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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 14:50:22 +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/t14811191657raefxp00ojn9ix.htm/, Retrieved Tue, 07 May 2024 07:46:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298120, Retrieved Tue, 07 May 2024 07:46:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [Paper N1268] [2016-12-07 13:50:22] [3146b6c9a81fba6ba78c11f749c05198] [Current]
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Dataseries X:
3719.8
3646.4
3644.6
3713.2
3708.4
3689.6
3652
3590.2
3549.6
3580.6
3599.8
3647
3693.8
3755.6
3832.6
3917.4
4004
4086
4108.8
4179.2
4210.6
4276.6
4361.2
4452
4496.4
4581.6
4694
4749
4790
4837
4915
4929.8
5058
5150
5240
5318
5397.2
5474.6
5500.8
5552
5637.8
5622.8
5633.8
5567.8
5522




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=298120&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=298120&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298120&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
13719.83719.8000
23646.43649.65533320866-14.052811726607-3.25533320866432-1.36814464957143
33644.63647.97116616641-8.10168457469457-3.371166166414440.311574292274444
43713.23716.93048827530.5918156255917-3.730488274998411.9145054023706
53708.43712.0490866982312.5761589291984-3.64908669822537-0.879313810907245
63689.63693.21373518913-3.42985433968426-3.61373518913023-0.778671828456621
736523655.59488569956-20.8701744391092-3.59488569956045-0.847783001216672
83590.23593.78383267267-41.7631954294106-3.58383267267202-1.01542946422533
93549.63553.1839864418-41.1694135940818-3.583986441804420.0288573098121403
103580.63584.18865670741-4.32849230478494-3.588656707413751.79041918581985
113599.83603.389402046097.68231345567205-3.589402046092410.583707481469384
1236473650.5900148507327.8552784140863-3.590014850731090.980375796361104
133693.83660.0723013737118.742867872037333.727698626288-0.514893712506008
143755.63757.024361866254.369930366953-1.424361866197421.56905177065481
153832.63834.1037777215966.0437124030034-1.503777721591630.558328980687093
163917.43918.9359146216775.6424993520762-1.535914621667890.464705169423267
1740044005.5450993556581.2394483691952-1.545099355652280.271754082500712
1840864087.545411380681.6277504021911-1.54541138059680.0188667481655667
194108.84110.3335973497151.5963530410039-1.53359734970676-1.45940371745077
204179.24180.7354458737761.1953082718056-1.53544587377350.46648883247487
214210.64212.1340120330345.9853849864542-1.53401203302819-0.739177047568205
224276.64278.1344835213956.2024398471127-1.534483521385460.496533063144599
234361.24362.7348109944870.6988128623018-1.534810994478690.704501694368898
2444524453.5349244660880.960056432439-1.534924466084670.498680906437759
254496.44486.5059811854956.78628233802339.89401881451171-1.26581151947134
264581.64581.9795968300975.1747948907365-0.3795968300872710.847778027806419
2746944694.4641625184894.3069757169027-0.4641625184773720.920215612213501
2847494749.4205227878774.2088644026164-0.420522787869026-0.97431916121125
2947904790.4024817921457.249801985127-0.402481792138994-0.823695383584785
3048374837.3997562650952.0169990314285-0.39975626509278-0.254270120719523
3149154915.4031383545565.2810848536274-0.4031383545497480.64459253651896
324929.84930.1999217850439.5113891471627-0.399921785039447-1.25235802379439
3350585058.4026881052284.7851621959968-0.4026881052162082.20023262769232
3451505150.4027982672588.4681898864807-0.4027982672480870.178989494692052
3552405240.4028097166189.2501475540876-0.4028097166072380.0380019564074112
3653185318.4027685537683.5071781288724-0.402768553763588-0.279099625784793
375397.25393.5614677143779.28211529718333.63853228563235-0.215775528768994
385474.65474.910362163180.2837141371072-0.3103621631021560.046965082744895
395500.85501.0195131065152.536004595091-0.219513106507935-1.33820870717318
4055525552.2184160105151.8531794245331-0.21841601051065-0.0331234684583184
415637.85638.0320579422669.1873393548124-0.2320579422559790.842043896463388
425622.85623.0154978359126.2084570739257-0.215497835913097-2.08848880728135
435633.85634.0140334184618.4447232697079-0.214033418460484-0.377296208244342
445567.85568.01005306747-24.6627453332629-0.210053067470074-2.09494514928934
4555225522.20956535045-35.4528900977199-0.209565350445817-0.524383966037831

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 3719.8 & 3719.8 & 0 & 0 & 0 \tabularnewline
2 & 3646.4 & 3649.65533320866 & -14.052811726607 & -3.25533320866432 & -1.36814464957143 \tabularnewline
3 & 3644.6 & 3647.97116616641 & -8.10168457469457 & -3.37116616641444 & 0.311574292274444 \tabularnewline
4 & 3713.2 & 3716.930488275 & 30.5918156255917 & -3.73048827499841 & 1.9145054023706 \tabularnewline
5 & 3708.4 & 3712.04908669823 & 12.5761589291984 & -3.64908669822537 & -0.879313810907245 \tabularnewline
6 & 3689.6 & 3693.21373518913 & -3.42985433968426 & -3.61373518913023 & -0.778671828456621 \tabularnewline
7 & 3652 & 3655.59488569956 & -20.8701744391092 & -3.59488569956045 & -0.847783001216672 \tabularnewline
8 & 3590.2 & 3593.78383267267 & -41.7631954294106 & -3.58383267267202 & -1.01542946422533 \tabularnewline
9 & 3549.6 & 3553.1839864418 & -41.1694135940818 & -3.58398644180442 & 0.0288573098121403 \tabularnewline
10 & 3580.6 & 3584.18865670741 & -4.32849230478494 & -3.58865670741375 & 1.79041918581985 \tabularnewline
11 & 3599.8 & 3603.38940204609 & 7.68231345567205 & -3.58940204609241 & 0.583707481469384 \tabularnewline
12 & 3647 & 3650.59001485073 & 27.8552784140863 & -3.59001485073109 & 0.980375796361104 \tabularnewline
13 & 3693.8 & 3660.07230137371 & 18.7428678720373 & 33.727698626288 & -0.514893712506008 \tabularnewline
14 & 3755.6 & 3757.0243618662 & 54.369930366953 & -1.42436186619742 & 1.56905177065481 \tabularnewline
15 & 3832.6 & 3834.10377772159 & 66.0437124030034 & -1.50377772159163 & 0.558328980687093 \tabularnewline
16 & 3917.4 & 3918.93591462167 & 75.6424993520762 & -1.53591462166789 & 0.464705169423267 \tabularnewline
17 & 4004 & 4005.54509935565 & 81.2394483691952 & -1.54509935565228 & 0.271754082500712 \tabularnewline
18 & 4086 & 4087.5454113806 & 81.6277504021911 & -1.5454113805968 & 0.0188667481655667 \tabularnewline
19 & 4108.8 & 4110.33359734971 & 51.5963530410039 & -1.53359734970676 & -1.45940371745077 \tabularnewline
20 & 4179.2 & 4180.73544587377 & 61.1953082718056 & -1.5354458737735 & 0.46648883247487 \tabularnewline
21 & 4210.6 & 4212.13401203303 & 45.9853849864542 & -1.53401203302819 & -0.739177047568205 \tabularnewline
22 & 4276.6 & 4278.13448352139 & 56.2024398471127 & -1.53448352138546 & 0.496533063144599 \tabularnewline
23 & 4361.2 & 4362.73481099448 & 70.6988128623018 & -1.53481099447869 & 0.704501694368898 \tabularnewline
24 & 4452 & 4453.53492446608 & 80.960056432439 & -1.53492446608467 & 0.498680906437759 \tabularnewline
25 & 4496.4 & 4486.50598118549 & 56.7862823380233 & 9.89401881451171 & -1.26581151947134 \tabularnewline
26 & 4581.6 & 4581.97959683009 & 75.1747948907365 & -0.379596830087271 & 0.847778027806419 \tabularnewline
27 & 4694 & 4694.46416251848 & 94.3069757169027 & -0.464162518477372 & 0.920215612213501 \tabularnewline
28 & 4749 & 4749.42052278787 & 74.2088644026164 & -0.420522787869026 & -0.97431916121125 \tabularnewline
29 & 4790 & 4790.40248179214 & 57.249801985127 & -0.402481792138994 & -0.823695383584785 \tabularnewline
30 & 4837 & 4837.39975626509 & 52.0169990314285 & -0.39975626509278 & -0.254270120719523 \tabularnewline
31 & 4915 & 4915.40313835455 & 65.2810848536274 & -0.403138354549748 & 0.64459253651896 \tabularnewline
32 & 4929.8 & 4930.19992178504 & 39.5113891471627 & -0.399921785039447 & -1.25235802379439 \tabularnewline
33 & 5058 & 5058.40268810522 & 84.7851621959968 & -0.402688105216208 & 2.20023262769232 \tabularnewline
34 & 5150 & 5150.40279826725 & 88.4681898864807 & -0.402798267248087 & 0.178989494692052 \tabularnewline
35 & 5240 & 5240.40280971661 & 89.2501475540876 & -0.402809716607238 & 0.0380019564074112 \tabularnewline
36 & 5318 & 5318.40276855376 & 83.5071781288724 & -0.402768553763588 & -0.279099625784793 \tabularnewline
37 & 5397.2 & 5393.56146771437 & 79.2821152971833 & 3.63853228563235 & -0.215775528768994 \tabularnewline
38 & 5474.6 & 5474.9103621631 & 80.2837141371072 & -0.310362163102156 & 0.046965082744895 \tabularnewline
39 & 5500.8 & 5501.01951310651 & 52.536004595091 & -0.219513106507935 & -1.33820870717318 \tabularnewline
40 & 5552 & 5552.21841601051 & 51.8531794245331 & -0.21841601051065 & -0.0331234684583184 \tabularnewline
41 & 5637.8 & 5638.03205794226 & 69.1873393548124 & -0.232057942255979 & 0.842043896463388 \tabularnewline
42 & 5622.8 & 5623.01549783591 & 26.2084570739257 & -0.215497835913097 & -2.08848880728135 \tabularnewline
43 & 5633.8 & 5634.01403341846 & 18.4447232697079 & -0.214033418460484 & -0.377296208244342 \tabularnewline
44 & 5567.8 & 5568.01005306747 & -24.6627453332629 & -0.210053067470074 & -2.09494514928934 \tabularnewline
45 & 5522 & 5522.20956535045 & -35.4528900977199 & -0.209565350445817 & -0.524383966037831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298120&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]3719.8[/C][C]3719.8[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]3646.4[/C][C]3649.65533320866[/C][C]-14.052811726607[/C][C]-3.25533320866432[/C][C]-1.36814464957143[/C][/ROW]
[ROW][C]3[/C][C]3644.6[/C][C]3647.97116616641[/C][C]-8.10168457469457[/C][C]-3.37116616641444[/C][C]0.311574292274444[/C][/ROW]
[ROW][C]4[/C][C]3713.2[/C][C]3716.930488275[/C][C]30.5918156255917[/C][C]-3.73048827499841[/C][C]1.9145054023706[/C][/ROW]
[ROW][C]5[/C][C]3708.4[/C][C]3712.04908669823[/C][C]12.5761589291984[/C][C]-3.64908669822537[/C][C]-0.879313810907245[/C][/ROW]
[ROW][C]6[/C][C]3689.6[/C][C]3693.21373518913[/C][C]-3.42985433968426[/C][C]-3.61373518913023[/C][C]-0.778671828456621[/C][/ROW]
[ROW][C]7[/C][C]3652[/C][C]3655.59488569956[/C][C]-20.8701744391092[/C][C]-3.59488569956045[/C][C]-0.847783001216672[/C][/ROW]
[ROW][C]8[/C][C]3590.2[/C][C]3593.78383267267[/C][C]-41.7631954294106[/C][C]-3.58383267267202[/C][C]-1.01542946422533[/C][/ROW]
[ROW][C]9[/C][C]3549.6[/C][C]3553.1839864418[/C][C]-41.1694135940818[/C][C]-3.58398644180442[/C][C]0.0288573098121403[/C][/ROW]
[ROW][C]10[/C][C]3580.6[/C][C]3584.18865670741[/C][C]-4.32849230478494[/C][C]-3.58865670741375[/C][C]1.79041918581985[/C][/ROW]
[ROW][C]11[/C][C]3599.8[/C][C]3603.38940204609[/C][C]7.68231345567205[/C][C]-3.58940204609241[/C][C]0.583707481469384[/C][/ROW]
[ROW][C]12[/C][C]3647[/C][C]3650.59001485073[/C][C]27.8552784140863[/C][C]-3.59001485073109[/C][C]0.980375796361104[/C][/ROW]
[ROW][C]13[/C][C]3693.8[/C][C]3660.07230137371[/C][C]18.7428678720373[/C][C]33.727698626288[/C][C]-0.514893712506008[/C][/ROW]
[ROW][C]14[/C][C]3755.6[/C][C]3757.0243618662[/C][C]54.369930366953[/C][C]-1.42436186619742[/C][C]1.56905177065481[/C][/ROW]
[ROW][C]15[/C][C]3832.6[/C][C]3834.10377772159[/C][C]66.0437124030034[/C][C]-1.50377772159163[/C][C]0.558328980687093[/C][/ROW]
[ROW][C]16[/C][C]3917.4[/C][C]3918.93591462167[/C][C]75.6424993520762[/C][C]-1.53591462166789[/C][C]0.464705169423267[/C][/ROW]
[ROW][C]17[/C][C]4004[/C][C]4005.54509935565[/C][C]81.2394483691952[/C][C]-1.54509935565228[/C][C]0.271754082500712[/C][/ROW]
[ROW][C]18[/C][C]4086[/C][C]4087.5454113806[/C][C]81.6277504021911[/C][C]-1.5454113805968[/C][C]0.0188667481655667[/C][/ROW]
[ROW][C]19[/C][C]4108.8[/C][C]4110.33359734971[/C][C]51.5963530410039[/C][C]-1.53359734970676[/C][C]-1.45940371745077[/C][/ROW]
[ROW][C]20[/C][C]4179.2[/C][C]4180.73544587377[/C][C]61.1953082718056[/C][C]-1.5354458737735[/C][C]0.46648883247487[/C][/ROW]
[ROW][C]21[/C][C]4210.6[/C][C]4212.13401203303[/C][C]45.9853849864542[/C][C]-1.53401203302819[/C][C]-0.739177047568205[/C][/ROW]
[ROW][C]22[/C][C]4276.6[/C][C]4278.13448352139[/C][C]56.2024398471127[/C][C]-1.53448352138546[/C][C]0.496533063144599[/C][/ROW]
[ROW][C]23[/C][C]4361.2[/C][C]4362.73481099448[/C][C]70.6988128623018[/C][C]-1.53481099447869[/C][C]0.704501694368898[/C][/ROW]
[ROW][C]24[/C][C]4452[/C][C]4453.53492446608[/C][C]80.960056432439[/C][C]-1.53492446608467[/C][C]0.498680906437759[/C][/ROW]
[ROW][C]25[/C][C]4496.4[/C][C]4486.50598118549[/C][C]56.7862823380233[/C][C]9.89401881451171[/C][C]-1.26581151947134[/C][/ROW]
[ROW][C]26[/C][C]4581.6[/C][C]4581.97959683009[/C][C]75.1747948907365[/C][C]-0.379596830087271[/C][C]0.847778027806419[/C][/ROW]
[ROW][C]27[/C][C]4694[/C][C]4694.46416251848[/C][C]94.3069757169027[/C][C]-0.464162518477372[/C][C]0.920215612213501[/C][/ROW]
[ROW][C]28[/C][C]4749[/C][C]4749.42052278787[/C][C]74.2088644026164[/C][C]-0.420522787869026[/C][C]-0.97431916121125[/C][/ROW]
[ROW][C]29[/C][C]4790[/C][C]4790.40248179214[/C][C]57.249801985127[/C][C]-0.402481792138994[/C][C]-0.823695383584785[/C][/ROW]
[ROW][C]30[/C][C]4837[/C][C]4837.39975626509[/C][C]52.0169990314285[/C][C]-0.39975626509278[/C][C]-0.254270120719523[/C][/ROW]
[ROW][C]31[/C][C]4915[/C][C]4915.40313835455[/C][C]65.2810848536274[/C][C]-0.403138354549748[/C][C]0.64459253651896[/C][/ROW]
[ROW][C]32[/C][C]4929.8[/C][C]4930.19992178504[/C][C]39.5113891471627[/C][C]-0.399921785039447[/C][C]-1.25235802379439[/C][/ROW]
[ROW][C]33[/C][C]5058[/C][C]5058.40268810522[/C][C]84.7851621959968[/C][C]-0.402688105216208[/C][C]2.20023262769232[/C][/ROW]
[ROW][C]34[/C][C]5150[/C][C]5150.40279826725[/C][C]88.4681898864807[/C][C]-0.402798267248087[/C][C]0.178989494692052[/C][/ROW]
[ROW][C]35[/C][C]5240[/C][C]5240.40280971661[/C][C]89.2501475540876[/C][C]-0.402809716607238[/C][C]0.0380019564074112[/C][/ROW]
[ROW][C]36[/C][C]5318[/C][C]5318.40276855376[/C][C]83.5071781288724[/C][C]-0.402768553763588[/C][C]-0.279099625784793[/C][/ROW]
[ROW][C]37[/C][C]5397.2[/C][C]5393.56146771437[/C][C]79.2821152971833[/C][C]3.63853228563235[/C][C]-0.215775528768994[/C][/ROW]
[ROW][C]38[/C][C]5474.6[/C][C]5474.9103621631[/C][C]80.2837141371072[/C][C]-0.310362163102156[/C][C]0.046965082744895[/C][/ROW]
[ROW][C]39[/C][C]5500.8[/C][C]5501.01951310651[/C][C]52.536004595091[/C][C]-0.219513106507935[/C][C]-1.33820870717318[/C][/ROW]
[ROW][C]40[/C][C]5552[/C][C]5552.21841601051[/C][C]51.8531794245331[/C][C]-0.21841601051065[/C][C]-0.0331234684583184[/C][/ROW]
[ROW][C]41[/C][C]5637.8[/C][C]5638.03205794226[/C][C]69.1873393548124[/C][C]-0.232057942255979[/C][C]0.842043896463388[/C][/ROW]
[ROW][C]42[/C][C]5622.8[/C][C]5623.01549783591[/C][C]26.2084570739257[/C][C]-0.215497835913097[/C][C]-2.08848880728135[/C][/ROW]
[ROW][C]43[/C][C]5633.8[/C][C]5634.01403341846[/C][C]18.4447232697079[/C][C]-0.214033418460484[/C][C]-0.377296208244342[/C][/ROW]
[ROW][C]44[/C][C]5567.8[/C][C]5568.01005306747[/C][C]-24.6627453332629[/C][C]-0.210053067470074[/C][C]-2.09494514928934[/C][/ROW]
[ROW][C]45[/C][C]5522[/C][C]5522.20956535045[/C][C]-35.4528900977199[/C][C]-0.209565350445817[/C][C]-0.524383966037831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298120&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298120&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
13719.83719.8000
23646.43649.65533320866-14.052811726607-3.25533320866432-1.36814464957143
33644.63647.97116616641-8.10168457469457-3.371166166414440.311574292274444
43713.23716.93048827530.5918156255917-3.730488274998411.9145054023706
53708.43712.0490866982312.5761589291984-3.64908669822537-0.879313810907245
63689.63693.21373518913-3.42985433968426-3.61373518913023-0.778671828456621
736523655.59488569956-20.8701744391092-3.59488569956045-0.847783001216672
83590.23593.78383267267-41.7631954294106-3.58383267267202-1.01542946422533
93549.63553.1839864418-41.1694135940818-3.583986441804420.0288573098121403
103580.63584.18865670741-4.32849230478494-3.588656707413751.79041918581985
113599.83603.389402046097.68231345567205-3.589402046092410.583707481469384
1236473650.5900148507327.8552784140863-3.590014850731090.980375796361104
133693.83660.0723013737118.742867872037333.727698626288-0.514893712506008
143755.63757.024361866254.369930366953-1.424361866197421.56905177065481
153832.63834.1037777215966.0437124030034-1.503777721591630.558328980687093
163917.43918.9359146216775.6424993520762-1.535914621667890.464705169423267
1740044005.5450993556581.2394483691952-1.545099355652280.271754082500712
1840864087.545411380681.6277504021911-1.54541138059680.0188667481655667
194108.84110.3335973497151.5963530410039-1.53359734970676-1.45940371745077
204179.24180.7354458737761.1953082718056-1.53544587377350.46648883247487
214210.64212.1340120330345.9853849864542-1.53401203302819-0.739177047568205
224276.64278.1344835213956.2024398471127-1.534483521385460.496533063144599
234361.24362.7348109944870.6988128623018-1.534810994478690.704501694368898
2444524453.5349244660880.960056432439-1.534924466084670.498680906437759
254496.44486.5059811854956.78628233802339.89401881451171-1.26581151947134
264581.64581.9795968300975.1747948907365-0.3795968300872710.847778027806419
2746944694.4641625184894.3069757169027-0.4641625184773720.920215612213501
2847494749.4205227878774.2088644026164-0.420522787869026-0.97431916121125
2947904790.4024817921457.249801985127-0.402481792138994-0.823695383584785
3048374837.3997562650952.0169990314285-0.39975626509278-0.254270120719523
3149154915.4031383545565.2810848536274-0.4031383545497480.64459253651896
324929.84930.1999217850439.5113891471627-0.399921785039447-1.25235802379439
3350585058.4026881052284.7851621959968-0.4026881052162082.20023262769232
3451505150.4027982672588.4681898864807-0.4027982672480870.178989494692052
3552405240.4028097166189.2501475540876-0.4028097166072380.0380019564074112
3653185318.4027685537683.5071781288724-0.402768553763588-0.279099625784793
375397.25393.5614677143779.28211529718333.63853228563235-0.215775528768994
385474.65474.910362163180.2837141371072-0.3103621631021560.046965082744895
395500.85501.0195131065152.536004595091-0.219513106507935-1.33820870717318
4055525552.2184160105151.8531794245331-0.21841601051065-0.0331234684583184
415637.85638.0320579422669.1873393548124-0.2320579422559790.842043896463388
425622.85623.0154978359126.2084570739257-0.215497835913097-2.08848880728135
435633.85634.0140334184618.4447232697079-0.214033418460484-0.377296208244342
445567.85568.01005306747-24.6627453332629-0.210053067470074-2.09494514928934
4555225522.20956535045-35.4528900977199-0.209565350445817-0.524383966037831







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15533.258950708345570.85448914746-37.5955384391155
25535.641453113615564.16447653879-28.523023425188
35544.76999932575557.47446393013-12.7044646044251
45542.56211978215550.78445132146-8.22233153936513
55538.062943164985544.0944387128-6.03149554782111
65548.773322933065537.4044261041411.3688968289198
75570.443271639885530.7144134954739.7288581444074
85578.872803870725524.0244008868154.8484029839141
95558.461926151545517.3343882781541.1275378733991
105532.310628551215510.6443756694821.6662528817332
115476.46890149135503.95436306082-27.48546156952
125449.086716865215497.26435045215-48.1776335869389
135452.978799404375490.57433784349-37.5955384391155
145455.361301809645483.88432523483-28.523023425188
155464.489848021745477.19431262616-12.7044646044251
165462.281968478135470.5043000175-8.22233153936513
175457.782791861015463.81428740883-6.03149554782112
185468.493171629095457.1242748001711.3688968289198

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5533.25895070834 & 5570.85448914746 & -37.5955384391155 \tabularnewline
2 & 5535.64145311361 & 5564.16447653879 & -28.523023425188 \tabularnewline
3 & 5544.7699993257 & 5557.47446393013 & -12.7044646044251 \tabularnewline
4 & 5542.5621197821 & 5550.78445132146 & -8.22233153936513 \tabularnewline
5 & 5538.06294316498 & 5544.0944387128 & -6.03149554782111 \tabularnewline
6 & 5548.77332293306 & 5537.40442610414 & 11.3688968289198 \tabularnewline
7 & 5570.44327163988 & 5530.71441349547 & 39.7288581444074 \tabularnewline
8 & 5578.87280387072 & 5524.02440088681 & 54.8484029839141 \tabularnewline
9 & 5558.46192615154 & 5517.33438827815 & 41.1275378733991 \tabularnewline
10 & 5532.31062855121 & 5510.64437566948 & 21.6662528817332 \tabularnewline
11 & 5476.4689014913 & 5503.95436306082 & -27.48546156952 \tabularnewline
12 & 5449.08671686521 & 5497.26435045215 & -48.1776335869389 \tabularnewline
13 & 5452.97879940437 & 5490.57433784349 & -37.5955384391155 \tabularnewline
14 & 5455.36130180964 & 5483.88432523483 & -28.523023425188 \tabularnewline
15 & 5464.48984802174 & 5477.19431262616 & -12.7044646044251 \tabularnewline
16 & 5462.28196847813 & 5470.5043000175 & -8.22233153936513 \tabularnewline
17 & 5457.78279186101 & 5463.81428740883 & -6.03149554782112 \tabularnewline
18 & 5468.49317162909 & 5457.12427480017 & 11.3688968289198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298120&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]5533.25895070834[/C][C]5570.85448914746[/C][C]-37.5955384391155[/C][/ROW]
[ROW][C]2[/C][C]5535.64145311361[/C][C]5564.16447653879[/C][C]-28.523023425188[/C][/ROW]
[ROW][C]3[/C][C]5544.7699993257[/C][C]5557.47446393013[/C][C]-12.7044646044251[/C][/ROW]
[ROW][C]4[/C][C]5542.5621197821[/C][C]5550.78445132146[/C][C]-8.22233153936513[/C][/ROW]
[ROW][C]5[/C][C]5538.06294316498[/C][C]5544.0944387128[/C][C]-6.03149554782111[/C][/ROW]
[ROW][C]6[/C][C]5548.77332293306[/C][C]5537.40442610414[/C][C]11.3688968289198[/C][/ROW]
[ROW][C]7[/C][C]5570.44327163988[/C][C]5530.71441349547[/C][C]39.7288581444074[/C][/ROW]
[ROW][C]8[/C][C]5578.87280387072[/C][C]5524.02440088681[/C][C]54.8484029839141[/C][/ROW]
[ROW][C]9[/C][C]5558.46192615154[/C][C]5517.33438827815[/C][C]41.1275378733991[/C][/ROW]
[ROW][C]10[/C][C]5532.31062855121[/C][C]5510.64437566948[/C][C]21.6662528817332[/C][/ROW]
[ROW][C]11[/C][C]5476.4689014913[/C][C]5503.95436306082[/C][C]-27.48546156952[/C][/ROW]
[ROW][C]12[/C][C]5449.08671686521[/C][C]5497.26435045215[/C][C]-48.1776335869389[/C][/ROW]
[ROW][C]13[/C][C]5452.97879940437[/C][C]5490.57433784349[/C][C]-37.5955384391155[/C][/ROW]
[ROW][C]14[/C][C]5455.36130180964[/C][C]5483.88432523483[/C][C]-28.523023425188[/C][/ROW]
[ROW][C]15[/C][C]5464.48984802174[/C][C]5477.19431262616[/C][C]-12.7044646044251[/C][/ROW]
[ROW][C]16[/C][C]5462.28196847813[/C][C]5470.5043000175[/C][C]-8.22233153936513[/C][/ROW]
[ROW][C]17[/C][C]5457.78279186101[/C][C]5463.81428740883[/C][C]-6.03149554782112[/C][/ROW]
[ROW][C]18[/C][C]5468.49317162909[/C][C]5457.12427480017[/C][C]11.3688968289198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298120&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298120&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
15533.258950708345570.85448914746-37.5955384391155
25535.641453113615564.16447653879-28.523023425188
35544.76999932575557.47446393013-12.7044646044251
45542.56211978215550.78445132146-8.22233153936513
55538.062943164985544.0944387128-6.03149554782111
65548.773322933065537.4044261041411.3688968289198
75570.443271639885530.7144134954739.7288581444074
85578.872803870725524.0244008868154.8484029839141
95558.461926151545517.3343882781541.1275378733991
105532.310628551215510.6443756694821.6662528817332
115476.46890149135503.95436306082-27.48546156952
125449.086716865215497.26435045215-48.1776335869389
135452.978799404375490.57433784349-37.5955384391155
145455.361301809645483.88432523483-28.523023425188
155464.489848021745477.19431262616-12.7044646044251
165462.281968478135470.5043000175-8.22233153936513
175457.782791861015463.81428740883-6.03149554782112
185468.493171629095457.1242748001711.3688968289198



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')