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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 computationFri, 16 Dec 2016 10:23:05 +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/16/t1481880222fhyfh74sy7dqf66.htm/, Retrieved Fri, 01 Nov 2024 03:34:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300163, Retrieved Fri, 01 Nov 2024 03:34:16 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
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...] [2016-12-16 09:23:05] [f9bc84b6ee189f10a7b2ad2152f37fb9] [Current]
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Dataseries X:
9137.8
9009.4
8926.6
9145
9186.2
9152.2
9093.6
9199.2
9310.6
9282
9248.4
9341.6
9478.8
9438
9374.6
9488.8
9631.8
9588.4
9514.6
9623.2
9744.6
9685.8
9598
9703.4
9817.8
9762.6
9669.6
9789.2
9917.4
9864.4
9779.2
9898.8
10048.8
9983.4
9913.4
10031.6
10184.6
10125
10065.4
10188.6
10350.4
10320.6
10232.6
10357.2
10520.2
10473.8
10407
10536
10700.2
10664.2
10606
10716.6
10882.8
10849.4
10794
10907.8




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=300163&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=300163&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300163&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
19137.89137.8000
29009.49036.91374290196-29.3231747036913-24.9061725986854-1.36803155180749
38926.68975.86298630502-39.6555460200153-43.191097903604-1.36030507271296
491459083.1847549152315.229317877111529.80183000658546.52846574252853
59186.29111.7730737098520.119157234093472.1257207978940.548185308496574
69152.29155.8023912085629.1018350662604-7.730519141775330.939330295793296
79093.69178.8800424559726.857281571205-84.2369600140192-0.240295274428903
89199.29186.0838112382419.473576786008716.5876796014693-0.787530838590919
99310.69228.8340845047128.135221019936977.81485892354080.922588836753509
1092829276.6051288678235.47913120347972.007352150419580.779844713383364
119248.49322.9163989616939.5200027509701-76.37336379307060.42987852714248
129341.69345.4423982052233.1703971995923-0.911717333527747-0.675826739313681
139478.89395.5378670397839.48323821388980.36522631215860.671370834788322
1494389438.0573585972840.6168273227712-0.5789594820420280.120563449852548
159374.69459.2996158553833.3873110242948-81.3781459972403-0.768793298379821
169488.89493.2832605840933.6098986466022-4.585641916947290.0236776897528971
179631.89541.7382685839939.149325104281887.51678200861910.589080822519324
189588.49582.8217129802639.87116027998135.246451618168420.0767731585023369
199514.69607.2026163123434.0906281126469-89.9463017934775-0.614738900847215
209623.29635.2305418605431.8280708118638-10.9905618965207-0.240639383743078
219744.69660.4707483350329.36964922811385.2589977903985-0.261449281117428
229685.89680.5675775806325.90917640555346.82286246753824-0.36803389356651
2395989693.2668849918520.9795469063894-93.0014188848501-0.52426541715484
249703.49711.9891547525120.1371736751348-8.20201148803648-0.0895886781867955
259817.89729.9495347193819.324841665864888.2237851803248-0.0863919525290333
269762.69750.4362866028719.758443012588211.96443989071240.0461143297970676
279669.69765.1121604691517.8617365267612-94.6404921930609-0.201716535149023
289789.29791.0969778223420.8931009890776-3.290115178845260.322390516292191
299917.49822.9276127791624.974756204088292.59657895690610.434088648289508
309864.49850.5490073070225.962425876939213.39708664878540.105040094560759
319779.29877.0265297843326.1546490059236-97.91486999104880.0204431656727263
329898.89904.7913794038126.7555418108043-6.267532952296020.0639057742571116
3310048.89947.1787235824332.588999008920998.94038644914370.620395579230928
349983.49974.8250053258730.74448165211929.42268278228209-0.19616688378979
359913.410009.692040284632.2829311411289-96.9990678161340.163616088509146
3610031.610042.586426804932.5111133251862-11.09129286753230.0242674764355631
3710184.610080.739022520234.6163949310166102.8934499835620.223899434630257
381012510116.626129285235.09059764162818.155940617759680.0504320806412743
3910065.410158.614078968637.6645431636496-94.39699110673760.273742462008648
4010188.610199.881470228239.009049667967-11.89936720100140.142990027138478
4110350.410244.831321685341.2260309135827104.549816789810.235778849794686
4210320.610303.92368088947.893365735290313.61220159865570.709079778632746
4310232.610338.597588652542.9601443620956-103.73042040799-0.524654537426528
4410357.210375.089707600440.5464144474782-16.7804259693619-0.256703331957468
4510520.210418.321616544441.5485840421252101.4178148104140.106582045881916
4610473.810457.372264778740.616407373360316.8561371093209-0.0991382071452314
471040710504.437097484343.0228229542481-98.54301765034810.255925441727831
481053610551.480314660444.5231488157688-16.16982175973510.159561616248277
4910700.210597.656988260445.1402091984643102.2594283359750.0656251781086539
5010664.210647.068183946646.734050779254116.39933178923170.16950713514438
511060610701.419507900949.5766555861964-96.72588823083250.302314736159805
5210716.610740.794626337745.7696582698032-22.4450386363549-0.404879139981824
5310882.810783.46950843144.614753432715299.8612529883845-0.122825638756031
5410849.410832.031714321546.087858974905716.69128826422640.156666699610487
551079410883.885613886348.2396230405662-90.87450345787660.228842920505978
5610907.810930.827794317947.7554449742446-22.8052798479123-0.0514929701232941

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 9137.8 & 9137.8 & 0 & 0 & 0 \tabularnewline
2 & 9009.4 & 9036.91374290196 & -29.3231747036913 & -24.9061725986854 & -1.36803155180749 \tabularnewline
3 & 8926.6 & 8975.86298630502 & -39.6555460200153 & -43.191097903604 & -1.36030507271296 \tabularnewline
4 & 9145 & 9083.18475491523 & 15.2293178771115 & 29.8018300065854 & 6.52846574252853 \tabularnewline
5 & 9186.2 & 9111.77307370985 & 20.1191572340934 & 72.125720797894 & 0.548185308496574 \tabularnewline
6 & 9152.2 & 9155.80239120856 & 29.1018350662604 & -7.73051914177533 & 0.939330295793296 \tabularnewline
7 & 9093.6 & 9178.88004245597 & 26.857281571205 & -84.2369600140192 & -0.240295274428903 \tabularnewline
8 & 9199.2 & 9186.08381123824 & 19.4735767860087 & 16.5876796014693 & -0.787530838590919 \tabularnewline
9 & 9310.6 & 9228.83408450471 & 28.1352210199369 & 77.8148589235408 & 0.922588836753509 \tabularnewline
10 & 9282 & 9276.60512886782 & 35.4791312034797 & 2.00735215041958 & 0.779844713383364 \tabularnewline
11 & 9248.4 & 9322.91639896169 & 39.5200027509701 & -76.3733637930706 & 0.42987852714248 \tabularnewline
12 & 9341.6 & 9345.44239820522 & 33.1703971995923 & -0.911717333527747 & -0.675826739313681 \tabularnewline
13 & 9478.8 & 9395.53786703978 & 39.483238213889 & 80.3652263121586 & 0.671370834788322 \tabularnewline
14 & 9438 & 9438.05735859728 & 40.6168273227712 & -0.578959482042028 & 0.120563449852548 \tabularnewline
15 & 9374.6 & 9459.29961585538 & 33.3873110242948 & -81.3781459972403 & -0.768793298379821 \tabularnewline
16 & 9488.8 & 9493.28326058409 & 33.6098986466022 & -4.58564191694729 & 0.0236776897528971 \tabularnewline
17 & 9631.8 & 9541.73826858399 & 39.1493251042818 & 87.5167820086191 & 0.589080822519324 \tabularnewline
18 & 9588.4 & 9582.82171298026 & 39.8711602799813 & 5.24645161816842 & 0.0767731585023369 \tabularnewline
19 & 9514.6 & 9607.20261631234 & 34.0906281126469 & -89.9463017934775 & -0.614738900847215 \tabularnewline
20 & 9623.2 & 9635.23054186054 & 31.8280708118638 & -10.9905618965207 & -0.240639383743078 \tabularnewline
21 & 9744.6 & 9660.47074833503 & 29.369649228113 & 85.2589977903985 & -0.261449281117428 \tabularnewline
22 & 9685.8 & 9680.56757758063 & 25.9091764055534 & 6.82286246753824 & -0.36803389356651 \tabularnewline
23 & 9598 & 9693.26688499185 & 20.9795469063894 & -93.0014188848501 & -0.52426541715484 \tabularnewline
24 & 9703.4 & 9711.98915475251 & 20.1371736751348 & -8.20201148803648 & -0.0895886781867955 \tabularnewline
25 & 9817.8 & 9729.94953471938 & 19.3248416658648 & 88.2237851803248 & -0.0863919525290333 \tabularnewline
26 & 9762.6 & 9750.43628660287 & 19.7584430125882 & 11.9644398907124 & 0.0461143297970676 \tabularnewline
27 & 9669.6 & 9765.11216046915 & 17.8617365267612 & -94.6404921930609 & -0.201716535149023 \tabularnewline
28 & 9789.2 & 9791.09697782234 & 20.8931009890776 & -3.29011517884526 & 0.322390516292191 \tabularnewline
29 & 9917.4 & 9822.92761277916 & 24.9747562040882 & 92.5965789569061 & 0.434088648289508 \tabularnewline
30 & 9864.4 & 9850.54900730702 & 25.9624258769392 & 13.3970866487854 & 0.105040094560759 \tabularnewline
31 & 9779.2 & 9877.02652978433 & 26.1546490059236 & -97.9148699910488 & 0.0204431656727263 \tabularnewline
32 & 9898.8 & 9904.79137940381 & 26.7555418108043 & -6.26753295229602 & 0.0639057742571116 \tabularnewline
33 & 10048.8 & 9947.17872358243 & 32.5889990089209 & 98.9403864491437 & 0.620395579230928 \tabularnewline
34 & 9983.4 & 9974.82500532587 & 30.7444816521192 & 9.42268278228209 & -0.19616688378979 \tabularnewline
35 & 9913.4 & 10009.6920402846 & 32.2829311411289 & -96.999067816134 & 0.163616088509146 \tabularnewline
36 & 10031.6 & 10042.5864268049 & 32.5111133251862 & -11.0912928675323 & 0.0242674764355631 \tabularnewline
37 & 10184.6 & 10080.7390225202 & 34.6163949310166 & 102.893449983562 & 0.223899434630257 \tabularnewline
38 & 10125 & 10116.6261292852 & 35.0905976416281 & 8.15594061775968 & 0.0504320806412743 \tabularnewline
39 & 10065.4 & 10158.6140789686 & 37.6645431636496 & -94.3969911067376 & 0.273742462008648 \tabularnewline
40 & 10188.6 & 10199.8814702282 & 39.009049667967 & -11.8993672010014 & 0.142990027138478 \tabularnewline
41 & 10350.4 & 10244.8313216853 & 41.2260309135827 & 104.54981678981 & 0.235778849794686 \tabularnewline
42 & 10320.6 & 10303.923680889 & 47.8933657352903 & 13.6122015986557 & 0.709079778632746 \tabularnewline
43 & 10232.6 & 10338.5975886525 & 42.9601443620956 & -103.73042040799 & -0.524654537426528 \tabularnewline
44 & 10357.2 & 10375.0897076004 & 40.5464144474782 & -16.7804259693619 & -0.256703331957468 \tabularnewline
45 & 10520.2 & 10418.3216165444 & 41.5485840421252 & 101.417814810414 & 0.106582045881916 \tabularnewline
46 & 10473.8 & 10457.3722647787 & 40.6164073733603 & 16.8561371093209 & -0.0991382071452314 \tabularnewline
47 & 10407 & 10504.4370974843 & 43.0228229542481 & -98.5430176503481 & 0.255925441727831 \tabularnewline
48 & 10536 & 10551.4803146604 & 44.5231488157688 & -16.1698217597351 & 0.159561616248277 \tabularnewline
49 & 10700.2 & 10597.6569882604 & 45.1402091984643 & 102.259428335975 & 0.0656251781086539 \tabularnewline
50 & 10664.2 & 10647.0681839466 & 46.7340507792541 & 16.3993317892317 & 0.16950713514438 \tabularnewline
51 & 10606 & 10701.4195079009 & 49.5766555861964 & -96.7258882308325 & 0.302314736159805 \tabularnewline
52 & 10716.6 & 10740.7946263377 & 45.7696582698032 & -22.4450386363549 & -0.404879139981824 \tabularnewline
53 & 10882.8 & 10783.469508431 & 44.6147534327152 & 99.8612529883845 & -0.122825638756031 \tabularnewline
54 & 10849.4 & 10832.0317143215 & 46.0878589749057 & 16.6912882642264 & 0.156666699610487 \tabularnewline
55 & 10794 & 10883.8856138863 & 48.2396230405662 & -90.8745034578766 & 0.228842920505978 \tabularnewline
56 & 10907.8 & 10930.8277943179 & 47.7554449742446 & -22.8052798479123 & -0.0514929701232941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300163&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]9137.8[/C][C]9137.8[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]9009.4[/C][C]9036.91374290196[/C][C]-29.3231747036913[/C][C]-24.9061725986854[/C][C]-1.36803155180749[/C][/ROW]
[ROW][C]3[/C][C]8926.6[/C][C]8975.86298630502[/C][C]-39.6555460200153[/C][C]-43.191097903604[/C][C]-1.36030507271296[/C][/ROW]
[ROW][C]4[/C][C]9145[/C][C]9083.18475491523[/C][C]15.2293178771115[/C][C]29.8018300065854[/C][C]6.52846574252853[/C][/ROW]
[ROW][C]5[/C][C]9186.2[/C][C]9111.77307370985[/C][C]20.1191572340934[/C][C]72.125720797894[/C][C]0.548185308496574[/C][/ROW]
[ROW][C]6[/C][C]9152.2[/C][C]9155.80239120856[/C][C]29.1018350662604[/C][C]-7.73051914177533[/C][C]0.939330295793296[/C][/ROW]
[ROW][C]7[/C][C]9093.6[/C][C]9178.88004245597[/C][C]26.857281571205[/C][C]-84.2369600140192[/C][C]-0.240295274428903[/C][/ROW]
[ROW][C]8[/C][C]9199.2[/C][C]9186.08381123824[/C][C]19.4735767860087[/C][C]16.5876796014693[/C][C]-0.787530838590919[/C][/ROW]
[ROW][C]9[/C][C]9310.6[/C][C]9228.83408450471[/C][C]28.1352210199369[/C][C]77.8148589235408[/C][C]0.922588836753509[/C][/ROW]
[ROW][C]10[/C][C]9282[/C][C]9276.60512886782[/C][C]35.4791312034797[/C][C]2.00735215041958[/C][C]0.779844713383364[/C][/ROW]
[ROW][C]11[/C][C]9248.4[/C][C]9322.91639896169[/C][C]39.5200027509701[/C][C]-76.3733637930706[/C][C]0.42987852714248[/C][/ROW]
[ROW][C]12[/C][C]9341.6[/C][C]9345.44239820522[/C][C]33.1703971995923[/C][C]-0.911717333527747[/C][C]-0.675826739313681[/C][/ROW]
[ROW][C]13[/C][C]9478.8[/C][C]9395.53786703978[/C][C]39.483238213889[/C][C]80.3652263121586[/C][C]0.671370834788322[/C][/ROW]
[ROW][C]14[/C][C]9438[/C][C]9438.05735859728[/C][C]40.6168273227712[/C][C]-0.578959482042028[/C][C]0.120563449852548[/C][/ROW]
[ROW][C]15[/C][C]9374.6[/C][C]9459.29961585538[/C][C]33.3873110242948[/C][C]-81.3781459972403[/C][C]-0.768793298379821[/C][/ROW]
[ROW][C]16[/C][C]9488.8[/C][C]9493.28326058409[/C][C]33.6098986466022[/C][C]-4.58564191694729[/C][C]0.0236776897528971[/C][/ROW]
[ROW][C]17[/C][C]9631.8[/C][C]9541.73826858399[/C][C]39.1493251042818[/C][C]87.5167820086191[/C][C]0.589080822519324[/C][/ROW]
[ROW][C]18[/C][C]9588.4[/C][C]9582.82171298026[/C][C]39.8711602799813[/C][C]5.24645161816842[/C][C]0.0767731585023369[/C][/ROW]
[ROW][C]19[/C][C]9514.6[/C][C]9607.20261631234[/C][C]34.0906281126469[/C][C]-89.9463017934775[/C][C]-0.614738900847215[/C][/ROW]
[ROW][C]20[/C][C]9623.2[/C][C]9635.23054186054[/C][C]31.8280708118638[/C][C]-10.9905618965207[/C][C]-0.240639383743078[/C][/ROW]
[ROW][C]21[/C][C]9744.6[/C][C]9660.47074833503[/C][C]29.369649228113[/C][C]85.2589977903985[/C][C]-0.261449281117428[/C][/ROW]
[ROW][C]22[/C][C]9685.8[/C][C]9680.56757758063[/C][C]25.9091764055534[/C][C]6.82286246753824[/C][C]-0.36803389356651[/C][/ROW]
[ROW][C]23[/C][C]9598[/C][C]9693.26688499185[/C][C]20.9795469063894[/C][C]-93.0014188848501[/C][C]-0.52426541715484[/C][/ROW]
[ROW][C]24[/C][C]9703.4[/C][C]9711.98915475251[/C][C]20.1371736751348[/C][C]-8.20201148803648[/C][C]-0.0895886781867955[/C][/ROW]
[ROW][C]25[/C][C]9817.8[/C][C]9729.94953471938[/C][C]19.3248416658648[/C][C]88.2237851803248[/C][C]-0.0863919525290333[/C][/ROW]
[ROW][C]26[/C][C]9762.6[/C][C]9750.43628660287[/C][C]19.7584430125882[/C][C]11.9644398907124[/C][C]0.0461143297970676[/C][/ROW]
[ROW][C]27[/C][C]9669.6[/C][C]9765.11216046915[/C][C]17.8617365267612[/C][C]-94.6404921930609[/C][C]-0.201716535149023[/C][/ROW]
[ROW][C]28[/C][C]9789.2[/C][C]9791.09697782234[/C][C]20.8931009890776[/C][C]-3.29011517884526[/C][C]0.322390516292191[/C][/ROW]
[ROW][C]29[/C][C]9917.4[/C][C]9822.92761277916[/C][C]24.9747562040882[/C][C]92.5965789569061[/C][C]0.434088648289508[/C][/ROW]
[ROW][C]30[/C][C]9864.4[/C][C]9850.54900730702[/C][C]25.9624258769392[/C][C]13.3970866487854[/C][C]0.105040094560759[/C][/ROW]
[ROW][C]31[/C][C]9779.2[/C][C]9877.02652978433[/C][C]26.1546490059236[/C][C]-97.9148699910488[/C][C]0.0204431656727263[/C][/ROW]
[ROW][C]32[/C][C]9898.8[/C][C]9904.79137940381[/C][C]26.7555418108043[/C][C]-6.26753295229602[/C][C]0.0639057742571116[/C][/ROW]
[ROW][C]33[/C][C]10048.8[/C][C]9947.17872358243[/C][C]32.5889990089209[/C][C]98.9403864491437[/C][C]0.620395579230928[/C][/ROW]
[ROW][C]34[/C][C]9983.4[/C][C]9974.82500532587[/C][C]30.7444816521192[/C][C]9.42268278228209[/C][C]-0.19616688378979[/C][/ROW]
[ROW][C]35[/C][C]9913.4[/C][C]10009.6920402846[/C][C]32.2829311411289[/C][C]-96.999067816134[/C][C]0.163616088509146[/C][/ROW]
[ROW][C]36[/C][C]10031.6[/C][C]10042.5864268049[/C][C]32.5111133251862[/C][C]-11.0912928675323[/C][C]0.0242674764355631[/C][/ROW]
[ROW][C]37[/C][C]10184.6[/C][C]10080.7390225202[/C][C]34.6163949310166[/C][C]102.893449983562[/C][C]0.223899434630257[/C][/ROW]
[ROW][C]38[/C][C]10125[/C][C]10116.6261292852[/C][C]35.0905976416281[/C][C]8.15594061775968[/C][C]0.0504320806412743[/C][/ROW]
[ROW][C]39[/C][C]10065.4[/C][C]10158.6140789686[/C][C]37.6645431636496[/C][C]-94.3969911067376[/C][C]0.273742462008648[/C][/ROW]
[ROW][C]40[/C][C]10188.6[/C][C]10199.8814702282[/C][C]39.009049667967[/C][C]-11.8993672010014[/C][C]0.142990027138478[/C][/ROW]
[ROW][C]41[/C][C]10350.4[/C][C]10244.8313216853[/C][C]41.2260309135827[/C][C]104.54981678981[/C][C]0.235778849794686[/C][/ROW]
[ROW][C]42[/C][C]10320.6[/C][C]10303.923680889[/C][C]47.8933657352903[/C][C]13.6122015986557[/C][C]0.709079778632746[/C][/ROW]
[ROW][C]43[/C][C]10232.6[/C][C]10338.5975886525[/C][C]42.9601443620956[/C][C]-103.73042040799[/C][C]-0.524654537426528[/C][/ROW]
[ROW][C]44[/C][C]10357.2[/C][C]10375.0897076004[/C][C]40.5464144474782[/C][C]-16.7804259693619[/C][C]-0.256703331957468[/C][/ROW]
[ROW][C]45[/C][C]10520.2[/C][C]10418.3216165444[/C][C]41.5485840421252[/C][C]101.417814810414[/C][C]0.106582045881916[/C][/ROW]
[ROW][C]46[/C][C]10473.8[/C][C]10457.3722647787[/C][C]40.6164073733603[/C][C]16.8561371093209[/C][C]-0.0991382071452314[/C][/ROW]
[ROW][C]47[/C][C]10407[/C][C]10504.4370974843[/C][C]43.0228229542481[/C][C]-98.5430176503481[/C][C]0.255925441727831[/C][/ROW]
[ROW][C]48[/C][C]10536[/C][C]10551.4803146604[/C][C]44.5231488157688[/C][C]-16.1698217597351[/C][C]0.159561616248277[/C][/ROW]
[ROW][C]49[/C][C]10700.2[/C][C]10597.6569882604[/C][C]45.1402091984643[/C][C]102.259428335975[/C][C]0.0656251781086539[/C][/ROW]
[ROW][C]50[/C][C]10664.2[/C][C]10647.0681839466[/C][C]46.7340507792541[/C][C]16.3993317892317[/C][C]0.16950713514438[/C][/ROW]
[ROW][C]51[/C][C]10606[/C][C]10701.4195079009[/C][C]49.5766555861964[/C][C]-96.7258882308325[/C][C]0.302314736159805[/C][/ROW]
[ROW][C]52[/C][C]10716.6[/C][C]10740.7946263377[/C][C]45.7696582698032[/C][C]-22.4450386363549[/C][C]-0.404879139981824[/C][/ROW]
[ROW][C]53[/C][C]10882.8[/C][C]10783.469508431[/C][C]44.6147534327152[/C][C]99.8612529883845[/C][C]-0.122825638756031[/C][/ROW]
[ROW][C]54[/C][C]10849.4[/C][C]10832.0317143215[/C][C]46.0878589749057[/C][C]16.6912882642264[/C][C]0.156666699610487[/C][/ROW]
[ROW][C]55[/C][C]10794[/C][C]10883.8856138863[/C][C]48.2396230405662[/C][C]-90.8745034578766[/C][C]0.228842920505978[/C][/ROW]
[ROW][C]56[/C][C]10907.8[/C][C]10930.8277943179[/C][C]47.7554449742446[/C][C]-22.8052798479123[/C][C]-0.0514929701232941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300163&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300163&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
19137.89137.8000
29009.49036.91374290196-29.3231747036913-24.9061725986854-1.36803155180749
38926.68975.86298630502-39.6555460200153-43.191097903604-1.36030507271296
491459083.1847549152315.229317877111529.80183000658546.52846574252853
59186.29111.7730737098520.119157234093472.1257207978940.548185308496574
69152.29155.8023912085629.1018350662604-7.730519141775330.939330295793296
79093.69178.8800424559726.857281571205-84.2369600140192-0.240295274428903
89199.29186.0838112382419.473576786008716.5876796014693-0.787530838590919
99310.69228.8340845047128.135221019936977.81485892354080.922588836753509
1092829276.6051288678235.47913120347972.007352150419580.779844713383364
119248.49322.9163989616939.5200027509701-76.37336379307060.42987852714248
129341.69345.4423982052233.1703971995923-0.911717333527747-0.675826739313681
139478.89395.5378670397839.48323821388980.36522631215860.671370834788322
1494389438.0573585972840.6168273227712-0.5789594820420280.120563449852548
159374.69459.2996158553833.3873110242948-81.3781459972403-0.768793298379821
169488.89493.2832605840933.6098986466022-4.585641916947290.0236776897528971
179631.89541.7382685839939.149325104281887.51678200861910.589080822519324
189588.49582.8217129802639.87116027998135.246451618168420.0767731585023369
199514.69607.2026163123434.0906281126469-89.9463017934775-0.614738900847215
209623.29635.2305418605431.8280708118638-10.9905618965207-0.240639383743078
219744.69660.4707483350329.36964922811385.2589977903985-0.261449281117428
229685.89680.5675775806325.90917640555346.82286246753824-0.36803389356651
2395989693.2668849918520.9795469063894-93.0014188848501-0.52426541715484
249703.49711.9891547525120.1371736751348-8.20201148803648-0.0895886781867955
259817.89729.9495347193819.324841665864888.2237851803248-0.0863919525290333
269762.69750.4362866028719.758443012588211.96443989071240.0461143297970676
279669.69765.1121604691517.8617365267612-94.6404921930609-0.201716535149023
289789.29791.0969778223420.8931009890776-3.290115178845260.322390516292191
299917.49822.9276127791624.974756204088292.59657895690610.434088648289508
309864.49850.5490073070225.962425876939213.39708664878540.105040094560759
319779.29877.0265297843326.1546490059236-97.91486999104880.0204431656727263
329898.89904.7913794038126.7555418108043-6.267532952296020.0639057742571116
3310048.89947.1787235824332.588999008920998.94038644914370.620395579230928
349983.49974.8250053258730.74448165211929.42268278228209-0.19616688378979
359913.410009.692040284632.2829311411289-96.9990678161340.163616088509146
3610031.610042.586426804932.5111133251862-11.09129286753230.0242674764355631
3710184.610080.739022520234.6163949310166102.8934499835620.223899434630257
381012510116.626129285235.09059764162818.155940617759680.0504320806412743
3910065.410158.614078968637.6645431636496-94.39699110673760.273742462008648
4010188.610199.881470228239.009049667967-11.89936720100140.142990027138478
4110350.410244.831321685341.2260309135827104.549816789810.235778849794686
4210320.610303.92368088947.893365735290313.61220159865570.709079778632746
4310232.610338.597588652542.9601443620956-103.73042040799-0.524654537426528
4410357.210375.089707600440.5464144474782-16.7804259693619-0.256703331957468
4510520.210418.321616544441.5485840421252101.4178148104140.106582045881916
4610473.810457.372264778740.616407373360316.8561371093209-0.0991382071452314
471040710504.437097484343.0228229542481-98.54301765034810.255925441727831
481053610551.480314660444.5231488157688-16.16982175973510.159561616248277
4910700.210597.656988260445.1402091984643102.2594283359750.0656251781086539
5010664.210647.068183946646.734050779254116.39933178923170.16950713514438
511060610701.419507900949.5766555861964-96.72588823083250.302314736159805
5210716.610740.794626337745.7696582698032-22.4450386363549-0.404879139981824
5310882.810783.46950843144.614753432715299.8612529883845-0.122825638756031
5410849.410832.031714321546.087858974905716.69128826422640.156666699610487
551079410883.885613886348.2396230405662-90.87450345787660.228842920505978
5610907.810930.827794317947.7554449742446-22.8052798479123-0.0514929701232941







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
111076.936940300410978.584396750198.3525435503379
211041.249328701411026.340142255914.9091864455069
310983.640929245411074.0958877617-90.4549585162836
411099.044861787911121.8516332675-22.8067714795611
511267.959922323611169.607378773398.3525435503379
611232.272310724611217.363124279114.9091864455069
711174.663911268611265.1188697849-90.4549585162836
811290.067843811211312.8746152907-22.8067714795611
911458.982904346911360.630360796598.3525435503379
1011423.295292747811408.386106302314.9091864455069
1111365.686893291811456.1418518081-90.4549585162836
1211481.090825834411503.8975973139-22.8067714795611

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 11076.9369403004 & 10978.5843967501 & 98.3525435503379 \tabularnewline
2 & 11041.2493287014 & 11026.3401422559 & 14.9091864455069 \tabularnewline
3 & 10983.6409292454 & 11074.0958877617 & -90.4549585162836 \tabularnewline
4 & 11099.0448617879 & 11121.8516332675 & -22.8067714795611 \tabularnewline
5 & 11267.9599223236 & 11169.6073787733 & 98.3525435503379 \tabularnewline
6 & 11232.2723107246 & 11217.3631242791 & 14.9091864455069 \tabularnewline
7 & 11174.6639112686 & 11265.1188697849 & -90.4549585162836 \tabularnewline
8 & 11290.0678438112 & 11312.8746152907 & -22.8067714795611 \tabularnewline
9 & 11458.9829043469 & 11360.6303607965 & 98.3525435503379 \tabularnewline
10 & 11423.2952927478 & 11408.3861063023 & 14.9091864455069 \tabularnewline
11 & 11365.6868932918 & 11456.1418518081 & -90.4549585162836 \tabularnewline
12 & 11481.0908258344 & 11503.8975973139 & -22.8067714795611 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300163&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]11076.9369403004[/C][C]10978.5843967501[/C][C]98.3525435503379[/C][/ROW]
[ROW][C]2[/C][C]11041.2493287014[/C][C]11026.3401422559[/C][C]14.9091864455069[/C][/ROW]
[ROW][C]3[/C][C]10983.6409292454[/C][C]11074.0958877617[/C][C]-90.4549585162836[/C][/ROW]
[ROW][C]4[/C][C]11099.0448617879[/C][C]11121.8516332675[/C][C]-22.8067714795611[/C][/ROW]
[ROW][C]5[/C][C]11267.9599223236[/C][C]11169.6073787733[/C][C]98.3525435503379[/C][/ROW]
[ROW][C]6[/C][C]11232.2723107246[/C][C]11217.3631242791[/C][C]14.9091864455069[/C][/ROW]
[ROW][C]7[/C][C]11174.6639112686[/C][C]11265.1188697849[/C][C]-90.4549585162836[/C][/ROW]
[ROW][C]8[/C][C]11290.0678438112[/C][C]11312.8746152907[/C][C]-22.8067714795611[/C][/ROW]
[ROW][C]9[/C][C]11458.9829043469[/C][C]11360.6303607965[/C][C]98.3525435503379[/C][/ROW]
[ROW][C]10[/C][C]11423.2952927478[/C][C]11408.3861063023[/C][C]14.9091864455069[/C][/ROW]
[ROW][C]11[/C][C]11365.6868932918[/C][C]11456.1418518081[/C][C]-90.4549585162836[/C][/ROW]
[ROW][C]12[/C][C]11481.0908258344[/C][C]11503.8975973139[/C][C]-22.8067714795611[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300163&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300163&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
111076.936940300410978.584396750198.3525435503379
211041.249328701411026.340142255914.9091864455069
310983.640929245411074.0958877617-90.4549585162836
411099.044861787911121.8516332675-22.8067714795611
511267.959922323611169.607378773398.3525435503379
611232.272310724611217.363124279114.9091864455069
711174.663911268611265.1188697849-90.4549585162836
811290.067843811211312.8746152907-22.8067714795611
911458.982904346911360.630360796598.3525435503379
1011423.295292747811408.386106302314.9091864455069
1111365.686893291811456.1418518081-90.4549585162836
1211481.090825834411503.8975973139-22.8067714795611



Parameters (Session):
par1 = 4 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 4 ; 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')