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R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Fri, 23 Dec 2011 11:13:56 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324656862do95uzu4fbkvbj0.htm/, Retrieved Sun, 17 May 2026 01:13:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160549, Retrieved Sun, 17 May 2026 01:13:26 +0000

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Estimated Impact

408

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] [Unemployment] [2010-11-30 13:26:46] [b98453cac15ba1066b407e146608df68]
- R  D    [Structural Time Series Models] [paper- STSM] [2011-12-23 13:08:59] [c2267e575f67090c7e8d960bdccd246a]
-    D        [Structural Time Series Models] [paper- Loess] [2011-12-23 16:13:56] [fe2dc4bc83c881ccd49ef12feaba2b65] [Current]

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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	'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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160549&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160549&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160549&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	'Gertrude Mary Cox' @ cox.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	590	590	0	0	0
2	580	583.283865255502	-2.9752149420575	-3.2838652555019	-0.888883210196761
3	574	574.59315734654	-5.80851754828858	-0.59315734653974	-0.525786612507606
4	573	571.273116902043	-4.44897147375991	1.72688309795728	0.226176933831935
5	573	571.623060001106	-1.84391845547631	1.37693999889388	0.421510588493358
6	620	605.795390898595	17.5296828294619	14.2046091014051	3.19282578103008
7	626	629.153342758548	20.6752953885225	-3.15334275854843	0.522069078189157
8	620	629.965514716297	9.92344769740635	-9.96551471629725	-1.78431483101233
9	588	602.040894545007	-10.5759351441779	-14.0408945450073	-3.40139455420698
10	566	570.228873222773	-22.0754964766754	-4.22887322277343	-1.9081612249883
11	557	552.547532170963	-19.6966098125037	4.45246782903712	0.394738448428917
12	561	553.320759973915	-8.61589120067738	7.67924002608527	1.83866397556424
13	549	546.31875576528	-7.75653833099919	2.68124423472048	0.149474022932546
14	532	532.834199972709	-10.7952270630508	-0.83419997270873	-0.498120659844999
15	526	523.386800625702	-10.1100426052606	2.61319937429851	0.112822778331973
16	511	512.648916237073	-10.4345519738008	-1.64891623707322	-0.0548549324446512
17	499	509.979312712935	-6.35806331578892	-10.9793127129351	0.675608409796844
18	555	533.508507434709	9.25464986968828	21.4914925652909	2.57081722651233
19	565	558.225152357246	17.311045850928	6.77484764275428	1.33404669754017
20	542	550.518287578003	4.24647268900382	-8.51828757800251	-2.16823512210897
21	527	537.686696744475	-4.68900396036749	-10.6866967444747	-1.48272449404469
22	510	520.484708577501	-11.2375471357242	-10.4847085775012	-1.08661954520033
23	514	513.865138664441	-8.82430201274722	0.134861335559445	0.400506558360965
24	517	508.304616881595	-7.12210485959475	8.69538311840484	0.28338598181224
25	508	501.687272980594	-6.85824626303759	6.31272701940556	0.04419121030494
26	493	492.593863579878	-8.02240798507279	0.40613642012234	-0.192530690425326
27	490	484.913465120857	-7.84695208661093	5.08653487914338	0.0289903758229804
28	469	476.12991027015	-8.32793889734134	-7.12991027014965	-0.0804268108971488
29	478	492.376360292948	4.4070641897294	-14.3763602929475	2.12098603734532
30	528	509.561212965181	11.0299996011733	18.4387870348186	1.09516323492062
31	534	519.126840147896	10.2732072580394	14.8731598521041	-0.125216106363323
32	518	522.229416818185	6.56726070506355	-4.22941681818469	-0.614568534847593
33	506	516.942893769889	0.433065417893171	-10.9428937698892	-1.0179067725843
34	502	514.817937559795	-0.890979322125457	-12.8179375597953	-0.219735021776374
35	516	516.113504287233	0.239852217410683	-0.113504287233148	0.187813428821908
36	528	518.146226943398	1.1671887053512	9.85377305660229	0.15433208535223
37	533	522.837547458959	2.99273808629801	10.1624525410407	0.303745119249397
38	536	531.596188921867	5.97097538783978	4.40381107813323	0.493016824981042
39	537	534.444769569382	4.3692999116915	2.55523043061844	-0.265196202061861
40	524	540.868870678239	5.42271411911422	-16.8688706782386	0.175432347463346
41	536	553.383027010338	9.07566253382764	-17.3830270103384	0.608276123054868
42	587	566.979421661622	11.4079345635513	20.0205783383779	0.386665470633031
43	597	578.859404594582	11.6510136761302	18.140595405418	0.0402416333376524
44	581	583.388057801933	7.98767881965705	-2.38805780193285	-0.607154863189412
45	564	578.707893574547	1.47108239911033	-14.707893574547	-1.08118054091213
46	558	573.326821273653	-2.05445435837996	-15.3268212736526	-0.585292883313566
47	575	574.00477587745	-0.648451757142419	0.995224122549569	0.233620621622018
48	580	572.354998623477	-1.16413402070116	7.6450013765231	-0.0857470486819306
49	575	567.661867026551	-2.98274243829626	7.33813297344923	-0.301995026758463
50	563	559.043614379996	-5.88025235516809	3.95638562000403	-0.479881464049787
51	552	551.075091163591	-6.94971065329523	0.924908836409229	-0.177227829260922
52	537	553.336679533017	-2.23506840951835	-16.3366795330166	0.783980873955845
53	545	561.45229204517	3.07773492748901	-16.4522920451703	0.884043996639682
54	601	576.860935246781	9.41702520935234	24.1390647532195	1.05214564893283
55	604	584.378439124899	8.44152756198894	19.6215608751011	-0.161607284549462
56	586	585.859548502455	4.87254537252376	0.140451497544846	-0.591406821930943
57	564	580.529469156378	-0.355570040660422	-16.5294691563785	-0.867265434159036
58	549	569.635123689856	-5.75649833237995	-20.6351236898564	-0.896845136193524
59	551	553.289968303978	-11.1864477931511	-2.28996830397836	-0.90237256212942
60	556	544.141545805495	-10.1402674118424	11.8584541945053	0.173854118757816
61	548	536.385720401466	-8.91600274313338	11.6142795985336	0.203150990936535
62	540	532.738101465533	-6.21608288501837	7.26189853446697	0.447300748702044
63	531	532.145980628222	-3.34146890058393	-1.14598062822232	0.476566178043485
64	521	538.938649422686	1.83626458418406	-17.9386494226857	0.860409114716508
65	519	541.761101709955	2.34107813259782	-22.7611017099554	0.0839528196284191
66	572	546.660489905537	3.6524626692752	25.3395100944632	0.217739346922561
67	581	556.394881735438	6.7681243366046	24.6051182645618	0.516422862745321
68	563	560.257354740393	5.28190973459651	2.74264525960711	-0.246285585789814
69	548	560.974079816011	2.94920073474937	-12.974079816011	-0.386926733195902
70	539	557.462466543419	-0.352195877765391	-18.4624665434194	-0.548248666619341

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 590 & 590 & 0 & 0 & 0 \tabularnewline
2 & 580 & 583.283865255502 & -2.9752149420575 & -3.2838652555019 & -0.888883210196761 \tabularnewline
3 & 574 & 574.59315734654 & -5.80851754828858 & -0.59315734653974 & -0.525786612507606 \tabularnewline
4 & 573 & 571.273116902043 & -4.44897147375991 & 1.72688309795728 & 0.226176933831935 \tabularnewline
5 & 573 & 571.623060001106 & -1.84391845547631 & 1.37693999889388 & 0.421510588493358 \tabularnewline
6 & 620 & 605.795390898595 & 17.5296828294619 & 14.2046091014051 & 3.19282578103008 \tabularnewline
7 & 626 & 629.153342758548 & 20.6752953885225 & -3.15334275854843 & 0.522069078189157 \tabularnewline
8 & 620 & 629.965514716297 & 9.92344769740635 & -9.96551471629725 & -1.78431483101233 \tabularnewline
9 & 588 & 602.040894545007 & -10.5759351441779 & -14.0408945450073 & -3.40139455420698 \tabularnewline
10 & 566 & 570.228873222773 & -22.0754964766754 & -4.22887322277343 & -1.9081612249883 \tabularnewline
11 & 557 & 552.547532170963 & -19.6966098125037 & 4.45246782903712 & 0.394738448428917 \tabularnewline
12 & 561 & 553.320759973915 & -8.61589120067738 & 7.67924002608527 & 1.83866397556424 \tabularnewline
13 & 549 & 546.31875576528 & -7.75653833099919 & 2.68124423472048 & 0.149474022932546 \tabularnewline
14 & 532 & 532.834199972709 & -10.7952270630508 & -0.83419997270873 & -0.498120659844999 \tabularnewline
15 & 526 & 523.386800625702 & -10.1100426052606 & 2.61319937429851 & 0.112822778331973 \tabularnewline
16 & 511 & 512.648916237073 & -10.4345519738008 & -1.64891623707322 & -0.0548549324446512 \tabularnewline
17 & 499 & 509.979312712935 & -6.35806331578892 & -10.9793127129351 & 0.675608409796844 \tabularnewline
18 & 555 & 533.508507434709 & 9.25464986968828 & 21.4914925652909 & 2.57081722651233 \tabularnewline
19 & 565 & 558.225152357246 & 17.311045850928 & 6.77484764275428 & 1.33404669754017 \tabularnewline
20 & 542 & 550.518287578003 & 4.24647268900382 & -8.51828757800251 & -2.16823512210897 \tabularnewline
21 & 527 & 537.686696744475 & -4.68900396036749 & -10.6866967444747 & -1.48272449404469 \tabularnewline
22 & 510 & 520.484708577501 & -11.2375471357242 & -10.4847085775012 & -1.08661954520033 \tabularnewline
23 & 514 & 513.865138664441 & -8.82430201274722 & 0.134861335559445 & 0.400506558360965 \tabularnewline
24 & 517 & 508.304616881595 & -7.12210485959475 & 8.69538311840484 & 0.28338598181224 \tabularnewline
25 & 508 & 501.687272980594 & -6.85824626303759 & 6.31272701940556 & 0.04419121030494 \tabularnewline
26 & 493 & 492.593863579878 & -8.02240798507279 & 0.40613642012234 & -0.192530690425326 \tabularnewline
27 & 490 & 484.913465120857 & -7.84695208661093 & 5.08653487914338 & 0.0289903758229804 \tabularnewline
28 & 469 & 476.12991027015 & -8.32793889734134 & -7.12991027014965 & -0.0804268108971488 \tabularnewline
29 & 478 & 492.376360292948 & 4.4070641897294 & -14.3763602929475 & 2.12098603734532 \tabularnewline
30 & 528 & 509.561212965181 & 11.0299996011733 & 18.4387870348186 & 1.09516323492062 \tabularnewline
31 & 534 & 519.126840147896 & 10.2732072580394 & 14.8731598521041 & -0.125216106363323 \tabularnewline
32 & 518 & 522.229416818185 & 6.56726070506355 & -4.22941681818469 & -0.614568534847593 \tabularnewline
33 & 506 & 516.942893769889 & 0.433065417893171 & -10.9428937698892 & -1.0179067725843 \tabularnewline
34 & 502 & 514.817937559795 & -0.890979322125457 & -12.8179375597953 & -0.219735021776374 \tabularnewline
35 & 516 & 516.113504287233 & 0.239852217410683 & -0.113504287233148 & 0.187813428821908 \tabularnewline
36 & 528 & 518.146226943398 & 1.1671887053512 & 9.85377305660229 & 0.15433208535223 \tabularnewline
37 & 533 & 522.837547458959 & 2.99273808629801 & 10.1624525410407 & 0.303745119249397 \tabularnewline
38 & 536 & 531.596188921867 & 5.97097538783978 & 4.40381107813323 & 0.493016824981042 \tabularnewline
39 & 537 & 534.444769569382 & 4.3692999116915 & 2.55523043061844 & -0.265196202061861 \tabularnewline
40 & 524 & 540.868870678239 & 5.42271411911422 & -16.8688706782386 & 0.175432347463346 \tabularnewline
41 & 536 & 553.383027010338 & 9.07566253382764 & -17.3830270103384 & 0.608276123054868 \tabularnewline
42 & 587 & 566.979421661622 & 11.4079345635513 & 20.0205783383779 & 0.386665470633031 \tabularnewline
43 & 597 & 578.859404594582 & 11.6510136761302 & 18.140595405418 & 0.0402416333376524 \tabularnewline
44 & 581 & 583.388057801933 & 7.98767881965705 & -2.38805780193285 & -0.607154863189412 \tabularnewline
45 & 564 & 578.707893574547 & 1.47108239911033 & -14.707893574547 & -1.08118054091213 \tabularnewline
46 & 558 & 573.326821273653 & -2.05445435837996 & -15.3268212736526 & -0.585292883313566 \tabularnewline
47 & 575 & 574.00477587745 & -0.648451757142419 & 0.995224122549569 & 0.233620621622018 \tabularnewline
48 & 580 & 572.354998623477 & -1.16413402070116 & 7.6450013765231 & -0.0857470486819306 \tabularnewline
49 & 575 & 567.661867026551 & -2.98274243829626 & 7.33813297344923 & -0.301995026758463 \tabularnewline
50 & 563 & 559.043614379996 & -5.88025235516809 & 3.95638562000403 & -0.479881464049787 \tabularnewline
51 & 552 & 551.075091163591 & -6.94971065329523 & 0.924908836409229 & -0.177227829260922 \tabularnewline
52 & 537 & 553.336679533017 & -2.23506840951835 & -16.3366795330166 & 0.783980873955845 \tabularnewline
53 & 545 & 561.45229204517 & 3.07773492748901 & -16.4522920451703 & 0.884043996639682 \tabularnewline
54 & 601 & 576.860935246781 & 9.41702520935234 & 24.1390647532195 & 1.05214564893283 \tabularnewline
55 & 604 & 584.378439124899 & 8.44152756198894 & 19.6215608751011 & -0.161607284549462 \tabularnewline
56 & 586 & 585.859548502455 & 4.87254537252376 & 0.140451497544846 & -0.591406821930943 \tabularnewline
57 & 564 & 580.529469156378 & -0.355570040660422 & -16.5294691563785 & -0.867265434159036 \tabularnewline
58 & 549 & 569.635123689856 & -5.75649833237995 & -20.6351236898564 & -0.896845136193524 \tabularnewline
59 & 551 & 553.289968303978 & -11.1864477931511 & -2.28996830397836 & -0.90237256212942 \tabularnewline
60 & 556 & 544.141545805495 & -10.1402674118424 & 11.8584541945053 & 0.173854118757816 \tabularnewline
61 & 548 & 536.385720401466 & -8.91600274313338 & 11.6142795985336 & 0.203150990936535 \tabularnewline
62 & 540 & 532.738101465533 & -6.21608288501837 & 7.26189853446697 & 0.447300748702044 \tabularnewline
63 & 531 & 532.145980628222 & -3.34146890058393 & -1.14598062822232 & 0.476566178043485 \tabularnewline
64 & 521 & 538.938649422686 & 1.83626458418406 & -17.9386494226857 & 0.860409114716508 \tabularnewline
65 & 519 & 541.761101709955 & 2.34107813259782 & -22.7611017099554 & 0.0839528196284191 \tabularnewline
66 & 572 & 546.660489905537 & 3.6524626692752 & 25.3395100944632 & 0.217739346922561 \tabularnewline
67 & 581 & 556.394881735438 & 6.7681243366046 & 24.6051182645618 & 0.516422862745321 \tabularnewline
68 & 563 & 560.257354740393 & 5.28190973459651 & 2.74264525960711 & -0.246285585789814 \tabularnewline
69 & 548 & 560.974079816011 & 2.94920073474937 & -12.974079816011 & -0.386926733195902 \tabularnewline
70 & 539 & 557.462466543419 & -0.352195877765391 & -18.4624665434194 & -0.548248666619341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160549&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]590[/C][C]590[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]580[/C][C]583.283865255502[/C][C]-2.9752149420575[/C][C]-3.2838652555019[/C][C]-0.888883210196761[/C][/ROW]
[ROW][C]3[/C][C]574[/C][C]574.59315734654[/C][C]-5.80851754828858[/C][C]-0.59315734653974[/C][C]-0.525786612507606[/C][/ROW]
[ROW][C]4[/C][C]573[/C][C]571.273116902043[/C][C]-4.44897147375991[/C][C]1.72688309795728[/C][C]0.226176933831935[/C][/ROW]
[ROW][C]5[/C][C]573[/C][C]571.623060001106[/C][C]-1.84391845547631[/C][C]1.37693999889388[/C][C]0.421510588493358[/C][/ROW]
[ROW][C]6[/C][C]620[/C][C]605.795390898595[/C][C]17.5296828294619[/C][C]14.2046091014051[/C][C]3.19282578103008[/C][/ROW]
[ROW][C]7[/C][C]626[/C][C]629.153342758548[/C][C]20.6752953885225[/C][C]-3.15334275854843[/C][C]0.522069078189157[/C][/ROW]
[ROW][C]8[/C][C]620[/C][C]629.965514716297[/C][C]9.92344769740635[/C][C]-9.96551471629725[/C][C]-1.78431483101233[/C][/ROW]
[ROW][C]9[/C][C]588[/C][C]602.040894545007[/C][C]-10.5759351441779[/C][C]-14.0408945450073[/C][C]-3.40139455420698[/C][/ROW]
[ROW][C]10[/C][C]566[/C][C]570.228873222773[/C][C]-22.0754964766754[/C][C]-4.22887322277343[/C][C]-1.9081612249883[/C][/ROW]
[ROW][C]11[/C][C]557[/C][C]552.547532170963[/C][C]-19.6966098125037[/C][C]4.45246782903712[/C][C]0.394738448428917[/C][/ROW]
[ROW][C]12[/C][C]561[/C][C]553.320759973915[/C][C]-8.61589120067738[/C][C]7.67924002608527[/C][C]1.83866397556424[/C][/ROW]
[ROW][C]13[/C][C]549[/C][C]546.31875576528[/C][C]-7.75653833099919[/C][C]2.68124423472048[/C][C]0.149474022932546[/C][/ROW]
[ROW][C]14[/C][C]532[/C][C]532.834199972709[/C][C]-10.7952270630508[/C][C]-0.83419997270873[/C][C]-0.498120659844999[/C][/ROW]
[ROW][C]15[/C][C]526[/C][C]523.386800625702[/C][C]-10.1100426052606[/C][C]2.61319937429851[/C][C]0.112822778331973[/C][/ROW]
[ROW][C]16[/C][C]511[/C][C]512.648916237073[/C][C]-10.4345519738008[/C][C]-1.64891623707322[/C][C]-0.0548549324446512[/C][/ROW]
[ROW][C]17[/C][C]499[/C][C]509.979312712935[/C][C]-6.35806331578892[/C][C]-10.9793127129351[/C][C]0.675608409796844[/C][/ROW]
[ROW][C]18[/C][C]555[/C][C]533.508507434709[/C][C]9.25464986968828[/C][C]21.4914925652909[/C][C]2.57081722651233[/C][/ROW]
[ROW][C]19[/C][C]565[/C][C]558.225152357246[/C][C]17.311045850928[/C][C]6.77484764275428[/C][C]1.33404669754017[/C][/ROW]
[ROW][C]20[/C][C]542[/C][C]550.518287578003[/C][C]4.24647268900382[/C][C]-8.51828757800251[/C][C]-2.16823512210897[/C][/ROW]
[ROW][C]21[/C][C]527[/C][C]537.686696744475[/C][C]-4.68900396036749[/C][C]-10.6866967444747[/C][C]-1.48272449404469[/C][/ROW]
[ROW][C]22[/C][C]510[/C][C]520.484708577501[/C][C]-11.2375471357242[/C][C]-10.4847085775012[/C][C]-1.08661954520033[/C][/ROW]
[ROW][C]23[/C][C]514[/C][C]513.865138664441[/C][C]-8.82430201274722[/C][C]0.134861335559445[/C][C]0.400506558360965[/C][/ROW]
[ROW][C]24[/C][C]517[/C][C]508.304616881595[/C][C]-7.12210485959475[/C][C]8.69538311840484[/C][C]0.28338598181224[/C][/ROW]
[ROW][C]25[/C][C]508[/C][C]501.687272980594[/C][C]-6.85824626303759[/C][C]6.31272701940556[/C][C]0.04419121030494[/C][/ROW]
[ROW][C]26[/C][C]493[/C][C]492.593863579878[/C][C]-8.02240798507279[/C][C]0.40613642012234[/C][C]-0.192530690425326[/C][/ROW]
[ROW][C]27[/C][C]490[/C][C]484.913465120857[/C][C]-7.84695208661093[/C][C]5.08653487914338[/C][C]0.0289903758229804[/C][/ROW]
[ROW][C]28[/C][C]469[/C][C]476.12991027015[/C][C]-8.32793889734134[/C][C]-7.12991027014965[/C][C]-0.0804268108971488[/C][/ROW]
[ROW][C]29[/C][C]478[/C][C]492.376360292948[/C][C]4.4070641897294[/C][C]-14.3763602929475[/C][C]2.12098603734532[/C][/ROW]
[ROW][C]30[/C][C]528[/C][C]509.561212965181[/C][C]11.0299996011733[/C][C]18.4387870348186[/C][C]1.09516323492062[/C][/ROW]
[ROW][C]31[/C][C]534[/C][C]519.126840147896[/C][C]10.2732072580394[/C][C]14.8731598521041[/C][C]-0.125216106363323[/C][/ROW]
[ROW][C]32[/C][C]518[/C][C]522.229416818185[/C][C]6.56726070506355[/C][C]-4.22941681818469[/C][C]-0.614568534847593[/C][/ROW]
[ROW][C]33[/C][C]506[/C][C]516.942893769889[/C][C]0.433065417893171[/C][C]-10.9428937698892[/C][C]-1.0179067725843[/C][/ROW]
[ROW][C]34[/C][C]502[/C][C]514.817937559795[/C][C]-0.890979322125457[/C][C]-12.8179375597953[/C][C]-0.219735021776374[/C][/ROW]
[ROW][C]35[/C][C]516[/C][C]516.113504287233[/C][C]0.239852217410683[/C][C]-0.113504287233148[/C][C]0.187813428821908[/C][/ROW]
[ROW][C]36[/C][C]528[/C][C]518.146226943398[/C][C]1.1671887053512[/C][C]9.85377305660229[/C][C]0.15433208535223[/C][/ROW]
[ROW][C]37[/C][C]533[/C][C]522.837547458959[/C][C]2.99273808629801[/C][C]10.1624525410407[/C][C]0.303745119249397[/C][/ROW]
[ROW][C]38[/C][C]536[/C][C]531.596188921867[/C][C]5.97097538783978[/C][C]4.40381107813323[/C][C]0.493016824981042[/C][/ROW]
[ROW][C]39[/C][C]537[/C][C]534.444769569382[/C][C]4.3692999116915[/C][C]2.55523043061844[/C][C]-0.265196202061861[/C][/ROW]
[ROW][C]40[/C][C]524[/C][C]540.868870678239[/C][C]5.42271411911422[/C][C]-16.8688706782386[/C][C]0.175432347463346[/C][/ROW]
[ROW][C]41[/C][C]536[/C][C]553.383027010338[/C][C]9.07566253382764[/C][C]-17.3830270103384[/C][C]0.608276123054868[/C][/ROW]
[ROW][C]42[/C][C]587[/C][C]566.979421661622[/C][C]11.4079345635513[/C][C]20.0205783383779[/C][C]0.386665470633031[/C][/ROW]
[ROW][C]43[/C][C]597[/C][C]578.859404594582[/C][C]11.6510136761302[/C][C]18.140595405418[/C][C]0.0402416333376524[/C][/ROW]
[ROW][C]44[/C][C]581[/C][C]583.388057801933[/C][C]7.98767881965705[/C][C]-2.38805780193285[/C][C]-0.607154863189412[/C][/ROW]
[ROW][C]45[/C][C]564[/C][C]578.707893574547[/C][C]1.47108239911033[/C][C]-14.707893574547[/C][C]-1.08118054091213[/C][/ROW]
[ROW][C]46[/C][C]558[/C][C]573.326821273653[/C][C]-2.05445435837996[/C][C]-15.3268212736526[/C][C]-0.585292883313566[/C][/ROW]
[ROW][C]47[/C][C]575[/C][C]574.00477587745[/C][C]-0.648451757142419[/C][C]0.995224122549569[/C][C]0.233620621622018[/C][/ROW]
[ROW][C]48[/C][C]580[/C][C]572.354998623477[/C][C]-1.16413402070116[/C][C]7.6450013765231[/C][C]-0.0857470486819306[/C][/ROW]
[ROW][C]49[/C][C]575[/C][C]567.661867026551[/C][C]-2.98274243829626[/C][C]7.33813297344923[/C][C]-0.301995026758463[/C][/ROW]
[ROW][C]50[/C][C]563[/C][C]559.043614379996[/C][C]-5.88025235516809[/C][C]3.95638562000403[/C][C]-0.479881464049787[/C][/ROW]
[ROW][C]51[/C][C]552[/C][C]551.075091163591[/C][C]-6.94971065329523[/C][C]0.924908836409229[/C][C]-0.177227829260922[/C][/ROW]
[ROW][C]52[/C][C]537[/C][C]553.336679533017[/C][C]-2.23506840951835[/C][C]-16.3366795330166[/C][C]0.783980873955845[/C][/ROW]
[ROW][C]53[/C][C]545[/C][C]561.45229204517[/C][C]3.07773492748901[/C][C]-16.4522920451703[/C][C]0.884043996639682[/C][/ROW]
[ROW][C]54[/C][C]601[/C][C]576.860935246781[/C][C]9.41702520935234[/C][C]24.1390647532195[/C][C]1.05214564893283[/C][/ROW]
[ROW][C]55[/C][C]604[/C][C]584.378439124899[/C][C]8.44152756198894[/C][C]19.6215608751011[/C][C]-0.161607284549462[/C][/ROW]
[ROW][C]56[/C][C]586[/C][C]585.859548502455[/C][C]4.87254537252376[/C][C]0.140451497544846[/C][C]-0.591406821930943[/C][/ROW]
[ROW][C]57[/C][C]564[/C][C]580.529469156378[/C][C]-0.355570040660422[/C][C]-16.5294691563785[/C][C]-0.867265434159036[/C][/ROW]
[ROW][C]58[/C][C]549[/C][C]569.635123689856[/C][C]-5.75649833237995[/C][C]-20.6351236898564[/C][C]-0.896845136193524[/C][/ROW]
[ROW][C]59[/C][C]551[/C][C]553.289968303978[/C][C]-11.1864477931511[/C][C]-2.28996830397836[/C][C]-0.90237256212942[/C][/ROW]
[ROW][C]60[/C][C]556[/C][C]544.141545805495[/C][C]-10.1402674118424[/C][C]11.8584541945053[/C][C]0.173854118757816[/C][/ROW]
[ROW][C]61[/C][C]548[/C][C]536.385720401466[/C][C]-8.91600274313338[/C][C]11.6142795985336[/C][C]0.203150990936535[/C][/ROW]
[ROW][C]62[/C][C]540[/C][C]532.738101465533[/C][C]-6.21608288501837[/C][C]7.26189853446697[/C][C]0.447300748702044[/C][/ROW]
[ROW][C]63[/C][C]531[/C][C]532.145980628222[/C][C]-3.34146890058393[/C][C]-1.14598062822232[/C][C]0.476566178043485[/C][/ROW]
[ROW][C]64[/C][C]521[/C][C]538.938649422686[/C][C]1.83626458418406[/C][C]-17.9386494226857[/C][C]0.860409114716508[/C][/ROW]
[ROW][C]65[/C][C]519[/C][C]541.761101709955[/C][C]2.34107813259782[/C][C]-22.7611017099554[/C][C]0.0839528196284191[/C][/ROW]
[ROW][C]66[/C][C]572[/C][C]546.660489905537[/C][C]3.6524626692752[/C][C]25.3395100944632[/C][C]0.217739346922561[/C][/ROW]
[ROW][C]67[/C][C]581[/C][C]556.394881735438[/C][C]6.7681243366046[/C][C]24.6051182645618[/C][C]0.516422862745321[/C][/ROW]
[ROW][C]68[/C][C]563[/C][C]560.257354740393[/C][C]5.28190973459651[/C][C]2.74264525960711[/C][C]-0.246285585789814[/C][/ROW]
[ROW][C]69[/C][C]548[/C][C]560.974079816011[/C][C]2.94920073474937[/C][C]-12.974079816011[/C][C]-0.386926733195902[/C][/ROW]
[ROW][C]70[/C][C]539[/C][C]557.462466543419[/C][C]-0.352195877765391[/C][C]-18.4624665434194[/C][C]-0.548248666619341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160549&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160549&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	590	590	0	0	0
2	580	583.283865255502	-2.9752149420575	-3.2838652555019	-0.888883210196761
3	574	574.59315734654	-5.80851754828858	-0.59315734653974	-0.525786612507606
4	573	571.273116902043	-4.44897147375991	1.72688309795728	0.226176933831935
5	573	571.623060001106	-1.84391845547631	1.37693999889388	0.421510588493358
6	620	605.795390898595	17.5296828294619	14.2046091014051	3.19282578103008
7	626	629.153342758548	20.6752953885225	-3.15334275854843	0.522069078189157
8	620	629.965514716297	9.92344769740635	-9.96551471629725	-1.78431483101233
9	588	602.040894545007	-10.5759351441779	-14.0408945450073	-3.40139455420698
10	566	570.228873222773	-22.0754964766754	-4.22887322277343	-1.9081612249883
11	557	552.547532170963	-19.6966098125037	4.45246782903712	0.394738448428917
12	561	553.320759973915	-8.61589120067738	7.67924002608527	1.83866397556424
13	549	546.31875576528	-7.75653833099919	2.68124423472048	0.149474022932546
14	532	532.834199972709	-10.7952270630508	-0.83419997270873	-0.498120659844999
15	526	523.386800625702	-10.1100426052606	2.61319937429851	0.112822778331973
16	511	512.648916237073	-10.4345519738008	-1.64891623707322	-0.0548549324446512
17	499	509.979312712935	-6.35806331578892	-10.9793127129351	0.675608409796844
18	555	533.508507434709	9.25464986968828	21.4914925652909	2.57081722651233
19	565	558.225152357246	17.311045850928	6.77484764275428	1.33404669754017
20	542	550.518287578003	4.24647268900382	-8.51828757800251	-2.16823512210897
21	527	537.686696744475	-4.68900396036749	-10.6866967444747	-1.48272449404469
22	510	520.484708577501	-11.2375471357242	-10.4847085775012	-1.08661954520033
23	514	513.865138664441	-8.82430201274722	0.134861335559445	0.400506558360965
24	517	508.304616881595	-7.12210485959475	8.69538311840484	0.28338598181224
25	508	501.687272980594	-6.85824626303759	6.31272701940556	0.04419121030494
26	493	492.593863579878	-8.02240798507279	0.40613642012234	-0.192530690425326
27	490	484.913465120857	-7.84695208661093	5.08653487914338	0.0289903758229804
28	469	476.12991027015	-8.32793889734134	-7.12991027014965	-0.0804268108971488
29	478	492.376360292948	4.4070641897294	-14.3763602929475	2.12098603734532
30	528	509.561212965181	11.0299996011733	18.4387870348186	1.09516323492062
31	534	519.126840147896	10.2732072580394	14.8731598521041	-0.125216106363323
32	518	522.229416818185	6.56726070506355	-4.22941681818469	-0.614568534847593
33	506	516.942893769889	0.433065417893171	-10.9428937698892	-1.0179067725843
34	502	514.817937559795	-0.890979322125457	-12.8179375597953	-0.219735021776374
35	516	516.113504287233	0.239852217410683	-0.113504287233148	0.187813428821908
36	528	518.146226943398	1.1671887053512	9.85377305660229	0.15433208535223
37	533	522.837547458959	2.99273808629801	10.1624525410407	0.303745119249397
38	536	531.596188921867	5.97097538783978	4.40381107813323	0.493016824981042
39	537	534.444769569382	4.3692999116915	2.55523043061844	-0.265196202061861
40	524	540.868870678239	5.42271411911422	-16.8688706782386	0.175432347463346
41	536	553.383027010338	9.07566253382764	-17.3830270103384	0.608276123054868
42	587	566.979421661622	11.4079345635513	20.0205783383779	0.386665470633031
43	597	578.859404594582	11.6510136761302	18.140595405418	0.0402416333376524
44	581	583.388057801933	7.98767881965705	-2.38805780193285	-0.607154863189412
45	564	578.707893574547	1.47108239911033	-14.707893574547	-1.08118054091213
46	558	573.326821273653	-2.05445435837996	-15.3268212736526	-0.585292883313566
47	575	574.00477587745	-0.648451757142419	0.995224122549569	0.233620621622018
48	580	572.354998623477	-1.16413402070116	7.6450013765231	-0.0857470486819306
49	575	567.661867026551	-2.98274243829626	7.33813297344923	-0.301995026758463
50	563	559.043614379996	-5.88025235516809	3.95638562000403	-0.479881464049787
51	552	551.075091163591	-6.94971065329523	0.924908836409229	-0.177227829260922
52	537	553.336679533017	-2.23506840951835	-16.3366795330166	0.783980873955845
53	545	561.45229204517	3.07773492748901	-16.4522920451703	0.884043996639682
54	601	576.860935246781	9.41702520935234	24.1390647532195	1.05214564893283
55	604	584.378439124899	8.44152756198894	19.6215608751011	-0.161607284549462
56	586	585.859548502455	4.87254537252376	0.140451497544846	-0.591406821930943
57	564	580.529469156378	-0.355570040660422	-16.5294691563785	-0.867265434159036
58	549	569.635123689856	-5.75649833237995	-20.6351236898564	-0.896845136193524
59	551	553.289968303978	-11.1864477931511	-2.28996830397836	-0.90237256212942
60	556	544.141545805495	-10.1402674118424	11.8584541945053	0.173854118757816
61	548	536.385720401466	-8.91600274313338	11.6142795985336	0.203150990936535
62	540	532.738101465533	-6.21608288501837	7.26189853446697	0.447300748702044
63	531	532.145980628222	-3.34146890058393	-1.14598062822232	0.476566178043485
64	521	538.938649422686	1.83626458418406	-17.9386494226857	0.860409114716508
65	519	541.761101709955	2.34107813259782	-22.7611017099554	0.0839528196284191
66	572	546.660489905537	3.6524626692752	25.3395100944632	0.217739346922561
67	581	556.394881735438	6.7681243366046	24.6051182645618	0.516422862745321
68	563	560.257354740393	5.28190973459651	2.74264525960711	-0.246285585789814
69	548	560.974079816011	2.94920073474937	-12.974079816011	-0.386926733195902
70	539	557.462466543419	-0.352195877765391	-18.4624665434194	-0.548248666619341

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