239691824418.8713697141578-0.116793378571091
50770768.4910335914019.26964651535121.508966408599410.146919471390606
51780783.7950657350979.80397501148534-3.795065735096470.188847925053805
52890886.76416038406818.05836228970543.23583961593222.9142241580806







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
1886.744630332313892.029099536671-5.28446920435794
2902.900021857439906.199671578511-3.29964972107195
3907.249591113965920.370243620352-13.1206525063869
4936.244631571606934.5408156621921.70381590941465
5934.115917993647948.711387704032-14.5954697103846
6946.672830287235962.881959745872-16.2091294586366
7970.739466134062977.052531787712-6.31306565365016
8980.441797667845991.223103829552-10.781306161707
91036.076886243211005.3936758713930.6832103718133
101043.933098390381019.5642479132324.3688504771476
111034.441213107721033.734819955070.706393152650735
121060.046864502081047.9053919969112.1414725051689

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 886.744630332313 & 892.029099536671 & -5.28446920435794 \tabularnewline
2 & 902.900021857439 & 906.199671578511 & -3.29964972107195 \tabularnewline
3 & 907.249591113965 & 920.370243620352 & -13.1206525063869 \tabularnewline
4 & 936.244631571606 & 934.540815662192 & 1.70381590941465 \tabularnewline
5 & 934.115917993647 & 948.711387704032 & -14.5954697103846 \tabularnewline
6 & 946.672830287235 & 962.881959745872 & -16.2091294586366 \tabularnewline
7 & 970.739466134062 & 977.052531787712 & -6.31306565365016 \tabularnewline
8 & 980.441797667845 & 991.223103829552 & -10.781306161707 \tabularnewline
9 & 1036.07688624321 & 1005.39367587139 & 30.6832103718133 \tabularnewline
10 & 1043.93309839038 & 1019.56424791323 & 24.3688504771476 \tabularnewline
11 & 1034.44121310772 & 1033.73481995507 & 0.706393152650735 \tabularnewline
12 & 1060.04686450208 & 1047.90539199691 & 12.1414725051689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303060&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]886.744630332313[/C][C]892.029099536671[/C][C]-5.28446920435794[/C][/ROW]
[ROW][C]2[/C][C]902.900021857439[/C][C]906.199671578511[/C][C]-3.29964972107195[/C][/ROW]
[ROW][C]3[/C][C]907.249591113965[/C][C]920.370243620352[/C][C]-13.1206525063869[/C][/ROW]
[ROW][C]4[/C][C]936.244631571606[/C][C]934.540815662192[/C][C]1.70381590941465[/C][/ROW]
[ROW][C]5[/C][C]934.115917993647[/C][C]948.711387704032[/C][C]-14.5954697103846[/C][/ROW]
[ROW][C]6[/C][C]946.672830287235[/C][C]962.881959745872[/C][C]-16.2091294586366[/C][/ROW]
[ROW][C]7[/C][C]970.739466134062[/C][C]977.052531787712[/C][C]-6.31306565365016[/C][/ROW]
[ROW][C]8[/C][C]980.441797667845[/C][C]991.223103829552[/C][C]-10.781306161707[/C][/ROW]
[ROW][C]9[/C][C]1036.07688624321[/C][C]1005.39367587139[/C][C]30.6832103718133[/C][/ROW]
[ROW][C]10[/C][C]1043.93309839038[/C][C]1019.56424791323[/C][C]24.3688504771476[/C][/ROW]
[ROW][C]11[/C][C]1034.44121310772[/C][C]1033.73481995507[/C][C]0.706393152650735[/C][/ROW]
[ROW][C]12[/C][C]1060.04686450208[/C][C]1047.90539199691[/C][C]12.1414725051689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303060&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303060&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
1886.744630332313892.029099536671-5.28446920435794
2902.900021857439906.199671578511-3.29964972107195
3907.249591113965920.370243620352-13.1206525063869
4936.244631571606934.5408156621921.70381590941465
5934.115917993647948.711387704032-14.5954697103846
6946.672830287235962.881959745872-16.2091294586366
7970.739466134062977.052531787712-6.31306565365016
8980.441797667845991.223103829552-10.781306161707
91036.076886243211005.3936758713930.6832103718133
101043.933098390381019.5642479132324.3688504771476
111034.441213107721033.734819955070.706393152650735
121060.046864502081047.9053919969112.1414725051689



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
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')