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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 08:08:59 -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/t13246457691kwiyaq05sf7m89.htm/, Retrieved Fri, 05 Jun 2026 08:58:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160373, Retrieved Fri, 05 Jun 2026 08:58:35 +0000

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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] [Unemployment] [2010-11-30 13:26:46] [b98453cac15ba1066b407e146608df68]
- R  D      [Structural Time Series Models] [paper- STSM] [2011-12-23 13:08:59] [fe2dc4bc83c881ccd49ef12feaba2b65] [Current]
-    D        [Structural Time Series Models] [paper- Loess] [2011-12-23 16:13:56] [c2267e575f67090c7e8d960bdccd246a] 
-    D        [Structural Time Series Models] [paper- STSM juist] [2011-12-23 16:19:11] [c2267e575f67090c7e8d960bdccd246a] 

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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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160373&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160373&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160373&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	539	539	0	0	0
2	548	546.753544793011	0.397143080817201	1.24645520698855	0.44712858924277
3	563	558.565725083752	0.781979675073757	4.43427491624753	0.972546151474376
4	581	575.275724481352	0.97700076219689	5.72427551864812	1.45208178248065
5	572	574.163751857567	0.964152395761841	-2.16375185756673	-0.190572921445446
6	519	533.862622401609	0.716027328492807	-14.8626224016091	-3.76175759509138
7	521	519.948536702457	0.620035375483989	1.05146329754346	-1.33324718618088
8	531	526.077166746795	0.657227402100163	4.92283325320508	0.501964932542649
9	540	536.376321836725	0.722156789238851	3.62367816327494	0.87861498874148
10	548	545.430741720259	0.777776098207648	2.56925827974103	0.75927346796338
11	556	553.565287070504	0.826497998751057	2.43471292949573	0.670376433743256
12	551	552.135520827456	0.811657443755842	-1.13552082745644	-0.205596903746852
13	549	554.542543988939	0.754635232417334	-5.54254398893936	0.163452904284107
14	564	563.876340375616	0.849791731686334	0.123659624383554	0.735049272541673
15	586	581.14274518651	1.18057434020651	4.85725481348956	1.40649243544317
16	604	594.26909964115	1.33488346008345	9.73090035885045	1.07800202005616
17	601	593.878837590513	1.32356562707927	7.12116240948682	-0.157216460266215
18	545	568.087387476185	1.20649342154399	-23.0873874761848	-2.47089417954927
19	537	544.607102013219	1.10406354892649	-7.60710201321883	-2.24851901410684
20	552	545.171803426523	1.10165091581791	6.82819657347732	-0.0491124850125779
21	563	555.914122995397	1.14807877493105	7.08587700460323	0.877882448852156
22	575	569.200727512775	1.20901000057965	5.79927248722464	1.1057027548664
23	580	575.593591449667	1.22998382307526	4.40640855033306	0.472036136421568
24	575	577.388508844972	1.22946321119298	-2.38850884497238	0.0514594419546725
25	558	572.434936443282	1.2914525337359	-14.4349364432821	-0.580801132869835
26	564	571.616129900859	1.28251379474981	-7.61612990085865	-0.188590727061626
27	581	578.226380584235	1.3502141436004	2.77361941576454	0.466259678451897
28	597	584.322253260604	1.4041643062841	12.6777467393964	0.426006836920021
29	587	575.545372161038	1.33015344029104	11.4546278389618	-0.925795510807402
30	536	558.505592872025	1.24469016960868	-22.505592872025	-1.67364002059097
31	524	539.173688300836	1.16607247572273	-15.1736883008362	-1.8743477724514
32	537	533.781598772294	1.14043046173884	3.21840122770591	-0.597273585473656
33	536	532.747956487727	1.13133479774172	3.25204351227318	-0.198007709107718
34	533	530.216492868482	1.11688707877469	2.78350713151854	-0.333570589834449
35	528	525.671986304618	1.10428733679365	2.32801369538204	-0.515122348507489
36	516	519.10861645389	1.11462576460456	-3.10861645389017	-0.699137809195316
37	502	516.638923674878	1.12700295095996	-14.6389236748777	-0.329568307098887
38	506	516.154624718705	1.12216290724492	-10.154624718705	-0.145051913182883
39	518	516.760880559443	1.1176184966484	1.23911944055714	-0.0457514290532186
40	534	517.551228649648	1.11452366533325	16.4487713503524	-0.0293613943129028
41	528	512.702354878616	1.07146471526712	15.2976451213843	-0.541093057422549
42	478	500.038623315714	1.00224691894239	-22.0386233157136	-1.25068923188515
43	469	487.547813342304	0.948917776729206	-18.5478133423045	-1.2292188337595
44	490	485.812759025596	0.939009241873324	4.18724097440369	-0.244500297552983
45	493	487.468661866743	0.941594887903305	5.53133813325686	0.065298150636658
46	508	497.967063281479	0.970262573467887	10.0329367185207	0.870010045415969
47	517	508.242463615091	0.983121724222516	8.75753638490874	0.846486943878698
48	514	514.41913411288	0.979368727092779	-0.419134112880059	0.473270046258806
49	510	521.752625341128	0.973428385476263	-11.7526253411277	0.579889712133723
50	527	533.053216131319	1.00222500759732	-6.05321613131948	0.93148971140863
51	542	539.414455103701	1.03820234336187	2.58554489629865	0.478745358203172
52	565	544.610705508539	1.07100147423121	20.3892944914608	0.373488506704132
53	555	538.502705442634	1.02213239297337	16.4972945573658	-0.650485080892467
54	499	523.619864153253	0.939435531161422	-24.6198641532534	-1.44725765977709
55	511	525.854706450712	0.944737336183422	-14.8547064507118	0.118006334471876
56	526	523.755783173277	0.933934331240605	2.2442168267235	-0.277293586706407
57	532	527.744437691911	0.943519607811861	4.25556230808935	0.278214470263291
58	549	537.660683795162	0.964721629734739	11.3393162048382	0.816607327382545
59	561	549.581900147544	0.976393260938688	11.4180998524557	0.996645286824413
60	557	557.90141859642	0.975582055553118	-0.901418596420197	0.668558043602576
61	566	574.794395677551	0.979507658413409	-8.79439567755103	1.44805094435192
62	588	590.870234531052	1.02084827909289	-2.8702345310518	1.36297856660038
63	620	610.942776638484	1.12573019295206	9.05722336151548	1.70923227024423
64	626	607.135454879467	1.09259986726402	18.8645451205332	-0.443785961554476
65	620	601.420887888615	1.04983268513042	18.5791121113847	-0.616380416224196
66	573	598.864423419921	1.03124478473187	-25.8644234199207	-0.327937741616727
67	573	590.858091334267	0.993887526702721	-17.8580913342672	-0.823119831350531
68	574	578.612609521934	0.948575639147331	-4.61260952193449	-1.20608528364176
69	580	578.048628629406	0.94433909109211	1.95137137059414	-0.13773462314534
70	590	580.92140151197	0.948169114275126	9.07859848802987	0.175473302652514

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 539 & 539 & 0 & 0 & 0 \tabularnewline
2 & 548 & 546.753544793011 & 0.397143080817201 & 1.24645520698855 & 0.44712858924277 \tabularnewline
3 & 563 & 558.565725083752 & 0.781979675073757 & 4.43427491624753 & 0.972546151474376 \tabularnewline
4 & 581 & 575.275724481352 & 0.97700076219689 & 5.72427551864812 & 1.45208178248065 \tabularnewline
5 & 572 & 574.163751857567 & 0.964152395761841 & -2.16375185756673 & -0.190572921445446 \tabularnewline
6 & 519 & 533.862622401609 & 0.716027328492807 & -14.8626224016091 & -3.76175759509138 \tabularnewline
7 & 521 & 519.948536702457 & 0.620035375483989 & 1.05146329754346 & -1.33324718618088 \tabularnewline
8 & 531 & 526.077166746795 & 0.657227402100163 & 4.92283325320508 & 0.501964932542649 \tabularnewline
9 & 540 & 536.376321836725 & 0.722156789238851 & 3.62367816327494 & 0.87861498874148 \tabularnewline
10 & 548 & 545.430741720259 & 0.777776098207648 & 2.56925827974103 & 0.75927346796338 \tabularnewline
11 & 556 & 553.565287070504 & 0.826497998751057 & 2.43471292949573 & 0.670376433743256 \tabularnewline
12 & 551 & 552.135520827456 & 0.811657443755842 & -1.13552082745644 & -0.205596903746852 \tabularnewline
13 & 549 & 554.542543988939 & 0.754635232417334 & -5.54254398893936 & 0.163452904284107 \tabularnewline
14 & 564 & 563.876340375616 & 0.849791731686334 & 0.123659624383554 & 0.735049272541673 \tabularnewline
15 & 586 & 581.14274518651 & 1.18057434020651 & 4.85725481348956 & 1.40649243544317 \tabularnewline
16 & 604 & 594.26909964115 & 1.33488346008345 & 9.73090035885045 & 1.07800202005616 \tabularnewline
17 & 601 & 593.878837590513 & 1.32356562707927 & 7.12116240948682 & -0.157216460266215 \tabularnewline
18 & 545 & 568.087387476185 & 1.20649342154399 & -23.0873874761848 & -2.47089417954927 \tabularnewline
19 & 537 & 544.607102013219 & 1.10406354892649 & -7.60710201321883 & -2.24851901410684 \tabularnewline
20 & 552 & 545.171803426523 & 1.10165091581791 & 6.82819657347732 & -0.0491124850125779 \tabularnewline
21 & 563 & 555.914122995397 & 1.14807877493105 & 7.08587700460323 & 0.877882448852156 \tabularnewline
22 & 575 & 569.200727512775 & 1.20901000057965 & 5.79927248722464 & 1.1057027548664 \tabularnewline
23 & 580 & 575.593591449667 & 1.22998382307526 & 4.40640855033306 & 0.472036136421568 \tabularnewline
24 & 575 & 577.388508844972 & 1.22946321119298 & -2.38850884497238 & 0.0514594419546725 \tabularnewline
25 & 558 & 572.434936443282 & 1.2914525337359 & -14.4349364432821 & -0.580801132869835 \tabularnewline
26 & 564 & 571.616129900859 & 1.28251379474981 & -7.61612990085865 & -0.188590727061626 \tabularnewline
27 & 581 & 578.226380584235 & 1.3502141436004 & 2.77361941576454 & 0.466259678451897 \tabularnewline
28 & 597 & 584.322253260604 & 1.4041643062841 & 12.6777467393964 & 0.426006836920021 \tabularnewline
29 & 587 & 575.545372161038 & 1.33015344029104 & 11.4546278389618 & -0.925795510807402 \tabularnewline
30 & 536 & 558.505592872025 & 1.24469016960868 & -22.505592872025 & -1.67364002059097 \tabularnewline
31 & 524 & 539.173688300836 & 1.16607247572273 & -15.1736883008362 & -1.8743477724514 \tabularnewline
32 & 537 & 533.781598772294 & 1.14043046173884 & 3.21840122770591 & -0.597273585473656 \tabularnewline
33 & 536 & 532.747956487727 & 1.13133479774172 & 3.25204351227318 & -0.198007709107718 \tabularnewline
34 & 533 & 530.216492868482 & 1.11688707877469 & 2.78350713151854 & -0.333570589834449 \tabularnewline
35 & 528 & 525.671986304618 & 1.10428733679365 & 2.32801369538204 & -0.515122348507489 \tabularnewline
36 & 516 & 519.10861645389 & 1.11462576460456 & -3.10861645389017 & -0.699137809195316 \tabularnewline
37 & 502 & 516.638923674878 & 1.12700295095996 & -14.6389236748777 & -0.329568307098887 \tabularnewline
38 & 506 & 516.154624718705 & 1.12216290724492 & -10.154624718705 & -0.145051913182883 \tabularnewline
39 & 518 & 516.760880559443 & 1.1176184966484 & 1.23911944055714 & -0.0457514290532186 \tabularnewline
40 & 534 & 517.551228649648 & 1.11452366533325 & 16.4487713503524 & -0.0293613943129028 \tabularnewline
41 & 528 & 512.702354878616 & 1.07146471526712 & 15.2976451213843 & -0.541093057422549 \tabularnewline
42 & 478 & 500.038623315714 & 1.00224691894239 & -22.0386233157136 & -1.25068923188515 \tabularnewline
43 & 469 & 487.547813342304 & 0.948917776729206 & -18.5478133423045 & -1.2292188337595 \tabularnewline
44 & 490 & 485.812759025596 & 0.939009241873324 & 4.18724097440369 & -0.244500297552983 \tabularnewline
45 & 493 & 487.468661866743 & 0.941594887903305 & 5.53133813325686 & 0.065298150636658 \tabularnewline
46 & 508 & 497.967063281479 & 0.970262573467887 & 10.0329367185207 & 0.870010045415969 \tabularnewline
47 & 517 & 508.242463615091 & 0.983121724222516 & 8.75753638490874 & 0.846486943878698 \tabularnewline
48 & 514 & 514.41913411288 & 0.979368727092779 & -0.419134112880059 & 0.473270046258806 \tabularnewline
49 & 510 & 521.752625341128 & 0.973428385476263 & -11.7526253411277 & 0.579889712133723 \tabularnewline
50 & 527 & 533.053216131319 & 1.00222500759732 & -6.05321613131948 & 0.93148971140863 \tabularnewline
51 & 542 & 539.414455103701 & 1.03820234336187 & 2.58554489629865 & 0.478745358203172 \tabularnewline
52 & 565 & 544.610705508539 & 1.07100147423121 & 20.3892944914608 & 0.373488506704132 \tabularnewline
53 & 555 & 538.502705442634 & 1.02213239297337 & 16.4972945573658 & -0.650485080892467 \tabularnewline
54 & 499 & 523.619864153253 & 0.939435531161422 & -24.6198641532534 & -1.44725765977709 \tabularnewline
55 & 511 & 525.854706450712 & 0.944737336183422 & -14.8547064507118 & 0.118006334471876 \tabularnewline
56 & 526 & 523.755783173277 & 0.933934331240605 & 2.2442168267235 & -0.277293586706407 \tabularnewline
57 & 532 & 527.744437691911 & 0.943519607811861 & 4.25556230808935 & 0.278214470263291 \tabularnewline
58 & 549 & 537.660683795162 & 0.964721629734739 & 11.3393162048382 & 0.816607327382545 \tabularnewline
59 & 561 & 549.581900147544 & 0.976393260938688 & 11.4180998524557 & 0.996645286824413 \tabularnewline
60 & 557 & 557.90141859642 & 0.975582055553118 & -0.901418596420197 & 0.668558043602576 \tabularnewline
61 & 566 & 574.794395677551 & 0.979507658413409 & -8.79439567755103 & 1.44805094435192 \tabularnewline
62 & 588 & 590.870234531052 & 1.02084827909289 & -2.8702345310518 & 1.36297856660038 \tabularnewline
63 & 620 & 610.942776638484 & 1.12573019295206 & 9.05722336151548 & 1.70923227024423 \tabularnewline
64 & 626 & 607.135454879467 & 1.09259986726402 & 18.8645451205332 & -0.443785961554476 \tabularnewline
65 & 620 & 601.420887888615 & 1.04983268513042 & 18.5791121113847 & -0.616380416224196 \tabularnewline
66 & 573 & 598.864423419921 & 1.03124478473187 & -25.8644234199207 & -0.327937741616727 \tabularnewline
67 & 573 & 590.858091334267 & 0.993887526702721 & -17.8580913342672 & -0.823119831350531 \tabularnewline
68 & 574 & 578.612609521934 & 0.948575639147331 & -4.61260952193449 & -1.20608528364176 \tabularnewline
69 & 580 & 578.048628629406 & 0.94433909109211 & 1.95137137059414 & -0.13773462314534 \tabularnewline
70 & 590 & 580.92140151197 & 0.948169114275126 & 9.07859848802987 & 0.175473302652514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160373&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]539[/C][C]539[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]548[/C][C]546.753544793011[/C][C]0.397143080817201[/C][C]1.24645520698855[/C][C]0.44712858924277[/C][/ROW]
[ROW][C]3[/C][C]563[/C][C]558.565725083752[/C][C]0.781979675073757[/C][C]4.43427491624753[/C][C]0.972546151474376[/C][/ROW]
[ROW][C]4[/C][C]581[/C][C]575.275724481352[/C][C]0.97700076219689[/C][C]5.72427551864812[/C][C]1.45208178248065[/C][/ROW]
[ROW][C]5[/C][C]572[/C][C]574.163751857567[/C][C]0.964152395761841[/C][C]-2.16375185756673[/C][C]-0.190572921445446[/C][/ROW]
[ROW][C]6[/C][C]519[/C][C]533.862622401609[/C][C]0.716027328492807[/C][C]-14.8626224016091[/C][C]-3.76175759509138[/C][/ROW]
[ROW][C]7[/C][C]521[/C][C]519.948536702457[/C][C]0.620035375483989[/C][C]1.05146329754346[/C][C]-1.33324718618088[/C][/ROW]
[ROW][C]8[/C][C]531[/C][C]526.077166746795[/C][C]0.657227402100163[/C][C]4.92283325320508[/C][C]0.501964932542649[/C][/ROW]
[ROW][C]9[/C][C]540[/C][C]536.376321836725[/C][C]0.722156789238851[/C][C]3.62367816327494[/C][C]0.87861498874148[/C][/ROW]
[ROW][C]10[/C][C]548[/C][C]545.430741720259[/C][C]0.777776098207648[/C][C]2.56925827974103[/C][C]0.75927346796338[/C][/ROW]
[ROW][C]11[/C][C]556[/C][C]553.565287070504[/C][C]0.826497998751057[/C][C]2.43471292949573[/C][C]0.670376433743256[/C][/ROW]
[ROW][C]12[/C][C]551[/C][C]552.135520827456[/C][C]0.811657443755842[/C][C]-1.13552082745644[/C][C]-0.205596903746852[/C][/ROW]
[ROW][C]13[/C][C]549[/C][C]554.542543988939[/C][C]0.754635232417334[/C][C]-5.54254398893936[/C][C]0.163452904284107[/C][/ROW]
[ROW][C]14[/C][C]564[/C][C]563.876340375616[/C][C]0.849791731686334[/C][C]0.123659624383554[/C][C]0.735049272541673[/C][/ROW]
[ROW][C]15[/C][C]586[/C][C]581.14274518651[/C][C]1.18057434020651[/C][C]4.85725481348956[/C][C]1.40649243544317[/C][/ROW]
[ROW][C]16[/C][C]604[/C][C]594.26909964115[/C][C]1.33488346008345[/C][C]9.73090035885045[/C][C]1.07800202005616[/C][/ROW]
[ROW][C]17[/C][C]601[/C][C]593.878837590513[/C][C]1.32356562707927[/C][C]7.12116240948682[/C][C]-0.157216460266215[/C][/ROW]
[ROW][C]18[/C][C]545[/C][C]568.087387476185[/C][C]1.20649342154399[/C][C]-23.0873874761848[/C][C]-2.47089417954927[/C][/ROW]
[ROW][C]19[/C][C]537[/C][C]544.607102013219[/C][C]1.10406354892649[/C][C]-7.60710201321883[/C][C]-2.24851901410684[/C][/ROW]
[ROW][C]20[/C][C]552[/C][C]545.171803426523[/C][C]1.10165091581791[/C][C]6.82819657347732[/C][C]-0.0491124850125779[/C][/ROW]
[ROW][C]21[/C][C]563[/C][C]555.914122995397[/C][C]1.14807877493105[/C][C]7.08587700460323[/C][C]0.877882448852156[/C][/ROW]
[ROW][C]22[/C][C]575[/C][C]569.200727512775[/C][C]1.20901000057965[/C][C]5.79927248722464[/C][C]1.1057027548664[/C][/ROW]
[ROW][C]23[/C][C]580[/C][C]575.593591449667[/C][C]1.22998382307526[/C][C]4.40640855033306[/C][C]0.472036136421568[/C][/ROW]
[ROW][C]24[/C][C]575[/C][C]577.388508844972[/C][C]1.22946321119298[/C][C]-2.38850884497238[/C][C]0.0514594419546725[/C][/ROW]
[ROW][C]25[/C][C]558[/C][C]572.434936443282[/C][C]1.2914525337359[/C][C]-14.4349364432821[/C][C]-0.580801132869835[/C][/ROW]
[ROW][C]26[/C][C]564[/C][C]571.616129900859[/C][C]1.28251379474981[/C][C]-7.61612990085865[/C][C]-0.188590727061626[/C][/ROW]
[ROW][C]27[/C][C]581[/C][C]578.226380584235[/C][C]1.3502141436004[/C][C]2.77361941576454[/C][C]0.466259678451897[/C][/ROW]
[ROW][C]28[/C][C]597[/C][C]584.322253260604[/C][C]1.4041643062841[/C][C]12.6777467393964[/C][C]0.426006836920021[/C][/ROW]
[ROW][C]29[/C][C]587[/C][C]575.545372161038[/C][C]1.33015344029104[/C][C]11.4546278389618[/C][C]-0.925795510807402[/C][/ROW]
[ROW][C]30[/C][C]536[/C][C]558.505592872025[/C][C]1.24469016960868[/C][C]-22.505592872025[/C][C]-1.67364002059097[/C][/ROW]
[ROW][C]31[/C][C]524[/C][C]539.173688300836[/C][C]1.16607247572273[/C][C]-15.1736883008362[/C][C]-1.8743477724514[/C][/ROW]
[ROW][C]32[/C][C]537[/C][C]533.781598772294[/C][C]1.14043046173884[/C][C]3.21840122770591[/C][C]-0.597273585473656[/C][/ROW]
[ROW][C]33[/C][C]536[/C][C]532.747956487727[/C][C]1.13133479774172[/C][C]3.25204351227318[/C][C]-0.198007709107718[/C][/ROW]
[ROW][C]34[/C][C]533[/C][C]530.216492868482[/C][C]1.11688707877469[/C][C]2.78350713151854[/C][C]-0.333570589834449[/C][/ROW]
[ROW][C]35[/C][C]528[/C][C]525.671986304618[/C][C]1.10428733679365[/C][C]2.32801369538204[/C][C]-0.515122348507489[/C][/ROW]
[ROW][C]36[/C][C]516[/C][C]519.10861645389[/C][C]1.11462576460456[/C][C]-3.10861645389017[/C][C]-0.699137809195316[/C][/ROW]
[ROW][C]37[/C][C]502[/C][C]516.638923674878[/C][C]1.12700295095996[/C][C]-14.6389236748777[/C][C]-0.329568307098887[/C][/ROW]
[ROW][C]38[/C][C]506[/C][C]516.154624718705[/C][C]1.12216290724492[/C][C]-10.154624718705[/C][C]-0.145051913182883[/C][/ROW]
[ROW][C]39[/C][C]518[/C][C]516.760880559443[/C][C]1.1176184966484[/C][C]1.23911944055714[/C][C]-0.0457514290532186[/C][/ROW]
[ROW][C]40[/C][C]534[/C][C]517.551228649648[/C][C]1.11452366533325[/C][C]16.4487713503524[/C][C]-0.0293613943129028[/C][/ROW]
[ROW][C]41[/C][C]528[/C][C]512.702354878616[/C][C]1.07146471526712[/C][C]15.2976451213843[/C][C]-0.541093057422549[/C][/ROW]
[ROW][C]42[/C][C]478[/C][C]500.038623315714[/C][C]1.00224691894239[/C][C]-22.0386233157136[/C][C]-1.25068923188515[/C][/ROW]
[ROW][C]43[/C][C]469[/C][C]487.547813342304[/C][C]0.948917776729206[/C][C]-18.5478133423045[/C][C]-1.2292188337595[/C][/ROW]
[ROW][C]44[/C][C]490[/C][C]485.812759025596[/C][C]0.939009241873324[/C][C]4.18724097440369[/C][C]-0.244500297552983[/C][/ROW]
[ROW][C]45[/C][C]493[/C][C]487.468661866743[/C][C]0.941594887903305[/C][C]5.53133813325686[/C][C]0.065298150636658[/C][/ROW]
[ROW][C]46[/C][C]508[/C][C]497.967063281479[/C][C]0.970262573467887[/C][C]10.0329367185207[/C][C]0.870010045415969[/C][/ROW]
[ROW][C]47[/C][C]517[/C][C]508.242463615091[/C][C]0.983121724222516[/C][C]8.75753638490874[/C][C]0.846486943878698[/C][/ROW]
[ROW][C]48[/C][C]514[/C][C]514.41913411288[/C][C]0.979368727092779[/C][C]-0.419134112880059[/C][C]0.473270046258806[/C][/ROW]
[ROW][C]49[/C][C]510[/C][C]521.752625341128[/C][C]0.973428385476263[/C][C]-11.7526253411277[/C][C]0.579889712133723[/C][/ROW]
[ROW][C]50[/C][C]527[/C][C]533.053216131319[/C][C]1.00222500759732[/C][C]-6.05321613131948[/C][C]0.93148971140863[/C][/ROW]
[ROW][C]51[/C][C]542[/C][C]539.414455103701[/C][C]1.03820234336187[/C][C]2.58554489629865[/C][C]0.478745358203172[/C][/ROW]
[ROW][C]52[/C][C]565[/C][C]544.610705508539[/C][C]1.07100147423121[/C][C]20.3892944914608[/C][C]0.373488506704132[/C][/ROW]
[ROW][C]53[/C][C]555[/C][C]538.502705442634[/C][C]1.02213239297337[/C][C]16.4972945573658[/C][C]-0.650485080892467[/C][/ROW]
[ROW][C]54[/C][C]499[/C][C]523.619864153253[/C][C]0.939435531161422[/C][C]-24.6198641532534[/C][C]-1.44725765977709[/C][/ROW]
[ROW][C]55[/C][C]511[/C][C]525.854706450712[/C][C]0.944737336183422[/C][C]-14.8547064507118[/C][C]0.118006334471876[/C][/ROW]
[ROW][C]56[/C][C]526[/C][C]523.755783173277[/C][C]0.933934331240605[/C][C]2.2442168267235[/C][C]-0.277293586706407[/C][/ROW]
[ROW][C]57[/C][C]532[/C][C]527.744437691911[/C][C]0.943519607811861[/C][C]4.25556230808935[/C][C]0.278214470263291[/C][/ROW]
[ROW][C]58[/C][C]549[/C][C]537.660683795162[/C][C]0.964721629734739[/C][C]11.3393162048382[/C][C]0.816607327382545[/C][/ROW]
[ROW][C]59[/C][C]561[/C][C]549.581900147544[/C][C]0.976393260938688[/C][C]11.4180998524557[/C][C]0.996645286824413[/C][/ROW]
[ROW][C]60[/C][C]557[/C][C]557.90141859642[/C][C]0.975582055553118[/C][C]-0.901418596420197[/C][C]0.668558043602576[/C][/ROW]
[ROW][C]61[/C][C]566[/C][C]574.794395677551[/C][C]0.979507658413409[/C][C]-8.79439567755103[/C][C]1.44805094435192[/C][/ROW]
[ROW][C]62[/C][C]588[/C][C]590.870234531052[/C][C]1.02084827909289[/C][C]-2.8702345310518[/C][C]1.36297856660038[/C][/ROW]
[ROW][C]63[/C][C]620[/C][C]610.942776638484[/C][C]1.12573019295206[/C][C]9.05722336151548[/C][C]1.70923227024423[/C][/ROW]
[ROW][C]64[/C][C]626[/C][C]607.135454879467[/C][C]1.09259986726402[/C][C]18.8645451205332[/C][C]-0.443785961554476[/C][/ROW]
[ROW][C]65[/C][C]620[/C][C]601.420887888615[/C][C]1.04983268513042[/C][C]18.5791121113847[/C][C]-0.616380416224196[/C][/ROW]
[ROW][C]66[/C][C]573[/C][C]598.864423419921[/C][C]1.03124478473187[/C][C]-25.8644234199207[/C][C]-0.327937741616727[/C][/ROW]
[ROW][C]67[/C][C]573[/C][C]590.858091334267[/C][C]0.993887526702721[/C][C]-17.8580913342672[/C][C]-0.823119831350531[/C][/ROW]
[ROW][C]68[/C][C]574[/C][C]578.612609521934[/C][C]0.948575639147331[/C][C]-4.61260952193449[/C][C]-1.20608528364176[/C][/ROW]
[ROW][C]69[/C][C]580[/C][C]578.048628629406[/C][C]0.94433909109211[/C][C]1.95137137059414[/C][C]-0.13773462314534[/C][/ROW]
[ROW][C]70[/C][C]590[/C][C]580.92140151197[/C][C]0.948169114275126[/C][C]9.07859848802987[/C][C]0.175473302652514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160373&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160373&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	539	539	0	0	0
2	548	546.753544793011	0.397143080817201	1.24645520698855	0.44712858924277
3	563	558.565725083752	0.781979675073757	4.43427491624753	0.972546151474376
4	581	575.275724481352	0.97700076219689	5.72427551864812	1.45208178248065
5	572	574.163751857567	0.964152395761841	-2.16375185756673	-0.190572921445446
6	519	533.862622401609	0.716027328492807	-14.8626224016091	-3.76175759509138
7	521	519.948536702457	0.620035375483989	1.05146329754346	-1.33324718618088
8	531	526.077166746795	0.657227402100163	4.92283325320508	0.501964932542649
9	540	536.376321836725	0.722156789238851	3.62367816327494	0.87861498874148
10	548	545.430741720259	0.777776098207648	2.56925827974103	0.75927346796338
11	556	553.565287070504	0.826497998751057	2.43471292949573	0.670376433743256
12	551	552.135520827456	0.811657443755842	-1.13552082745644	-0.205596903746852
13	549	554.542543988939	0.754635232417334	-5.54254398893936	0.163452904284107
14	564	563.876340375616	0.849791731686334	0.123659624383554	0.735049272541673
15	586	581.14274518651	1.18057434020651	4.85725481348956	1.40649243544317
16	604	594.26909964115	1.33488346008345	9.73090035885045	1.07800202005616
17	601	593.878837590513	1.32356562707927	7.12116240948682	-0.157216460266215
18	545	568.087387476185	1.20649342154399	-23.0873874761848	-2.47089417954927
19	537	544.607102013219	1.10406354892649	-7.60710201321883	-2.24851901410684
20	552	545.171803426523	1.10165091581791	6.82819657347732	-0.0491124850125779
21	563	555.914122995397	1.14807877493105	7.08587700460323	0.877882448852156
22	575	569.200727512775	1.20901000057965	5.79927248722464	1.1057027548664
23	580	575.593591449667	1.22998382307526	4.40640855033306	0.472036136421568
24	575	577.388508844972	1.22946321119298	-2.38850884497238	0.0514594419546725
25	558	572.434936443282	1.2914525337359	-14.4349364432821	-0.580801132869835
26	564	571.616129900859	1.28251379474981	-7.61612990085865	-0.188590727061626
27	581	578.226380584235	1.3502141436004	2.77361941576454	0.466259678451897
28	597	584.322253260604	1.4041643062841	12.6777467393964	0.426006836920021
29	587	575.545372161038	1.33015344029104	11.4546278389618	-0.925795510807402
30	536	558.505592872025	1.24469016960868	-22.505592872025	-1.67364002059097
31	524	539.173688300836	1.16607247572273	-15.1736883008362	-1.8743477724514
32	537	533.781598772294	1.14043046173884	3.21840122770591	-0.597273585473656
33	536	532.747956487727	1.13133479774172	3.25204351227318	-0.198007709107718
34	533	530.216492868482	1.11688707877469	2.78350713151854	-0.333570589834449
35	528	525.671986304618	1.10428733679365	2.32801369538204	-0.515122348507489
36	516	519.10861645389	1.11462576460456	-3.10861645389017	-0.699137809195316
37	502	516.638923674878	1.12700295095996	-14.6389236748777	-0.329568307098887
38	506	516.154624718705	1.12216290724492	-10.154624718705	-0.145051913182883
39	518	516.760880559443	1.1176184966484	1.23911944055714	-0.0457514290532186
40	534	517.551228649648	1.11452366533325	16.4487713503524	-0.0293613943129028
41	528	512.702354878616	1.07146471526712	15.2976451213843	-0.541093057422549
42	478	500.038623315714	1.00224691894239	-22.0386233157136	-1.25068923188515
43	469	487.547813342304	0.948917776729206	-18.5478133423045	-1.2292188337595
44	490	485.812759025596	0.939009241873324	4.18724097440369	-0.244500297552983
45	493	487.468661866743	0.941594887903305	5.53133813325686	0.065298150636658
46	508	497.967063281479	0.970262573467887	10.0329367185207	0.870010045415969
47	517	508.242463615091	0.983121724222516	8.75753638490874	0.846486943878698
48	514	514.41913411288	0.979368727092779	-0.419134112880059	0.473270046258806
49	510	521.752625341128	0.973428385476263	-11.7526253411277	0.579889712133723
50	527	533.053216131319	1.00222500759732	-6.05321613131948	0.93148971140863
51	542	539.414455103701	1.03820234336187	2.58554489629865	0.478745358203172
52	565	544.610705508539	1.07100147423121	20.3892944914608	0.373488506704132
53	555	538.502705442634	1.02213239297337	16.4972945573658	-0.650485080892467
54	499	523.619864153253	0.939435531161422	-24.6198641532534	-1.44725765977709
55	511	525.854706450712	0.944737336183422	-14.8547064507118	0.118006334471876
56	526	523.755783173277	0.933934331240605	2.2442168267235	-0.277293586706407
57	532	527.744437691911	0.943519607811861	4.25556230808935	0.278214470263291
58	549	537.660683795162	0.964721629734739	11.3393162048382	0.816607327382545
59	561	549.581900147544	0.976393260938688	11.4180998524557	0.996645286824413
60	557	557.90141859642	0.975582055553118	-0.901418596420197	0.668558043602576
61	566	574.794395677551	0.979507658413409	-8.79439567755103	1.44805094435192
62	588	590.870234531052	1.02084827909289	-2.8702345310518	1.36297856660038
63	620	610.942776638484	1.12573019295206	9.05722336151548	1.70923227024423
64	626	607.135454879467	1.09259986726402	18.8645451205332	-0.443785961554476
65	620	601.420887888615	1.04983268513042	18.5791121113847	-0.616380416224196
66	573	598.864423419921	1.03124478473187	-25.8644234199207	-0.327937741616727
67	573	590.858091334267	0.993887526702721	-17.8580913342672	-0.823119831350531
68	574	578.612609521934	0.948575639147331	-4.61260952193449	-1.20608528364176
69	580	578.048628629406	0.94433909109211	1.95137137059414	-0.13773462314534
70	590	580.92140151197	0.948169114275126	9.07859848802987	0.175473302652514

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