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Description of Statistical Computation

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 computationMon, 28 Nov 2011 14:20:25 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/28/t1322508074nxfi53ofnhpbk1w.htm/, Retrieved Fri, 22 May 2026 22:26:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147981, Retrieved Fri, 22 May 2026 22:26:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact396

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Structural Time Series Models] [HPC Retail Sales] [2008-03-06 16:52:55] [74be16979710d4c4e7c6647856088456]
- R  D    [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456]
- RM D        [Structural Time Series Models] [Structural Times ...] [2011-11-28 19:20:25] [5988e21ec0676b551e455a86717edc1d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
16111
15554
15220
14807
14291
14653
17006
18032
16558
16102
15055
15484
14596
14609
13923
14226
14056
14278
16142
16509
15680
14086
13129
13086
13096
12280
11534
11135
10903
10926
13220
13581
11788
11088
10434
11061
10828
10270
10360
9899
9395
9944
12117
12474
11106
10643
10227
11273
11516
11583
11605
11414
11181
12000
14007
14582
13251
12806
12645
13869
13342
13079
12513
12331
11882
12388
14394
14635
13218
12554
12031
12429

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147981&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147981&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147981&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
11611116111000
21555415707.1578701109-238.373199379973-153.157870110914-0.986921520857917
31522015218.6513035485-383.8844146331361.34869645150119-0.423177335931629
41480714798.9380024557-405.9917207818378.06199754426993-0.0601155834183752
51429114319.5635578157-450.653491371067-28.5635578156872-0.120062172985029
61465314452.3084443312-96.9786867596369200.6915556688260.965095209843632
71700616376.49636865311133.22664774101629.5036313468933.36463219893876
81803218073.61158857321476.95745960931-41.61158857318240.939643055324298
91655817389.6235623737159.784952585745-831.623562373653-3.6007543163481
101610216306.209108361-597.775325595062-204.209108360988-2.07098473034078
111505515129.998262288-950.203299777293-74.9982622880264-0.963447022214848
121548415107.3573067672-385.063817238757376.6426932327651.54494566606449
131459614631.2999875758-439.776966494676-35.2999875758049-0.155811572413377
141460914538.3138681418-233.79224036836470.68613185819910.555417886640459
151392313964.3068017629-428.502934401573-41.3068017628532-0.532763421081552
161422613881.5684467285-226.249233735648344.4315532715130.560948789615497
171405614121.365467480248.6043519523156-65.36546748022770.747557502466835
181427814718.0301562828369.803650525654-440.0301562828020.87359071443628
191614215652.4262751348700.682981862367489.5737248652330.904340364865186
201650916062.1116478223529.725555583555446.888352177701-0.46745750927805
211568016202.0329790539300.478961232075-522.032979053894-0.626665143851145
221408614729.7775427686-741.969901031038-643.777542768558-2.84991935974459
231312913516.1375713141-1018.96061128893-387.137571314135-0.757261137292597
241308612600.3457820511-958.494814431646485.6542179489360.165760646756757
251309612752.8185669101-305.873285658449343.1814330898621.79922547597847
261228012183.4481466583-459.82690297753196.5518533416634-0.419185052997084
271153411633.5957472715-511.649987773689-99.5957472715329-0.14144730957299
281113510983.8169865584-591.53587520212151.183013441618-0.220080146055882
291090310996.5794851027-239.444085129052-93.57948510274250.963125443254666
301092611459.0103263149168.544809946282-533.0103263149081.11120793443973
311322012495.5158426996672.103418589171724.4841573004151.37477375233359
321358113090.2127936681627.136946671841490.787206331942-0.12293343203697
331178812210.1470496663-249.519361007476-422.147049666256-2.39661836819089
341108811573.9079909211-474.426694345162-485.907990921064-0.614844356915292
351043410946.2435508298-563.444471811472-512.243550829775-0.243479848750701
361106110788.1808500101-327.996115019945272.8191499899450.645335125416699
371082810391.3729268966-368.022010200181436.627073103403-0.109704267596747
381027010025.5118300624-366.769540611805244.4881699376170.00341574211670297
391036010161.212394288-77.5621773780403198.7876057120360.789807501058655
40989910013.4815648264-117.998197630187-114.481564826361-0.11099036012648
4193959842.8056370354-148.497619774408-447.805637035404-0.0835271133960456
42994410568.4738968298357.519265411441-624.4738968297941.38070346164405
431211711288.1065035551566.738868020702828.8934964449310.571044856465069
441247411566.1959204337399.958415670934907.804079566298-0.455783469755779
451110611515.583617005139.421981347552-409.583617005005-0.712272522502774
461064311221.0014954107-111.538778244025-578.001495410691-0.686195344848816
471022710914.722125124-224.102575676616-687.722125124019-0.307984459859276
481127310874.7286738301-117.628298750157398.2713261698660.291600706259708
491151611001.521349624923.8120236304263514.4786503751360.386963451607012
501158311359.5467053627216.708586534797223.4532946373190.526427258011416
511160511399.8894636649115.315061012876205.110536335058-0.27700784947609
521141411519.5880478658117.83622048322-105.5880478658490.00690894833108458
531118111902.3152932659270.646728568393-721.3152932659490.418493495506452
541200012643.5715526209542.275914084137-643.5715526209430.741989084194113
551400713138.7050167535515.1042879864868.294983246495-0.0741766198257959
561458213535.5495762205446.9901967961781046.45042377946-0.186091585198799
571325113607.3949600671230.883636712646-356.394960067126-0.590786032650699
581280613426.4038645245-6.41250549390088-620.403864524543-0.648982759629444
591264513385.6455844492-26.2041684652556-740.645584449155-0.0541590810089083
601386913514.596297669163.266141397508354.4037023308890.244887436959226
611334213098.8460260388-212.9966864603243.153973961191-0.755284975183637
621307912763.6368768164-283.337262446099315.363123183575-0.192036319146921
631251312340.825113847-363.410740993439172.174886153029-0.218807542946963
641233112399.4595633839-121.063400788606-68.45956338390280.663611387871732
651188212679.0975464531109.507112933329-797.0975464531180.631319805918347
661238812990.743940572225.906344037854-602.7439405720040.318144827313882
671439413424.6227726873345.542882632574969.3772273127290.326688808160543
681463513541.5158312889214.1466406085261093.48416871112-0.358932873228857
691321813515.092897645175.9398715217001-297.092897645056-0.377807990313956
701255413295.2103324355-94.0399913671877-741.210332435505-0.464951582079873
711203112906.7847169163-263.283787139395-875.784716916332-0.46314290039223
721242912071.4053365642-592.41861001942357.594663435795-0.900535265814594

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 16111 & 16111 & 0 & 0 & 0 \tabularnewline
2 & 15554 & 15707.1578701109 & -238.373199379973 & -153.157870110914 & -0.986921520857917 \tabularnewline
3 & 15220 & 15218.6513035485 & -383.884414633136 & 1.34869645150119 & -0.423177335931629 \tabularnewline
4 & 14807 & 14798.9380024557 & -405.991720781837 & 8.06199754426993 & -0.0601155834183752 \tabularnewline
5 & 14291 & 14319.5635578157 & -450.653491371067 & -28.5635578156872 & -0.120062172985029 \tabularnewline
6 & 14653 & 14452.3084443312 & -96.9786867596369 & 200.691555668826 & 0.965095209843632 \tabularnewline
7 & 17006 & 16376.4963686531 & 1133.22664774101 & 629.503631346893 & 3.36463219893876 \tabularnewline
8 & 18032 & 18073.6115885732 & 1476.95745960931 & -41.6115885731824 & 0.939643055324298 \tabularnewline
9 & 16558 & 17389.6235623737 & 159.784952585745 & -831.623562373653 & -3.6007543163481 \tabularnewline
10 & 16102 & 16306.209108361 & -597.775325595062 & -204.209108360988 & -2.07098473034078 \tabularnewline
11 & 15055 & 15129.998262288 & -950.203299777293 & -74.9982622880264 & -0.963447022214848 \tabularnewline
12 & 15484 & 15107.3573067672 & -385.063817238757 & 376.642693232765 & 1.54494566606449 \tabularnewline
13 & 14596 & 14631.2999875758 & -439.776966494676 & -35.2999875758049 & -0.155811572413377 \tabularnewline
14 & 14609 & 14538.3138681418 & -233.792240368364 & 70.6861318581991 & 0.555417886640459 \tabularnewline
15 & 13923 & 13964.3068017629 & -428.502934401573 & -41.3068017628532 & -0.532763421081552 \tabularnewline
16 & 14226 & 13881.5684467285 & -226.249233735648 & 344.431553271513 & 0.560948789615497 \tabularnewline
17 & 14056 & 14121.3654674802 & 48.6043519523156 & -65.3654674802277 & 0.747557502466835 \tabularnewline
18 & 14278 & 14718.0301562828 & 369.803650525654 & -440.030156282802 & 0.87359071443628 \tabularnewline
19 & 16142 & 15652.4262751348 & 700.682981862367 & 489.573724865233 & 0.904340364865186 \tabularnewline
20 & 16509 & 16062.1116478223 & 529.725555583555 & 446.888352177701 & -0.46745750927805 \tabularnewline
21 & 15680 & 16202.0329790539 & 300.478961232075 & -522.032979053894 & -0.626665143851145 \tabularnewline
22 & 14086 & 14729.7775427686 & -741.969901031038 & -643.777542768558 & -2.84991935974459 \tabularnewline
23 & 13129 & 13516.1375713141 & -1018.96061128893 & -387.137571314135 & -0.757261137292597 \tabularnewline
24 & 13086 & 12600.3457820511 & -958.494814431646 & 485.654217948936 & 0.165760646756757 \tabularnewline
25 & 13096 & 12752.8185669101 & -305.873285658449 & 343.181433089862 & 1.79922547597847 \tabularnewline
26 & 12280 & 12183.4481466583 & -459.826902977531 & 96.5518533416634 & -0.419185052997084 \tabularnewline
27 & 11534 & 11633.5957472715 & -511.649987773689 & -99.5957472715329 & -0.14144730957299 \tabularnewline
28 & 11135 & 10983.8169865584 & -591.53587520212 & 151.183013441618 & -0.220080146055882 \tabularnewline
29 & 10903 & 10996.5794851027 & -239.444085129052 & -93.5794851027425 & 0.963125443254666 \tabularnewline
30 & 10926 & 11459.0103263149 & 168.544809946282 & -533.010326314908 & 1.11120793443973 \tabularnewline
31 & 13220 & 12495.5158426996 & 672.103418589171 & 724.484157300415 & 1.37477375233359 \tabularnewline
32 & 13581 & 13090.2127936681 & 627.136946671841 & 490.787206331942 & -0.12293343203697 \tabularnewline
33 & 11788 & 12210.1470496663 & -249.519361007476 & -422.147049666256 & -2.39661836819089 \tabularnewline
34 & 11088 & 11573.9079909211 & -474.426694345162 & -485.907990921064 & -0.614844356915292 \tabularnewline
35 & 10434 & 10946.2435508298 & -563.444471811472 & -512.243550829775 & -0.243479848750701 \tabularnewline
36 & 11061 & 10788.1808500101 & -327.996115019945 & 272.819149989945 & 0.645335125416699 \tabularnewline
37 & 10828 & 10391.3729268966 & -368.022010200181 & 436.627073103403 & -0.109704267596747 \tabularnewline
38 & 10270 & 10025.5118300624 & -366.769540611805 & 244.488169937617 & 0.00341574211670297 \tabularnewline
39 & 10360 & 10161.212394288 & -77.5621773780403 & 198.787605712036 & 0.789807501058655 \tabularnewline
40 & 9899 & 10013.4815648264 & -117.998197630187 & -114.481564826361 & -0.11099036012648 \tabularnewline
41 & 9395 & 9842.8056370354 & -148.497619774408 & -447.805637035404 & -0.0835271133960456 \tabularnewline
42 & 9944 & 10568.4738968298 & 357.519265411441 & -624.473896829794 & 1.38070346164405 \tabularnewline
43 & 12117 & 11288.1065035551 & 566.738868020702 & 828.893496444931 & 0.571044856465069 \tabularnewline
44 & 12474 & 11566.1959204337 & 399.958415670934 & 907.804079566298 & -0.455783469755779 \tabularnewline
45 & 11106 & 11515.583617005 & 139.421981347552 & -409.583617005005 & -0.712272522502774 \tabularnewline
46 & 10643 & 11221.0014954107 & -111.538778244025 & -578.001495410691 & -0.686195344848816 \tabularnewline
47 & 10227 & 10914.722125124 & -224.102575676616 & -687.722125124019 & -0.307984459859276 \tabularnewline
48 & 11273 & 10874.7286738301 & -117.628298750157 & 398.271326169866 & 0.291600706259708 \tabularnewline
49 & 11516 & 11001.5213496249 & 23.8120236304263 & 514.478650375136 & 0.386963451607012 \tabularnewline
50 & 11583 & 11359.5467053627 & 216.708586534797 & 223.453294637319 & 0.526427258011416 \tabularnewline
51 & 11605 & 11399.8894636649 & 115.315061012876 & 205.110536335058 & -0.27700784947609 \tabularnewline
52 & 11414 & 11519.5880478658 & 117.83622048322 & -105.588047865849 & 0.00690894833108458 \tabularnewline
53 & 11181 & 11902.3152932659 & 270.646728568393 & -721.315293265949 & 0.418493495506452 \tabularnewline
54 & 12000 & 12643.5715526209 & 542.275914084137 & -643.571552620943 & 0.741989084194113 \tabularnewline
55 & 14007 & 13138.7050167535 & 515.1042879864 & 868.294983246495 & -0.0741766198257959 \tabularnewline
56 & 14582 & 13535.5495762205 & 446.990196796178 & 1046.45042377946 & -0.186091585198799 \tabularnewline
57 & 13251 & 13607.3949600671 & 230.883636712646 & -356.394960067126 & -0.590786032650699 \tabularnewline
58 & 12806 & 13426.4038645245 & -6.41250549390088 & -620.403864524543 & -0.648982759629444 \tabularnewline
59 & 12645 & 13385.6455844492 & -26.2041684652556 & -740.645584449155 & -0.0541590810089083 \tabularnewline
60 & 13869 & 13514.5962976691 & 63.266141397508 & 354.403702330889 & 0.244887436959226 \tabularnewline
61 & 13342 & 13098.8460260388 & -212.9966864603 & 243.153973961191 & -0.755284975183637 \tabularnewline
62 & 13079 & 12763.6368768164 & -283.337262446099 & 315.363123183575 & -0.192036319146921 \tabularnewline
63 & 12513 & 12340.825113847 & -363.410740993439 & 172.174886153029 & -0.218807542946963 \tabularnewline
64 & 12331 & 12399.4595633839 & -121.063400788606 & -68.4595633839028 & 0.663611387871732 \tabularnewline
65 & 11882 & 12679.0975464531 & 109.507112933329 & -797.097546453118 & 0.631319805918347 \tabularnewline
66 & 12388 & 12990.743940572 & 225.906344037854 & -602.743940572004 & 0.318144827313882 \tabularnewline
67 & 14394 & 13424.6227726873 & 345.542882632574 & 969.377227312729 & 0.326688808160543 \tabularnewline
68 & 14635 & 13541.5158312889 & 214.146640608526 & 1093.48416871112 & -0.358932873228857 \tabularnewline
69 & 13218 & 13515.0928976451 & 75.9398715217001 & -297.092897645056 & -0.377807990313956 \tabularnewline
70 & 12554 & 13295.2103324355 & -94.0399913671877 & -741.210332435505 & -0.464951582079873 \tabularnewline
71 & 12031 & 12906.7847169163 & -263.283787139395 & -875.784716916332 & -0.46314290039223 \tabularnewline
72 & 12429 & 12071.4053365642 & -592.41861001942 & 357.594663435795 & -0.900535265814594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147981&T=1

[TABLE]
[ROW][C]Structural Time Series Model[/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]16111[/C][C]16111[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]15554[/C][C]15707.1578701109[/C][C]-238.373199379973[/C][C]-153.157870110914[/C][C]-0.986921520857917[/C][/ROW]
[ROW][C]3[/C][C]15220[/C][C]15218.6513035485[/C][C]-383.884414633136[/C][C]1.34869645150119[/C][C]-0.423177335931629[/C][/ROW]
[ROW][C]4[/C][C]14807[/C][C]14798.9380024557[/C][C]-405.991720781837[/C][C]8.06199754426993[/C][C]-0.0601155834183752[/C][/ROW]
[ROW][C]5[/C][C]14291[/C][C]14319.5635578157[/C][C]-450.653491371067[/C][C]-28.5635578156872[/C][C]-0.120062172985029[/C][/ROW]
[ROW][C]6[/C][C]14653[/C][C]14452.3084443312[/C][C]-96.9786867596369[/C][C]200.691555668826[/C][C]0.965095209843632[/C][/ROW]
[ROW][C]7[/C][C]17006[/C][C]16376.4963686531[/C][C]1133.22664774101[/C][C]629.503631346893[/C][C]3.36463219893876[/C][/ROW]
[ROW][C]8[/C][C]18032[/C][C]18073.6115885732[/C][C]1476.95745960931[/C][C]-41.6115885731824[/C][C]0.939643055324298[/C][/ROW]
[ROW][C]9[/C][C]16558[/C][C]17389.6235623737[/C][C]159.784952585745[/C][C]-831.623562373653[/C][C]-3.6007543163481[/C][/ROW]
[ROW][C]10[/C][C]16102[/C][C]16306.209108361[/C][C]-597.775325595062[/C][C]-204.209108360988[/C][C]-2.07098473034078[/C][/ROW]
[ROW][C]11[/C][C]15055[/C][C]15129.998262288[/C][C]-950.203299777293[/C][C]-74.9982622880264[/C][C]-0.963447022214848[/C][/ROW]
[ROW][C]12[/C][C]15484[/C][C]15107.3573067672[/C][C]-385.063817238757[/C][C]376.642693232765[/C][C]1.54494566606449[/C][/ROW]
[ROW][C]13[/C][C]14596[/C][C]14631.2999875758[/C][C]-439.776966494676[/C][C]-35.2999875758049[/C][C]-0.155811572413377[/C][/ROW]
[ROW][C]14[/C][C]14609[/C][C]14538.3138681418[/C][C]-233.792240368364[/C][C]70.6861318581991[/C][C]0.555417886640459[/C][/ROW]
[ROW][C]15[/C][C]13923[/C][C]13964.3068017629[/C][C]-428.502934401573[/C][C]-41.3068017628532[/C][C]-0.532763421081552[/C][/ROW]
[ROW][C]16[/C][C]14226[/C][C]13881.5684467285[/C][C]-226.249233735648[/C][C]344.431553271513[/C][C]0.560948789615497[/C][/ROW]
[ROW][C]17[/C][C]14056[/C][C]14121.3654674802[/C][C]48.6043519523156[/C][C]-65.3654674802277[/C][C]0.747557502466835[/C][/ROW]
[ROW][C]18[/C][C]14278[/C][C]14718.0301562828[/C][C]369.803650525654[/C][C]-440.030156282802[/C][C]0.87359071443628[/C][/ROW]
[ROW][C]19[/C][C]16142[/C][C]15652.4262751348[/C][C]700.682981862367[/C][C]489.573724865233[/C][C]0.904340364865186[/C][/ROW]
[ROW][C]20[/C][C]16509[/C][C]16062.1116478223[/C][C]529.725555583555[/C][C]446.888352177701[/C][C]-0.46745750927805[/C][/ROW]
[ROW][C]21[/C][C]15680[/C][C]16202.0329790539[/C][C]300.478961232075[/C][C]-522.032979053894[/C][C]-0.626665143851145[/C][/ROW]
[ROW][C]22[/C][C]14086[/C][C]14729.7775427686[/C][C]-741.969901031038[/C][C]-643.777542768558[/C][C]-2.84991935974459[/C][/ROW]
[ROW][C]23[/C][C]13129[/C][C]13516.1375713141[/C][C]-1018.96061128893[/C][C]-387.137571314135[/C][C]-0.757261137292597[/C][/ROW]
[ROW][C]24[/C][C]13086[/C][C]12600.3457820511[/C][C]-958.494814431646[/C][C]485.654217948936[/C][C]0.165760646756757[/C][/ROW]
[ROW][C]25[/C][C]13096[/C][C]12752.8185669101[/C][C]-305.873285658449[/C][C]343.181433089862[/C][C]1.79922547597847[/C][/ROW]
[ROW][C]26[/C][C]12280[/C][C]12183.4481466583[/C][C]-459.826902977531[/C][C]96.5518533416634[/C][C]-0.419185052997084[/C][/ROW]
[ROW][C]27[/C][C]11534[/C][C]11633.5957472715[/C][C]-511.649987773689[/C][C]-99.5957472715329[/C][C]-0.14144730957299[/C][/ROW]
[ROW][C]28[/C][C]11135[/C][C]10983.8169865584[/C][C]-591.53587520212[/C][C]151.183013441618[/C][C]-0.220080146055882[/C][/ROW]
[ROW][C]29[/C][C]10903[/C][C]10996.5794851027[/C][C]-239.444085129052[/C][C]-93.5794851027425[/C][C]0.963125443254666[/C][/ROW]
[ROW][C]30[/C][C]10926[/C][C]11459.0103263149[/C][C]168.544809946282[/C][C]-533.010326314908[/C][C]1.11120793443973[/C][/ROW]
[ROW][C]31[/C][C]13220[/C][C]12495.5158426996[/C][C]672.103418589171[/C][C]724.484157300415[/C][C]1.37477375233359[/C][/ROW]
[ROW][C]32[/C][C]13581[/C][C]13090.2127936681[/C][C]627.136946671841[/C][C]490.787206331942[/C][C]-0.12293343203697[/C][/ROW]
[ROW][C]33[/C][C]11788[/C][C]12210.1470496663[/C][C]-249.519361007476[/C][C]-422.147049666256[/C][C]-2.39661836819089[/C][/ROW]
[ROW][C]34[/C][C]11088[/C][C]11573.9079909211[/C][C]-474.426694345162[/C][C]-485.907990921064[/C][C]-0.614844356915292[/C][/ROW]
[ROW][C]35[/C][C]10434[/C][C]10946.2435508298[/C][C]-563.444471811472[/C][C]-512.243550829775[/C][C]-0.243479848750701[/C][/ROW]
[ROW][C]36[/C][C]11061[/C][C]10788.1808500101[/C][C]-327.996115019945[/C][C]272.819149989945[/C][C]0.645335125416699[/C][/ROW]
[ROW][C]37[/C][C]10828[/C][C]10391.3729268966[/C][C]-368.022010200181[/C][C]436.627073103403[/C][C]-0.109704267596747[/C][/ROW]
[ROW][C]38[/C][C]10270[/C][C]10025.5118300624[/C][C]-366.769540611805[/C][C]244.488169937617[/C][C]0.00341574211670297[/C][/ROW]
[ROW][C]39[/C][C]10360[/C][C]10161.212394288[/C][C]-77.5621773780403[/C][C]198.787605712036[/C][C]0.789807501058655[/C][/ROW]
[ROW][C]40[/C][C]9899[/C][C]10013.4815648264[/C][C]-117.998197630187[/C][C]-114.481564826361[/C][C]-0.11099036012648[/C][/ROW]
[ROW][C]41[/C][C]9395[/C][C]9842.8056370354[/C][C]-148.497619774408[/C][C]-447.805637035404[/C][C]-0.0835271133960456[/C][/ROW]
[ROW][C]42[/C][C]9944[/C][C]10568.4738968298[/C][C]357.519265411441[/C][C]-624.473896829794[/C][C]1.38070346164405[/C][/ROW]
[ROW][C]43[/C][C]12117[/C][C]11288.1065035551[/C][C]566.738868020702[/C][C]828.893496444931[/C][C]0.571044856465069[/C][/ROW]
[ROW][C]44[/C][C]12474[/C][C]11566.1959204337[/C][C]399.958415670934[/C][C]907.804079566298[/C][C]-0.455783469755779[/C][/ROW]
[ROW][C]45[/C][C]11106[/C][C]11515.583617005[/C][C]139.421981347552[/C][C]-409.583617005005[/C][C]-0.712272522502774[/C][/ROW]
[ROW][C]46[/C][C]10643[/C][C]11221.0014954107[/C][C]-111.538778244025[/C][C]-578.001495410691[/C][C]-0.686195344848816[/C][/ROW]
[ROW][C]47[/C][C]10227[/C][C]10914.722125124[/C][C]-224.102575676616[/C][C]-687.722125124019[/C][C]-0.307984459859276[/C][/ROW]
[ROW][C]48[/C][C]11273[/C][C]10874.7286738301[/C][C]-117.628298750157[/C][C]398.271326169866[/C][C]0.291600706259708[/C][/ROW]
[ROW][C]49[/C][C]11516[/C][C]11001.5213496249[/C][C]23.8120236304263[/C][C]514.478650375136[/C][C]0.386963451607012[/C][/ROW]
[ROW][C]50[/C][C]11583[/C][C]11359.5467053627[/C][C]216.708586534797[/C][C]223.453294637319[/C][C]0.526427258011416[/C][/ROW]
[ROW][C]51[/C][C]11605[/C][C]11399.8894636649[/C][C]115.315061012876[/C][C]205.110536335058[/C][C]-0.27700784947609[/C][/ROW]
[ROW][C]52[/C][C]11414[/C][C]11519.5880478658[/C][C]117.83622048322[/C][C]-105.588047865849[/C][C]0.00690894833108458[/C][/ROW]
[ROW][C]53[/C][C]11181[/C][C]11902.3152932659[/C][C]270.646728568393[/C][C]-721.315293265949[/C][C]0.418493495506452[/C][/ROW]
[ROW][C]54[/C][C]12000[/C][C]12643.5715526209[/C][C]542.275914084137[/C][C]-643.571552620943[/C][C]0.741989084194113[/C][/ROW]
[ROW][C]55[/C][C]14007[/C][C]13138.7050167535[/C][C]515.1042879864[/C][C]868.294983246495[/C][C]-0.0741766198257959[/C][/ROW]
[ROW][C]56[/C][C]14582[/C][C]13535.5495762205[/C][C]446.990196796178[/C][C]1046.45042377946[/C][C]-0.186091585198799[/C][/ROW]
[ROW][C]57[/C][C]13251[/C][C]13607.3949600671[/C][C]230.883636712646[/C][C]-356.394960067126[/C][C]-0.590786032650699[/C][/ROW]
[ROW][C]58[/C][C]12806[/C][C]13426.4038645245[/C][C]-6.41250549390088[/C][C]-620.403864524543[/C][C]-0.648982759629444[/C][/ROW]
[ROW][C]59[/C][C]12645[/C][C]13385.6455844492[/C][C]-26.2041684652556[/C][C]-740.645584449155[/C][C]-0.0541590810089083[/C][/ROW]
[ROW][C]60[/C][C]13869[/C][C]13514.5962976691[/C][C]63.266141397508[/C][C]354.403702330889[/C][C]0.244887436959226[/C][/ROW]
[ROW][C]61[/C][C]13342[/C][C]13098.8460260388[/C][C]-212.9966864603[/C][C]243.153973961191[/C][C]-0.755284975183637[/C][/ROW]
[ROW][C]62[/C][C]13079[/C][C]12763.6368768164[/C][C]-283.337262446099[/C][C]315.363123183575[/C][C]-0.192036319146921[/C][/ROW]
[ROW][C]63[/C][C]12513[/C][C]12340.825113847[/C][C]-363.410740993439[/C][C]172.174886153029[/C][C]-0.218807542946963[/C][/ROW]
[ROW][C]64[/C][C]12331[/C][C]12399.4595633839[/C][C]-121.063400788606[/C][C]-68.4595633839028[/C][C]0.663611387871732[/C][/ROW]
[ROW][C]65[/C][C]11882[/C][C]12679.0975464531[/C][C]109.507112933329[/C][C]-797.097546453118[/C][C]0.631319805918347[/C][/ROW]
[ROW][C]66[/C][C]12388[/C][C]12990.743940572[/C][C]225.906344037854[/C][C]-602.743940572004[/C][C]0.318144827313882[/C][/ROW]
[ROW][C]67[/C][C]14394[/C][C]13424.6227726873[/C][C]345.542882632574[/C][C]969.377227312729[/C][C]0.326688808160543[/C][/ROW]
[ROW][C]68[/C][C]14635[/C][C]13541.5158312889[/C][C]214.146640608526[/C][C]1093.48416871112[/C][C]-0.358932873228857[/C][/ROW]
[ROW][C]69[/C][C]13218[/C][C]13515.0928976451[/C][C]75.9398715217001[/C][C]-297.092897645056[/C][C]-0.377807990313956[/C][/ROW]
[ROW][C]70[/C][C]12554[/C][C]13295.2103324355[/C][C]-94.0399913671877[/C][C]-741.210332435505[/C][C]-0.464951582079873[/C][/ROW]
[ROW][C]71[/C][C]12031[/C][C]12906.7847169163[/C][C]-263.283787139395[/C][C]-875.784716916332[/C][C]-0.46314290039223[/C][/ROW]
[ROW][C]72[/C][C]12429[/C][C]12071.4053365642[/C][C]-592.41861001942[/C][C]357.594663435795[/C][C]-0.900535265814594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147981&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147981&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
11611116111000
21555415707.1578701109-238.373199379973-153.157870110914-0.986921520857917
31522015218.6513035485-383.8844146331361.34869645150119-0.423177335931629
41480714798.9380024557-405.9917207818378.06199754426993-0.0601155834183752
51429114319.5635578157-450.653491371067-28.5635578156872-0.120062172985029
61465314452.3084443312-96.9786867596369200.6915556688260.965095209843632
71700616376.49636865311133.22664774101629.5036313468933.36463219893876
81803218073.61158857321476.95745960931-41.61158857318240.939643055324298
91655817389.6235623737159.784952585745-831.623562373653-3.6007543163481
101610216306.209108361-597.775325595062-204.209108360988-2.07098473034078
111505515129.998262288-950.203299777293-74.9982622880264-0.963447022214848
121548415107.3573067672-385.063817238757376.6426932327651.54494566606449
131459614631.2999875758-439.776966494676-35.2999875758049-0.155811572413377
141460914538.3138681418-233.79224036836470.68613185819910.555417886640459
151392313964.3068017629-428.502934401573-41.3068017628532-0.532763421081552
161422613881.5684467285-226.249233735648344.4315532715130.560948789615497
171405614121.365467480248.6043519523156-65.36546748022770.747557502466835
181427814718.0301562828369.803650525654-440.0301562828020.87359071443628
191614215652.4262751348700.682981862367489.5737248652330.904340364865186
201650916062.1116478223529.725555583555446.888352177701-0.46745750927805
211568016202.0329790539300.478961232075-522.032979053894-0.626665143851145
221408614729.7775427686-741.969901031038-643.777542768558-2.84991935974459
231312913516.1375713141-1018.96061128893-387.137571314135-0.757261137292597
241308612600.3457820511-958.494814431646485.6542179489360.165760646756757
251309612752.8185669101-305.873285658449343.1814330898621.79922547597847
261228012183.4481466583-459.82690297753196.5518533416634-0.419185052997084
271153411633.5957472715-511.649987773689-99.5957472715329-0.14144730957299
281113510983.8169865584-591.53587520212151.183013441618-0.220080146055882
291090310996.5794851027-239.444085129052-93.57948510274250.963125443254666
301092611459.0103263149168.544809946282-533.0103263149081.11120793443973
311322012495.5158426996672.103418589171724.4841573004151.37477375233359
321358113090.2127936681627.136946671841490.787206331942-0.12293343203697
331178812210.1470496663-249.519361007476-422.147049666256-2.39661836819089
341108811573.9079909211-474.426694345162-485.907990921064-0.614844356915292
351043410946.2435508298-563.444471811472-512.243550829775-0.243479848750701
361106110788.1808500101-327.996115019945272.8191499899450.645335125416699
371082810391.3729268966-368.022010200181436.627073103403-0.109704267596747
381027010025.5118300624-366.769540611805244.4881699376170.00341574211670297
391036010161.212394288-77.5621773780403198.7876057120360.789807501058655
40989910013.4815648264-117.998197630187-114.481564826361-0.11099036012648
4193959842.8056370354-148.497619774408-447.805637035404-0.0835271133960456
42994410568.4738968298357.519265411441-624.4738968297941.38070346164405
431211711288.1065035551566.738868020702828.8934964449310.571044856465069
441247411566.1959204337399.958415670934907.804079566298-0.455783469755779
451110611515.583617005139.421981347552-409.583617005005-0.712272522502774
461064311221.0014954107-111.538778244025-578.001495410691-0.686195344848816
471022710914.722125124-224.102575676616-687.722125124019-0.307984459859276
481127310874.7286738301-117.628298750157398.2713261698660.291600706259708
491151611001.521349624923.8120236304263514.4786503751360.386963451607012
501158311359.5467053627216.708586534797223.4532946373190.526427258011416
511160511399.8894636649115.315061012876205.110536335058-0.27700784947609
521141411519.5880478658117.83622048322-105.5880478658490.00690894833108458
531118111902.3152932659270.646728568393-721.3152932659490.418493495506452
541200012643.5715526209542.275914084137-643.5715526209430.741989084194113
551400713138.7050167535515.1042879864868.294983246495-0.0741766198257959
561458213535.5495762205446.9901967961781046.45042377946-0.186091585198799
571325113607.3949600671230.883636712646-356.394960067126-0.590786032650699
581280613426.4038645245-6.41250549390088-620.403864524543-0.648982759629444
591264513385.6455844492-26.2041684652556-740.645584449155-0.0541590810089083
601386913514.596297669163.266141397508354.4037023308890.244887436959226
611334213098.8460260388-212.9966864603243.153973961191-0.755284975183637
621307912763.6368768164-283.337262446099315.363123183575-0.192036319146921
631251312340.825113847-363.410740993439172.174886153029-0.218807542946963
641233112399.4595633839-121.063400788606-68.45956338390280.663611387871732
651188212679.0975464531109.507112933329-797.0975464531180.631319805918347
661238812990.743940572225.906344037854-602.7439405720040.318144827313882
671439413424.6227726873345.542882632574969.3772273127290.326688808160543
681463513541.5158312889214.1466406085261093.48416871112-0.358932873228857
691321813515.092897645175.9398715217001-297.092897645056-0.377807990313956
701255413295.2103324355-94.0399913671877-741.210332435505-0.464951582079873
711203112906.7847169163-263.283787139395-875.784716916332-0.46314290039223
721242912071.4053365642-592.41861001942357.594663435795-0.900535265814594


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
m$coef
m$fitted
m$resid
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')
grid()
dev.off()
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='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()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model',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')