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R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Wed, 02 Dec 2009 13:59:19 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/02/t1259787606kuhdt0fv9a1qfly.htm/, Retrieved Tue, 21 Apr 2026 05:28:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62587, Retrieved Tue, 21 Apr 2026 05:28:48 +0000

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IsPrivate?

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Estimated Impact

412

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Structural Time Series Models] [] [2009-11-27 15:02:30] [b98453cac15ba1066b407e146608df68]
- R  D      [Structural Time Series Models] [] [2009-12-02 20:59:19] [7c5623390f136c6c339940134868d3e2] [Current]
- R P         [Structural Time Series Models] [] [2009-12-16 20:58:04] [00ae4ca1aa430eb3950856e282097098] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62587&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62587&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62587&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 Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	519	519	0	0	0
2	517	517.53488576319	-1.50931967068352	-0.534885763190245	-0.195917433969918
3	510	511.16081785952	-4.83640438677179	-1.16081785951987	-0.392237856250045
4	509	508.037137786154	-3.59297681257972	0.962862213845823	0.144093393598201
5	501	501.931210878454	-5.38261979234418	-0.931210878453754	-0.198503448653565
6	507	504.481454351377	0.225291191827157	2.5185456486234	0.62847050025145
7	569	554.95164228436	35.867331872617	14.0483577156393	3.99269021633074
8	580	586.062027693306	32.4901132096203	-6.06202769330635	-0.378037598250256
9	578	586.988624471589	10.0833547031088	-8.98862447158926	-2.50841293522469
10	565	570.172230981533	-9.00870670356781	-5.1722309815326	-2.13730328845535
11	547	548.41501673278	-18.0560584872628	-1.41501673278001	-1.01281832390928
12	555	548.559512126371	-5.13937789484071	6.4404878736286	1.44597793857026
13	562	558.837841072575	5.77274633040281	3.16215892742494	1.22544629398114
14	561	562.308458906698	4.13702027413221	-1.30845890669831	-0.186017119087309
15	555	557.687050697457	-1.87267524876861	-2.68705069745723	-0.668685054456384
16	544	542.403886365893	-11.0334912457731	1.59611363410696	-1.04188732497722
17	537	536.684457281772	-7.37502441697304	0.315542718228301	0.4098364124012
18	543	551.268255807669	7.6204892170364	-8.26825580766865	1.67404698884967
19	594	577.463147782637	20.2926889639789	16.5368522173628	1.41962649034373
20	611	607.760346136581	27.1302151031926	3.23965386341893	0.765654019379351
21	613	619.073585930938	16.3148820785158	-6.07358593093843	-1.21064162342642
22	611	616.16090698309	3.16786824404775	-5.16090698308993	-1.47186502087566
23	594	604.156010494937	-7.20248277329205	-10.1560104949366	-1.16094206889327
24	595	593.894944914613	-9.29072115986202	1.10505508538653	-0.233853818426585
25	591	586.786106270801	-7.80084535688394	4.21389372919851	0.167298240048712
26	589	584.679424821553	-3.9076773595721	4.32057517844665	0.436478595201897
27	584	580.491453784252	-4.09741968659976	3.50854621574841	-0.0211877937283579
28	573	572.376381552077	-6.80792453391357	0.623618447923053	-0.305025292554735
29	567	571.275527873055	-2.93767135303228	-4.2755278730546	0.434380592348358
30	569	581.139807467815	5.72276901437693	-12.1398074678145	0.967631686718844
31	621	604.783455390935	17.8162552110648	16.2165446090654	1.35334777357137
32	629	622.914321794534	18.0287501436880	6.085678205466	0.0237963385170933
33	628	631.273185881033	11.4919827271705	-3.27318588103264	-0.731760462375117
34	612	619.034372715256	-4.55084459529663	-7.034372715256	-1.79597672442147
35	595	605.602642402641	-10.5515908366955	-10.6026424026414	-0.671780986634648
36	597	596.117984864524	-9.83110419756276	0.882015135476252	0.0807106975335485
37	593	589.505590051469	-7.65594162463881	3.49440994853093	0.243935906296182
38	590	583.826580184859	-6.32036795774515	6.17341981514053	0.149496513561709
39	580	574.370230788928	-8.42874262687417	5.62976921107169	-0.235737801836184
40	574	571.936294220964	-4.40530367621779	2.06370577903589	0.451462185397122
41	573	578.775270023456	3.16303817899002	-5.77527002345611	0.848969328353827
42	573	590.423616178246	8.87255658476506	-17.4236161782464	0.638620028477297
43	620	604.478954183038	12.3531944414395	15.5210458169624	0.389364730856851
44	626	617.413377632499	12.7435337701036	8.58662236750144	0.0437003858891592
45	620	618.948409424444	5.2109568683047	1.05159057555633	-0.84329004262027
46	588	599.128070785592	-11.6137169992138	-11.1280707855923	-1.88348049229621
47	566	578.635295529771	-17.5798043371606	-12.6352955297715	-0.667966338555024
48	557	557.86847801415	-19.7210446513701	-0.868478014149465	-0.239866377758354
49	561	552.673817483451	-9.95541515873275	8.32618251654923	1.09422816963352
50	549	541.487802219984	-10.7821493913125	7.51219778001625	-0.0925134172564313
51	532	527.86983573287	-12.6818517297867	4.13016426713028	-0.212518265865295
52	526	524.353760526945	-6.54767085350996	1.64623947305465	0.687590183337382
53	511	520.026577030717	-5.05903817220852	-9.02657703071652	0.166892365403853
54	499	518.76078483126	-2.51522676542611	-19.7607848312599	0.284698009363485
55	555	535.884644676667	10.6385500832129	19.1153553233334	1.47152213130353
56	565	552.41137851768	14.5805359889659	12.5886214823201	0.441223277411353
57	542	540.482672361279	-3.17263792438587	1.51732763872071	-1.98749946266108
58	527	534.192382851342	-5.26087479406452	-7.19238285134166	-0.233788317873157
59	510	523.701322028714	-8.76379582719401	-13.7013220287140	-0.392233342365311
60	514	518.376693631045	-6.46002578594065	-4.37669363104481	0.258046937760827
61	517	508.663803878302	-8.6398232894806	8.33619612169845	-0.244128210074671
62	508	498.971407597004	-9.3446543170203	9.02859240299631	-0.0788689212302369
63	493	490.464523405607	-8.78471794516405	2.5354765943928	0.0626554170019082
64	490	486.563474934858	-5.52257960050777	3.43652506514171	0.365491028832501
65	469	480.416519265422	-5.94012292608596	-11.4165192654216	-0.0467943279911121
66	478	498.690151024325	10.260040052035	-20.6901510243251	1.81360380907420
67	528	511.418310545811	11.9100070657757	16.5816894541889	0.184608971279338
68	534	515.141021350741	6.44011800242520	18.8589786492590	-0.612165182048206
69	518	516.533998204122	3.06812512897663	1.4660017958784	-0.377486923997789
70	506	513.587580086199	-0.950712848649473	-7.58758008619888	-0.449964271024861
71	502	515.853248502042	1.19863293710772	-13.8532485020418	0.240690861429298
72	516	518.818108391217	2.37924407106951	-2.81810839121707	0.132227795184545

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 519 & 519 & 0 & 0 & 0 \tabularnewline
2 & 517 & 517.53488576319 & -1.50931967068352 & -0.534885763190245 & -0.195917433969918 \tabularnewline
3 & 510 & 511.16081785952 & -4.83640438677179 & -1.16081785951987 & -0.392237856250045 \tabularnewline
4 & 509 & 508.037137786154 & -3.59297681257972 & 0.962862213845823 & 0.144093393598201 \tabularnewline
5 & 501 & 501.931210878454 & -5.38261979234418 & -0.931210878453754 & -0.198503448653565 \tabularnewline
6 & 507 & 504.481454351377 & 0.225291191827157 & 2.5185456486234 & 0.62847050025145 \tabularnewline
7 & 569 & 554.95164228436 & 35.867331872617 & 14.0483577156393 & 3.99269021633074 \tabularnewline
8 & 580 & 586.062027693306 & 32.4901132096203 & -6.06202769330635 & -0.378037598250256 \tabularnewline
9 & 578 & 586.988624471589 & 10.0833547031088 & -8.98862447158926 & -2.50841293522469 \tabularnewline
10 & 565 & 570.172230981533 & -9.00870670356781 & -5.1722309815326 & -2.13730328845535 \tabularnewline
11 & 547 & 548.41501673278 & -18.0560584872628 & -1.41501673278001 & -1.01281832390928 \tabularnewline
12 & 555 & 548.559512126371 & -5.13937789484071 & 6.4404878736286 & 1.44597793857026 \tabularnewline
13 & 562 & 558.837841072575 & 5.77274633040281 & 3.16215892742494 & 1.22544629398114 \tabularnewline
14 & 561 & 562.308458906698 & 4.13702027413221 & -1.30845890669831 & -0.186017119087309 \tabularnewline
15 & 555 & 557.687050697457 & -1.87267524876861 & -2.68705069745723 & -0.668685054456384 \tabularnewline
16 & 544 & 542.403886365893 & -11.0334912457731 & 1.59611363410696 & -1.04188732497722 \tabularnewline
17 & 537 & 536.684457281772 & -7.37502441697304 & 0.315542718228301 & 0.4098364124012 \tabularnewline
18 & 543 & 551.268255807669 & 7.6204892170364 & -8.26825580766865 & 1.67404698884967 \tabularnewline
19 & 594 & 577.463147782637 & 20.2926889639789 & 16.5368522173628 & 1.41962649034373 \tabularnewline
20 & 611 & 607.760346136581 & 27.1302151031926 & 3.23965386341893 & 0.765654019379351 \tabularnewline
21 & 613 & 619.073585930938 & 16.3148820785158 & -6.07358593093843 & -1.21064162342642 \tabularnewline
22 & 611 & 616.16090698309 & 3.16786824404775 & -5.16090698308993 & -1.47186502087566 \tabularnewline
23 & 594 & 604.156010494937 & -7.20248277329205 & -10.1560104949366 & -1.16094206889327 \tabularnewline
24 & 595 & 593.894944914613 & -9.29072115986202 & 1.10505508538653 & -0.233853818426585 \tabularnewline
25 & 591 & 586.786106270801 & -7.80084535688394 & 4.21389372919851 & 0.167298240048712 \tabularnewline
26 & 589 & 584.679424821553 & -3.9076773595721 & 4.32057517844665 & 0.436478595201897 \tabularnewline
27 & 584 & 580.491453784252 & -4.09741968659976 & 3.50854621574841 & -0.0211877937283579 \tabularnewline
28 & 573 & 572.376381552077 & -6.80792453391357 & 0.623618447923053 & -0.305025292554735 \tabularnewline
29 & 567 & 571.275527873055 & -2.93767135303228 & -4.2755278730546 & 0.434380592348358 \tabularnewline
30 & 569 & 581.139807467815 & 5.72276901437693 & -12.1398074678145 & 0.967631686718844 \tabularnewline
31 & 621 & 604.783455390935 & 17.8162552110648 & 16.2165446090654 & 1.35334777357137 \tabularnewline
32 & 629 & 622.914321794534 & 18.0287501436880 & 6.085678205466 & 0.0237963385170933 \tabularnewline
33 & 628 & 631.273185881033 & 11.4919827271705 & -3.27318588103264 & -0.731760462375117 \tabularnewline
34 & 612 & 619.034372715256 & -4.55084459529663 & -7.034372715256 & -1.79597672442147 \tabularnewline
35 & 595 & 605.602642402641 & -10.5515908366955 & -10.6026424026414 & -0.671780986634648 \tabularnewline
36 & 597 & 596.117984864524 & -9.83110419756276 & 0.882015135476252 & 0.0807106975335485 \tabularnewline
37 & 593 & 589.505590051469 & -7.65594162463881 & 3.49440994853093 & 0.243935906296182 \tabularnewline
38 & 590 & 583.826580184859 & -6.32036795774515 & 6.17341981514053 & 0.149496513561709 \tabularnewline
39 & 580 & 574.370230788928 & -8.42874262687417 & 5.62976921107169 & -0.235737801836184 \tabularnewline
40 & 574 & 571.936294220964 & -4.40530367621779 & 2.06370577903589 & 0.451462185397122 \tabularnewline
41 & 573 & 578.775270023456 & 3.16303817899002 & -5.77527002345611 & 0.848969328353827 \tabularnewline
42 & 573 & 590.423616178246 & 8.87255658476506 & -17.4236161782464 & 0.638620028477297 \tabularnewline
43 & 620 & 604.478954183038 & 12.3531944414395 & 15.5210458169624 & 0.389364730856851 \tabularnewline
44 & 626 & 617.413377632499 & 12.7435337701036 & 8.58662236750144 & 0.0437003858891592 \tabularnewline
45 & 620 & 618.948409424444 & 5.2109568683047 & 1.05159057555633 & -0.84329004262027 \tabularnewline
46 & 588 & 599.128070785592 & -11.6137169992138 & -11.1280707855923 & -1.88348049229621 \tabularnewline
47 & 566 & 578.635295529771 & -17.5798043371606 & -12.6352955297715 & -0.667966338555024 \tabularnewline
48 & 557 & 557.86847801415 & -19.7210446513701 & -0.868478014149465 & -0.239866377758354 \tabularnewline
49 & 561 & 552.673817483451 & -9.95541515873275 & 8.32618251654923 & 1.09422816963352 \tabularnewline
50 & 549 & 541.487802219984 & -10.7821493913125 & 7.51219778001625 & -0.0925134172564313 \tabularnewline
51 & 532 & 527.86983573287 & -12.6818517297867 & 4.13016426713028 & -0.212518265865295 \tabularnewline
52 & 526 & 524.353760526945 & -6.54767085350996 & 1.64623947305465 & 0.687590183337382 \tabularnewline
53 & 511 & 520.026577030717 & -5.05903817220852 & -9.02657703071652 & 0.166892365403853 \tabularnewline
54 & 499 & 518.76078483126 & -2.51522676542611 & -19.7607848312599 & 0.284698009363485 \tabularnewline
55 & 555 & 535.884644676667 & 10.6385500832129 & 19.1153553233334 & 1.47152213130353 \tabularnewline
56 & 565 & 552.41137851768 & 14.5805359889659 & 12.5886214823201 & 0.441223277411353 \tabularnewline
57 & 542 & 540.482672361279 & -3.17263792438587 & 1.51732763872071 & -1.98749946266108 \tabularnewline
58 & 527 & 534.192382851342 & -5.26087479406452 & -7.19238285134166 & -0.233788317873157 \tabularnewline
59 & 510 & 523.701322028714 & -8.76379582719401 & -13.7013220287140 & -0.392233342365311 \tabularnewline
60 & 514 & 518.376693631045 & -6.46002578594065 & -4.37669363104481 & 0.258046937760827 \tabularnewline
61 & 517 & 508.663803878302 & -8.6398232894806 & 8.33619612169845 & -0.244128210074671 \tabularnewline
62 & 508 & 498.971407597004 & -9.3446543170203 & 9.02859240299631 & -0.0788689212302369 \tabularnewline
63 & 493 & 490.464523405607 & -8.78471794516405 & 2.5354765943928 & 0.0626554170019082 \tabularnewline
64 & 490 & 486.563474934858 & -5.52257960050777 & 3.43652506514171 & 0.365491028832501 \tabularnewline
65 & 469 & 480.416519265422 & -5.94012292608596 & -11.4165192654216 & -0.0467943279911121 \tabularnewline
66 & 478 & 498.690151024325 & 10.260040052035 & -20.6901510243251 & 1.81360380907420 \tabularnewline
67 & 528 & 511.418310545811 & 11.9100070657757 & 16.5816894541889 & 0.184608971279338 \tabularnewline
68 & 534 & 515.141021350741 & 6.44011800242520 & 18.8589786492590 & -0.612165182048206 \tabularnewline
69 & 518 & 516.533998204122 & 3.06812512897663 & 1.4660017958784 & -0.377486923997789 \tabularnewline
70 & 506 & 513.587580086199 & -0.950712848649473 & -7.58758008619888 & -0.449964271024861 \tabularnewline
71 & 502 & 515.853248502042 & 1.19863293710772 & -13.8532485020418 & 0.240690861429298 \tabularnewline
72 & 516 & 518.818108391217 & 2.37924407106951 & -2.81810839121707 & 0.132227795184545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62587&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]519[/C][C]519[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]517[/C][C]517.53488576319[/C][C]-1.50931967068352[/C][C]-0.534885763190245[/C][C]-0.195917433969918[/C][/ROW]
[ROW][C]3[/C][C]510[/C][C]511.16081785952[/C][C]-4.83640438677179[/C][C]-1.16081785951987[/C][C]-0.392237856250045[/C][/ROW]
[ROW][C]4[/C][C]509[/C][C]508.037137786154[/C][C]-3.59297681257972[/C][C]0.962862213845823[/C][C]0.144093393598201[/C][/ROW]
[ROW][C]5[/C][C]501[/C][C]501.931210878454[/C][C]-5.38261979234418[/C][C]-0.931210878453754[/C][C]-0.198503448653565[/C][/ROW]
[ROW][C]6[/C][C]507[/C][C]504.481454351377[/C][C]0.225291191827157[/C][C]2.5185456486234[/C][C]0.62847050025145[/C][/ROW]
[ROW][C]7[/C][C]569[/C][C]554.95164228436[/C][C]35.867331872617[/C][C]14.0483577156393[/C][C]3.99269021633074[/C][/ROW]
[ROW][C]8[/C][C]580[/C][C]586.062027693306[/C][C]32.4901132096203[/C][C]-6.06202769330635[/C][C]-0.378037598250256[/C][/ROW]
[ROW][C]9[/C][C]578[/C][C]586.988624471589[/C][C]10.0833547031088[/C][C]-8.98862447158926[/C][C]-2.50841293522469[/C][/ROW]
[ROW][C]10[/C][C]565[/C][C]570.172230981533[/C][C]-9.00870670356781[/C][C]-5.1722309815326[/C][C]-2.13730328845535[/C][/ROW]
[ROW][C]11[/C][C]547[/C][C]548.41501673278[/C][C]-18.0560584872628[/C][C]-1.41501673278001[/C][C]-1.01281832390928[/C][/ROW]
[ROW][C]12[/C][C]555[/C][C]548.559512126371[/C][C]-5.13937789484071[/C][C]6.4404878736286[/C][C]1.44597793857026[/C][/ROW]
[ROW][C]13[/C][C]562[/C][C]558.837841072575[/C][C]5.77274633040281[/C][C]3.16215892742494[/C][C]1.22544629398114[/C][/ROW]
[ROW][C]14[/C][C]561[/C][C]562.308458906698[/C][C]4.13702027413221[/C][C]-1.30845890669831[/C][C]-0.186017119087309[/C][/ROW]
[ROW][C]15[/C][C]555[/C][C]557.687050697457[/C][C]-1.87267524876861[/C][C]-2.68705069745723[/C][C]-0.668685054456384[/C][/ROW]
[ROW][C]16[/C][C]544[/C][C]542.403886365893[/C][C]-11.0334912457731[/C][C]1.59611363410696[/C][C]-1.04188732497722[/C][/ROW]
[ROW][C]17[/C][C]537[/C][C]536.684457281772[/C][C]-7.37502441697304[/C][C]0.315542718228301[/C][C]0.4098364124012[/C][/ROW]
[ROW][C]18[/C][C]543[/C][C]551.268255807669[/C][C]7.6204892170364[/C][C]-8.26825580766865[/C][C]1.67404698884967[/C][/ROW]
[ROW][C]19[/C][C]594[/C][C]577.463147782637[/C][C]20.2926889639789[/C][C]16.5368522173628[/C][C]1.41962649034373[/C][/ROW]
[ROW][C]20[/C][C]611[/C][C]607.760346136581[/C][C]27.1302151031926[/C][C]3.23965386341893[/C][C]0.765654019379351[/C][/ROW]
[ROW][C]21[/C][C]613[/C][C]619.073585930938[/C][C]16.3148820785158[/C][C]-6.07358593093843[/C][C]-1.21064162342642[/C][/ROW]
[ROW][C]22[/C][C]611[/C][C]616.16090698309[/C][C]3.16786824404775[/C][C]-5.16090698308993[/C][C]-1.47186502087566[/C][/ROW]
[ROW][C]23[/C][C]594[/C][C]604.156010494937[/C][C]-7.20248277329205[/C][C]-10.1560104949366[/C][C]-1.16094206889327[/C][/ROW]
[ROW][C]24[/C][C]595[/C][C]593.894944914613[/C][C]-9.29072115986202[/C][C]1.10505508538653[/C][C]-0.233853818426585[/C][/ROW]
[ROW][C]25[/C][C]591[/C][C]586.786106270801[/C][C]-7.80084535688394[/C][C]4.21389372919851[/C][C]0.167298240048712[/C][/ROW]
[ROW][C]26[/C][C]589[/C][C]584.679424821553[/C][C]-3.9076773595721[/C][C]4.32057517844665[/C][C]0.436478595201897[/C][/ROW]
[ROW][C]27[/C][C]584[/C][C]580.491453784252[/C][C]-4.09741968659976[/C][C]3.50854621574841[/C][C]-0.0211877937283579[/C][/ROW]
[ROW][C]28[/C][C]573[/C][C]572.376381552077[/C][C]-6.80792453391357[/C][C]0.623618447923053[/C][C]-0.305025292554735[/C][/ROW]
[ROW][C]29[/C][C]567[/C][C]571.275527873055[/C][C]-2.93767135303228[/C][C]-4.2755278730546[/C][C]0.434380592348358[/C][/ROW]
[ROW][C]30[/C][C]569[/C][C]581.139807467815[/C][C]5.72276901437693[/C][C]-12.1398074678145[/C][C]0.967631686718844[/C][/ROW]
[ROW][C]31[/C][C]621[/C][C]604.783455390935[/C][C]17.8162552110648[/C][C]16.2165446090654[/C][C]1.35334777357137[/C][/ROW]
[ROW][C]32[/C][C]629[/C][C]622.914321794534[/C][C]18.0287501436880[/C][C]6.085678205466[/C][C]0.0237963385170933[/C][/ROW]
[ROW][C]33[/C][C]628[/C][C]631.273185881033[/C][C]11.4919827271705[/C][C]-3.27318588103264[/C][C]-0.731760462375117[/C][/ROW]
[ROW][C]34[/C][C]612[/C][C]619.034372715256[/C][C]-4.55084459529663[/C][C]-7.034372715256[/C][C]-1.79597672442147[/C][/ROW]
[ROW][C]35[/C][C]595[/C][C]605.602642402641[/C][C]-10.5515908366955[/C][C]-10.6026424026414[/C][C]-0.671780986634648[/C][/ROW]
[ROW][C]36[/C][C]597[/C][C]596.117984864524[/C][C]-9.83110419756276[/C][C]0.882015135476252[/C][C]0.0807106975335485[/C][/ROW]
[ROW][C]37[/C][C]593[/C][C]589.505590051469[/C][C]-7.65594162463881[/C][C]3.49440994853093[/C][C]0.243935906296182[/C][/ROW]
[ROW][C]38[/C][C]590[/C][C]583.826580184859[/C][C]-6.32036795774515[/C][C]6.17341981514053[/C][C]0.149496513561709[/C][/ROW]
[ROW][C]39[/C][C]580[/C][C]574.370230788928[/C][C]-8.42874262687417[/C][C]5.62976921107169[/C][C]-0.235737801836184[/C][/ROW]
[ROW][C]40[/C][C]574[/C][C]571.936294220964[/C][C]-4.40530367621779[/C][C]2.06370577903589[/C][C]0.451462185397122[/C][/ROW]
[ROW][C]41[/C][C]573[/C][C]578.775270023456[/C][C]3.16303817899002[/C][C]-5.77527002345611[/C][C]0.848969328353827[/C][/ROW]
[ROW][C]42[/C][C]573[/C][C]590.423616178246[/C][C]8.87255658476506[/C][C]-17.4236161782464[/C][C]0.638620028477297[/C][/ROW]
[ROW][C]43[/C][C]620[/C][C]604.478954183038[/C][C]12.3531944414395[/C][C]15.5210458169624[/C][C]0.389364730856851[/C][/ROW]
[ROW][C]44[/C][C]626[/C][C]617.413377632499[/C][C]12.7435337701036[/C][C]8.58662236750144[/C][C]0.0437003858891592[/C][/ROW]
[ROW][C]45[/C][C]620[/C][C]618.948409424444[/C][C]5.2109568683047[/C][C]1.05159057555633[/C][C]-0.84329004262027[/C][/ROW]
[ROW][C]46[/C][C]588[/C][C]599.128070785592[/C][C]-11.6137169992138[/C][C]-11.1280707855923[/C][C]-1.88348049229621[/C][/ROW]
[ROW][C]47[/C][C]566[/C][C]578.635295529771[/C][C]-17.5798043371606[/C][C]-12.6352955297715[/C][C]-0.667966338555024[/C][/ROW]
[ROW][C]48[/C][C]557[/C][C]557.86847801415[/C][C]-19.7210446513701[/C][C]-0.868478014149465[/C][C]-0.239866377758354[/C][/ROW]
[ROW][C]49[/C][C]561[/C][C]552.673817483451[/C][C]-9.95541515873275[/C][C]8.32618251654923[/C][C]1.09422816963352[/C][/ROW]
[ROW][C]50[/C][C]549[/C][C]541.487802219984[/C][C]-10.7821493913125[/C][C]7.51219778001625[/C][C]-0.0925134172564313[/C][/ROW]
[ROW][C]51[/C][C]532[/C][C]527.86983573287[/C][C]-12.6818517297867[/C][C]4.13016426713028[/C][C]-0.212518265865295[/C][/ROW]
[ROW][C]52[/C][C]526[/C][C]524.353760526945[/C][C]-6.54767085350996[/C][C]1.64623947305465[/C][C]0.687590183337382[/C][/ROW]
[ROW][C]53[/C][C]511[/C][C]520.026577030717[/C][C]-5.05903817220852[/C][C]-9.02657703071652[/C][C]0.166892365403853[/C][/ROW]
[ROW][C]54[/C][C]499[/C][C]518.76078483126[/C][C]-2.51522676542611[/C][C]-19.7607848312599[/C][C]0.284698009363485[/C][/ROW]
[ROW][C]55[/C][C]555[/C][C]535.884644676667[/C][C]10.6385500832129[/C][C]19.1153553233334[/C][C]1.47152213130353[/C][/ROW]
[ROW][C]56[/C][C]565[/C][C]552.41137851768[/C][C]14.5805359889659[/C][C]12.5886214823201[/C][C]0.441223277411353[/C][/ROW]
[ROW][C]57[/C][C]542[/C][C]540.482672361279[/C][C]-3.17263792438587[/C][C]1.51732763872071[/C][C]-1.98749946266108[/C][/ROW]
[ROW][C]58[/C][C]527[/C][C]534.192382851342[/C][C]-5.26087479406452[/C][C]-7.19238285134166[/C][C]-0.233788317873157[/C][/ROW]
[ROW][C]59[/C][C]510[/C][C]523.701322028714[/C][C]-8.76379582719401[/C][C]-13.7013220287140[/C][C]-0.392233342365311[/C][/ROW]
[ROW][C]60[/C][C]514[/C][C]518.376693631045[/C][C]-6.46002578594065[/C][C]-4.37669363104481[/C][C]0.258046937760827[/C][/ROW]
[ROW][C]61[/C][C]517[/C][C]508.663803878302[/C][C]-8.6398232894806[/C][C]8.33619612169845[/C][C]-0.244128210074671[/C][/ROW]
[ROW][C]62[/C][C]508[/C][C]498.971407597004[/C][C]-9.3446543170203[/C][C]9.02859240299631[/C][C]-0.0788689212302369[/C][/ROW]
[ROW][C]63[/C][C]493[/C][C]490.464523405607[/C][C]-8.78471794516405[/C][C]2.5354765943928[/C][C]0.0626554170019082[/C][/ROW]
[ROW][C]64[/C][C]490[/C][C]486.563474934858[/C][C]-5.52257960050777[/C][C]3.43652506514171[/C][C]0.365491028832501[/C][/ROW]
[ROW][C]65[/C][C]469[/C][C]480.416519265422[/C][C]-5.94012292608596[/C][C]-11.4165192654216[/C][C]-0.0467943279911121[/C][/ROW]
[ROW][C]66[/C][C]478[/C][C]498.690151024325[/C][C]10.260040052035[/C][C]-20.6901510243251[/C][C]1.81360380907420[/C][/ROW]
[ROW][C]67[/C][C]528[/C][C]511.418310545811[/C][C]11.9100070657757[/C][C]16.5816894541889[/C][C]0.184608971279338[/C][/ROW]
[ROW][C]68[/C][C]534[/C][C]515.141021350741[/C][C]6.44011800242520[/C][C]18.8589786492590[/C][C]-0.612165182048206[/C][/ROW]
[ROW][C]69[/C][C]518[/C][C]516.533998204122[/C][C]3.06812512897663[/C][C]1.4660017958784[/C][C]-0.377486923997789[/C][/ROW]
[ROW][C]70[/C][C]506[/C][C]513.587580086199[/C][C]-0.950712848649473[/C][C]-7.58758008619888[/C][C]-0.449964271024861[/C][/ROW]
[ROW][C]71[/C][C]502[/C][C]515.853248502042[/C][C]1.19863293710772[/C][C]-13.8532485020418[/C][C]0.240690861429298[/C][/ROW]
[ROW][C]72[/C][C]516[/C][C]518.818108391217[/C][C]2.37924407106951[/C][C]-2.81810839121707[/C][C]0.132227795184545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62587&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62587&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
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	519	519	0	0	0
2	517	517.53488576319	-1.50931967068352	-0.534885763190245	-0.195917433969918
3	510	511.16081785952	-4.83640438677179	-1.16081785951987	-0.392237856250045
4	509	508.037137786154	-3.59297681257972	0.962862213845823	0.144093393598201
5	501	501.931210878454	-5.38261979234418	-0.931210878453754	-0.198503448653565
6	507	504.481454351377	0.225291191827157	2.5185456486234	0.62847050025145
7	569	554.95164228436	35.867331872617	14.0483577156393	3.99269021633074
8	580	586.062027693306	32.4901132096203	-6.06202769330635	-0.378037598250256
9	578	586.988624471589	10.0833547031088	-8.98862447158926	-2.50841293522469
10	565	570.172230981533	-9.00870670356781	-5.1722309815326	-2.13730328845535
11	547	548.41501673278	-18.0560584872628	-1.41501673278001	-1.01281832390928
12	555	548.559512126371	-5.13937789484071	6.4404878736286	1.44597793857026
13	562	558.837841072575	5.77274633040281	3.16215892742494	1.22544629398114
14	561	562.308458906698	4.13702027413221	-1.30845890669831	-0.186017119087309
15	555	557.687050697457	-1.87267524876861	-2.68705069745723	-0.668685054456384
16	544	542.403886365893	-11.0334912457731	1.59611363410696	-1.04188732497722
17	537	536.684457281772	-7.37502441697304	0.315542718228301	0.4098364124012
18	543	551.268255807669	7.6204892170364	-8.26825580766865	1.67404698884967
19	594	577.463147782637	20.2926889639789	16.5368522173628	1.41962649034373
20	611	607.760346136581	27.1302151031926	3.23965386341893	0.765654019379351
21	613	619.073585930938	16.3148820785158	-6.07358593093843	-1.21064162342642
22	611	616.16090698309	3.16786824404775	-5.16090698308993	-1.47186502087566
23	594	604.156010494937	-7.20248277329205	-10.1560104949366	-1.16094206889327
24	595	593.894944914613	-9.29072115986202	1.10505508538653	-0.233853818426585
25	591	586.786106270801	-7.80084535688394	4.21389372919851	0.167298240048712
26	589	584.679424821553	-3.9076773595721	4.32057517844665	0.436478595201897
27	584	580.491453784252	-4.09741968659976	3.50854621574841	-0.0211877937283579
28	573	572.376381552077	-6.80792453391357	0.623618447923053	-0.305025292554735
29	567	571.275527873055	-2.93767135303228	-4.2755278730546	0.434380592348358
30	569	581.139807467815	5.72276901437693	-12.1398074678145	0.967631686718844
31	621	604.783455390935	17.8162552110648	16.2165446090654	1.35334777357137
32	629	622.914321794534	18.0287501436880	6.085678205466	0.0237963385170933
33	628	631.273185881033	11.4919827271705	-3.27318588103264	-0.731760462375117
34	612	619.034372715256	-4.55084459529663	-7.034372715256	-1.79597672442147
35	595	605.602642402641	-10.5515908366955	-10.6026424026414	-0.671780986634648
36	597	596.117984864524	-9.83110419756276	0.882015135476252	0.0807106975335485
37	593	589.505590051469	-7.65594162463881	3.49440994853093	0.243935906296182
38	590	583.826580184859	-6.32036795774515	6.17341981514053	0.149496513561709
39	580	574.370230788928	-8.42874262687417	5.62976921107169	-0.235737801836184
40	574	571.936294220964	-4.40530367621779	2.06370577903589	0.451462185397122
41	573	578.775270023456	3.16303817899002	-5.77527002345611	0.848969328353827
42	573	590.423616178246	8.87255658476506	-17.4236161782464	0.638620028477297
43	620	604.478954183038	12.3531944414395	15.5210458169624	0.389364730856851
44	626	617.413377632499	12.7435337701036	8.58662236750144	0.0437003858891592
45	620	618.948409424444	5.2109568683047	1.05159057555633	-0.84329004262027
46	588	599.128070785592	-11.6137169992138	-11.1280707855923	-1.88348049229621
47	566	578.635295529771	-17.5798043371606	-12.6352955297715	-0.667966338555024
48	557	557.86847801415	-19.7210446513701	-0.868478014149465	-0.239866377758354
49	561	552.673817483451	-9.95541515873275	8.32618251654923	1.09422816963352
50	549	541.487802219984	-10.7821493913125	7.51219778001625	-0.0925134172564313
51	532	527.86983573287	-12.6818517297867	4.13016426713028	-0.212518265865295
52	526	524.353760526945	-6.54767085350996	1.64623947305465	0.687590183337382
53	511	520.026577030717	-5.05903817220852	-9.02657703071652	0.166892365403853
54	499	518.76078483126	-2.51522676542611	-19.7607848312599	0.284698009363485
55	555	535.884644676667	10.6385500832129	19.1153553233334	1.47152213130353
56	565	552.41137851768	14.5805359889659	12.5886214823201	0.441223277411353
57	542	540.482672361279	-3.17263792438587	1.51732763872071	-1.98749946266108
58	527	534.192382851342	-5.26087479406452	-7.19238285134166	-0.233788317873157
59	510	523.701322028714	-8.76379582719401	-13.7013220287140	-0.392233342365311
60	514	518.376693631045	-6.46002578594065	-4.37669363104481	0.258046937760827
61	517	508.663803878302	-8.6398232894806	8.33619612169845	-0.244128210074671
62	508	498.971407597004	-9.3446543170203	9.02859240299631	-0.0788689212302369
63	493	490.464523405607	-8.78471794516405	2.5354765943928	0.0626554170019082
64	490	486.563474934858	-5.52257960050777	3.43652506514171	0.365491028832501
65	469	480.416519265422	-5.94012292608596	-11.4165192654216	-0.0467943279911121
66	478	498.690151024325	10.260040052035	-20.6901510243251	1.81360380907420
67	528	511.418310545811	11.9100070657757	16.5816894541889	0.184608971279338
68	534	515.141021350741	6.44011800242520	18.8589786492590	-0.612165182048206
69	518	516.533998204122	3.06812512897663	1.4660017958784	-0.377486923997789
70	506	513.587580086199	-0.950712848649473	-7.58758008619888	-0.449964271024861
71	502	515.853248502042	1.19863293710772	-13.8532485020418	0.240690861429298
72	516	518.818108391217	2.37924407106951	-2.81810839121707	0.132227795184545

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

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$resid)
myfit <- mylevel+myseas
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$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()
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code