Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Tue, 01 Dec 2009 12:54:37 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/01/t125969733043fhia1j8lhq69j.htm/, Retrieved Sat, 06 Jun 2026 09:57:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62224, Retrieved Sat, 06 Jun 2026 09:57:10 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

489

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]
-    D      [Structural Time Series Models] [Structurele tijdr...] [2009-12-01 19:54:37] [6c304092df7982e5e12293b2743450a3] [Current]
-    D        [Structural Time Series Models] [Ad hoc forecasting] [2009-12-04 16:16:16] [34d27ebe78dc2d31581e8710befe8733] 
-   PD          [Structural Time Series Models] [tijdreeksanalyse ...] [2009-12-16 22:58:04] [34d27ebe78dc2d31581e8710befe8733] 
-    D        [Structural Time Series Models] [structurele tijdr...] [2009-12-04 19:23:56] [4f1a20f787b3465111b61213cdeef1a9] 
-    D        [Structural Time Series Models] [structurele tijdr...] [2009-12-04 19:23:56] [4f1a20f787b3465111b61213cdeef1a9] 
-    D          [Structural Time Series Models] [Structurele tijdr...] [2009-12-11 16:03:21] [4f1a20f787b3465111b61213cdeef1a9] 
-   PD            [Structural Time Series Models] [Structurele tijdr...] [2009-12-11 16:46:43] [4f1a20f787b3465111b61213cdeef1a9] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.2

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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62224&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62224&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	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	8.4	8.4	0	0	0
2	8.4	8.4	0	0	0
3	8.4	8.4	0	0	0
4	8.6	8.59450288184909	0.186336498471207	0.00549711815091083	0.542139808952547
5	8.9	8.89818757487719	0.298820878666345	0.00181242512281285	0.327604743032395
6	8.8	8.81218879419231	-0.0701036903600278	-0.0121887941923082	-1.0744078602474
7	8.3	8.30982820712854	-0.484497368791315	-0.00982820712853705	-1.20682693844648
8	7.5	7.50619437027392	-0.790443779007934	-0.00619437027391512	-0.890998953192124
9	7.2	7.1841981799698	-0.341356654372683	0.0158018200302004	1.30786355065082
10	7.4	7.38783991849545	0.181117624453733	0.0121600815045500	1.52158685435875
11	8.8	8.76940313327973	1.33195018155721	0.0305968667202731	3.35153664288356
12	9.3	9.33141796858167	0.593835381079452	-0.0314179685816659	-2.14959055962222
13	9.3	9.31206024620503	0.00614229913265951	-0.0120602462050237	-1.71219001997661
14	8.7	8.71417121390012	-0.573184008276645	-0.0141712139001166	-1.69423863951449
15	8.2	8.19291377757677	-0.524590012218204	0.00708622242323257	0.142937770280577
16	8.3	8.27870651858461	0.0460847758066103	0.0212934814153921	1.66000271945657
17	8.5	8.49082657038934	0.201233413953079	0.00917342961065437	0.451892590507891
18	8.6	8.61026011305591	0.124775165732414	-0.0102601130559145	-0.222666517111757
19	8.5	8.49906162872325	-0.0957893751730662	0.0009383712767499	-0.642344401582395
20	8.2	8.22059950369853	-0.266530263226196	-0.0205995036985341	-0.497243774358148
21	8.1	8.0671242661379	-0.160859902044925	0.0328757338620984	0.307740764488693
22	7.9	7.9519178929486	-0.118188339236399	-0.0519178929486033	0.124271169664202
23	8.6	8.51974095973871	0.523020367497446	0.080259040261289	1.86737445325227
24	8.7	8.7424253381197	0.242306274407083	-0.0424253381196999	-0.8175171896451
25	8.7	8.69797842724487	-0.0256417206056453	0.00202157275512926	-0.780709100960954
26	8.5	8.50132251246483	-0.185569562503805	-0.00132251246482670	-0.466614956822868
27	8.4	8.41811469353935	-0.0911547063213842	-0.0181146935393472	0.276352870301122
28	8.5	8.4836511593258	0.0535992036847195	0.0163488406741942	0.421298118657457
29	8.7	8.68738617815933	0.192128800651334	0.0126138218406734	0.403448763895573
30	8.7	8.71184394878778	0.0373675017945224	-0.0118439487877778	-0.450712780267858
31	8.6	8.59304152670997	-0.106783563881493	0.00695847329002688	-0.419806817830184
32	8.5	8.52145780871233	-0.0742934064926835	-0.0214578087123312	0.0946201826656657
33	8.3	8.25530817586004	-0.251378877726735	0.0446918241399638	-0.515720954263528
34	8	8.09985758883582	-0.162835388833424	-0.0998575888358217	0.257862671210054
35	8.2	8.10177341255155	-0.0107652022417415	0.0982265874484516	0.442870737944124
36	8.1	8.12955809375315	0.0248150432402895	-0.0295580937531451	0.103619748756330
37	8.1	8.08810141986608	-0.0363394533713269	0.0118985801339163	-0.178202264373939
38	8	8.00409711361563	-0.0803437981701123	-0.00409711361562836	-0.128225093271845
39	7.9	7.9241028133476	-0.080023604231224	-0.0241028133476076	0.000934916941762015
40	7.9	7.89861201034747	-0.0299689247701155	0.00138798965252551	0.145753330538329
41	8	7.97379475851115	0.0664268345841462	0.0262052414888480	0.280701723197123
42	8	8.00277087301101	0.0320854763466518	-0.00277087301101287	-0.100014939197683
43	7.9	7.91018055910298	-0.0822476986425896	-0.0101805591029809	-0.332968048500968
44	8	7.99301301521662	0.0691358795899048	0.00698698478337603	0.440870367703134
45	7.7	7.67726132357204	-0.283812957491661	0.0227386764279626	-1.02788278615441
46	7.2	7.3141959239161	-0.356489541200404	-0.114195923916094	-0.211653986485931
47	7.5	7.38278412037487	0.0333207469073576	0.117215879625126	1.13523790722274
48	7.3	7.33239981069436	-0.0434311786450603	-0.032399810694358	-0.223525681529458
49	7	7.00145157623927	-0.307046239928848	-0.00145157623927222	-0.768172856093289
50	7	6.98466972743133	-0.0409007030036084	0.0153302725686740	0.77512340161062
51	7	7.02053972426448	0.0291743944877572	-0.0205397242644795	0.204371834297510
52	7.2	7.20162942663088	0.168063168540456	-0.00162942663088353	0.404538839841147
53	7.3	7.27829417803854	0.0845877803907532	0.0217058219614643	-0.243056860738686
54	7.1	7.10447766873797	-0.151449040374118	-0.00447766873797478	-0.687434972770834
55	6.8	6.84491095858611	-0.250218854362103	-0.044910958586107	-0.287643356539499
56	6.4	6.37048585356149	-0.455039514945662	0.0295141464385114	-0.596493447011743
57	6.1	6.04662841713655	-0.335201367206379	0.0533715828634461	0.349001215668825
58	6.5	6.60630158823162	0.482295506431774	-0.106301588231619	2.38077547677439
59	7.7	7.56100590096338	0.913854115088924	0.138994099036624	1.25681899661878
60	7.9	7.93198033091878	0.417984603653717	-0.0319803309187814	-1.44415926819459
61	7.5	7.56674274440778	-0.297445557429344	-0.06674274440778	-2.08462594732407
62	6.9	6.90371487086696	-0.631307123974338	-0.00371487086695706	-0.972161148286413
63	6.6	6.61464816362608	-0.319647774563612	-0.0146481636260801	0.908425293627625
64	6.9	6.86899601328774	0.203719304920818	0.0310039867122609	1.52458534731289
65	7.7	7.63511448773715	0.716126230078677	0.0648855122628517	1.49193598767762
66	8	8.0266609508785	0.420394582704619	-0.0266609508785065	-0.861286443508214
67	8	8.03730886785195	0.0470167974500614	-0.0373088678519463	-1.08737666402777
68	7.7	7.66381937553885	-0.336168985306571	0.0361806244611525	-1.11593967357225
69	7.3	7.30718183205484	-0.354820772858166	-0.00718183205484464	-0.0543190866513019
70	7.4	7.53910678983084	0.17984804454146	-0.139106789830835	1.55710462546365
71	8.1	7.93571205300436	0.377362761122093	0.164287946995636	0.575216160067762
72	8.3	8.28099711948655	0.348136768855624	0.0190028805134527	-0.0851193254992055
73	8.2	8.24143453405873	-0.00513654574708017	-0.0414345340587352	-1.02927863813055

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 8.4 & 8.4 & 0 & 0 & 0 \tabularnewline
2 & 8.4 & 8.4 & 0 & 0 & 0 \tabularnewline
3 & 8.4 & 8.4 & 0 & 0 & 0 \tabularnewline
4 & 8.6 & 8.59450288184909 & 0.186336498471207 & 0.00549711815091083 & 0.542139808952547 \tabularnewline
5 & 8.9 & 8.89818757487719 & 0.298820878666345 & 0.00181242512281285 & 0.327604743032395 \tabularnewline
6 & 8.8 & 8.81218879419231 & -0.0701036903600278 & -0.0121887941923082 & -1.0744078602474 \tabularnewline
7 & 8.3 & 8.30982820712854 & -0.484497368791315 & -0.00982820712853705 & -1.20682693844648 \tabularnewline
8 & 7.5 & 7.50619437027392 & -0.790443779007934 & -0.00619437027391512 & -0.890998953192124 \tabularnewline
9 & 7.2 & 7.1841981799698 & -0.341356654372683 & 0.0158018200302004 & 1.30786355065082 \tabularnewline
10 & 7.4 & 7.38783991849545 & 0.181117624453733 & 0.0121600815045500 & 1.52158685435875 \tabularnewline
11 & 8.8 & 8.76940313327973 & 1.33195018155721 & 0.0305968667202731 & 3.35153664288356 \tabularnewline
12 & 9.3 & 9.33141796858167 & 0.593835381079452 & -0.0314179685816659 & -2.14959055962222 \tabularnewline
13 & 9.3 & 9.31206024620503 & 0.00614229913265951 & -0.0120602462050237 & -1.71219001997661 \tabularnewline
14 & 8.7 & 8.71417121390012 & -0.573184008276645 & -0.0141712139001166 & -1.69423863951449 \tabularnewline
15 & 8.2 & 8.19291377757677 & -0.524590012218204 & 0.00708622242323257 & 0.142937770280577 \tabularnewline
16 & 8.3 & 8.27870651858461 & 0.0460847758066103 & 0.0212934814153921 & 1.66000271945657 \tabularnewline
17 & 8.5 & 8.49082657038934 & 0.201233413953079 & 0.00917342961065437 & 0.451892590507891 \tabularnewline
18 & 8.6 & 8.61026011305591 & 0.124775165732414 & -0.0102601130559145 & -0.222666517111757 \tabularnewline
19 & 8.5 & 8.49906162872325 & -0.0957893751730662 & 0.0009383712767499 & -0.642344401582395 \tabularnewline
20 & 8.2 & 8.22059950369853 & -0.266530263226196 & -0.0205995036985341 & -0.497243774358148 \tabularnewline
21 & 8.1 & 8.0671242661379 & -0.160859902044925 & 0.0328757338620984 & 0.307740764488693 \tabularnewline
22 & 7.9 & 7.9519178929486 & -0.118188339236399 & -0.0519178929486033 & 0.124271169664202 \tabularnewline
23 & 8.6 & 8.51974095973871 & 0.523020367497446 & 0.080259040261289 & 1.86737445325227 \tabularnewline
24 & 8.7 & 8.7424253381197 & 0.242306274407083 & -0.0424253381196999 & -0.8175171896451 \tabularnewline
25 & 8.7 & 8.69797842724487 & -0.0256417206056453 & 0.00202157275512926 & -0.780709100960954 \tabularnewline
26 & 8.5 & 8.50132251246483 & -0.185569562503805 & -0.00132251246482670 & -0.466614956822868 \tabularnewline
27 & 8.4 & 8.41811469353935 & -0.0911547063213842 & -0.0181146935393472 & 0.276352870301122 \tabularnewline
28 & 8.5 & 8.4836511593258 & 0.0535992036847195 & 0.0163488406741942 & 0.421298118657457 \tabularnewline
29 & 8.7 & 8.68738617815933 & 0.192128800651334 & 0.0126138218406734 & 0.403448763895573 \tabularnewline
30 & 8.7 & 8.71184394878778 & 0.0373675017945224 & -0.0118439487877778 & -0.450712780267858 \tabularnewline
31 & 8.6 & 8.59304152670997 & -0.106783563881493 & 0.00695847329002688 & -0.419806817830184 \tabularnewline
32 & 8.5 & 8.52145780871233 & -0.0742934064926835 & -0.0214578087123312 & 0.0946201826656657 \tabularnewline
33 & 8.3 & 8.25530817586004 & -0.251378877726735 & 0.0446918241399638 & -0.515720954263528 \tabularnewline
34 & 8 & 8.09985758883582 & -0.162835388833424 & -0.0998575888358217 & 0.257862671210054 \tabularnewline
35 & 8.2 & 8.10177341255155 & -0.0107652022417415 & 0.0982265874484516 & 0.442870737944124 \tabularnewline
36 & 8.1 & 8.12955809375315 & 0.0248150432402895 & -0.0295580937531451 & 0.103619748756330 \tabularnewline
37 & 8.1 & 8.08810141986608 & -0.0363394533713269 & 0.0118985801339163 & -0.178202264373939 \tabularnewline
38 & 8 & 8.00409711361563 & -0.0803437981701123 & -0.00409711361562836 & -0.128225093271845 \tabularnewline
39 & 7.9 & 7.9241028133476 & -0.080023604231224 & -0.0241028133476076 & 0.000934916941762015 \tabularnewline
40 & 7.9 & 7.89861201034747 & -0.0299689247701155 & 0.00138798965252551 & 0.145753330538329 \tabularnewline
41 & 8 & 7.97379475851115 & 0.0664268345841462 & 0.0262052414888480 & 0.280701723197123 \tabularnewline
42 & 8 & 8.00277087301101 & 0.0320854763466518 & -0.00277087301101287 & -0.100014939197683 \tabularnewline
43 & 7.9 & 7.91018055910298 & -0.0822476986425896 & -0.0101805591029809 & -0.332968048500968 \tabularnewline
44 & 8 & 7.99301301521662 & 0.0691358795899048 & 0.00698698478337603 & 0.440870367703134 \tabularnewline
45 & 7.7 & 7.67726132357204 & -0.283812957491661 & 0.0227386764279626 & -1.02788278615441 \tabularnewline
46 & 7.2 & 7.3141959239161 & -0.356489541200404 & -0.114195923916094 & -0.211653986485931 \tabularnewline
47 & 7.5 & 7.38278412037487 & 0.0333207469073576 & 0.117215879625126 & 1.13523790722274 \tabularnewline
48 & 7.3 & 7.33239981069436 & -0.0434311786450603 & -0.032399810694358 & -0.223525681529458 \tabularnewline
49 & 7 & 7.00145157623927 & -0.307046239928848 & -0.00145157623927222 & -0.768172856093289 \tabularnewline
50 & 7 & 6.98466972743133 & -0.0409007030036084 & 0.0153302725686740 & 0.77512340161062 \tabularnewline
51 & 7 & 7.02053972426448 & 0.0291743944877572 & -0.0205397242644795 & 0.204371834297510 \tabularnewline
52 & 7.2 & 7.20162942663088 & 0.168063168540456 & -0.00162942663088353 & 0.404538839841147 \tabularnewline
53 & 7.3 & 7.27829417803854 & 0.0845877803907532 & 0.0217058219614643 & -0.243056860738686 \tabularnewline
54 & 7.1 & 7.10447766873797 & -0.151449040374118 & -0.00447766873797478 & -0.687434972770834 \tabularnewline
55 & 6.8 & 6.84491095858611 & -0.250218854362103 & -0.044910958586107 & -0.287643356539499 \tabularnewline
56 & 6.4 & 6.37048585356149 & -0.455039514945662 & 0.0295141464385114 & -0.596493447011743 \tabularnewline
57 & 6.1 & 6.04662841713655 & -0.335201367206379 & 0.0533715828634461 & 0.349001215668825 \tabularnewline
58 & 6.5 & 6.60630158823162 & 0.482295506431774 & -0.106301588231619 & 2.38077547677439 \tabularnewline
59 & 7.7 & 7.56100590096338 & 0.913854115088924 & 0.138994099036624 & 1.25681899661878 \tabularnewline
60 & 7.9 & 7.93198033091878 & 0.417984603653717 & -0.0319803309187814 & -1.44415926819459 \tabularnewline
61 & 7.5 & 7.56674274440778 & -0.297445557429344 & -0.06674274440778 & -2.08462594732407 \tabularnewline
62 & 6.9 & 6.90371487086696 & -0.631307123974338 & -0.00371487086695706 & -0.972161148286413 \tabularnewline
63 & 6.6 & 6.61464816362608 & -0.319647774563612 & -0.0146481636260801 & 0.908425293627625 \tabularnewline
64 & 6.9 & 6.86899601328774 & 0.203719304920818 & 0.0310039867122609 & 1.52458534731289 \tabularnewline
65 & 7.7 & 7.63511448773715 & 0.716126230078677 & 0.0648855122628517 & 1.49193598767762 \tabularnewline
66 & 8 & 8.0266609508785 & 0.420394582704619 & -0.0266609508785065 & -0.861286443508214 \tabularnewline
67 & 8 & 8.03730886785195 & 0.0470167974500614 & -0.0373088678519463 & -1.08737666402777 \tabularnewline
68 & 7.7 & 7.66381937553885 & -0.336168985306571 & 0.0361806244611525 & -1.11593967357225 \tabularnewline
69 & 7.3 & 7.30718183205484 & -0.354820772858166 & -0.00718183205484464 & -0.0543190866513019 \tabularnewline
70 & 7.4 & 7.53910678983084 & 0.17984804454146 & -0.139106789830835 & 1.55710462546365 \tabularnewline
71 & 8.1 & 7.93571205300436 & 0.377362761122093 & 0.164287946995636 & 0.575216160067762 \tabularnewline
72 & 8.3 & 8.28099711948655 & 0.348136768855624 & 0.0190028805134527 & -0.0851193254992055 \tabularnewline
73 & 8.2 & 8.24143453405873 & -0.00513654574708017 & -0.0414345340587352 & -1.02927863813055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62224&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]8.4[/C][C]8.4[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]8.4[/C][C]8.4[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]8.4[/C][C]8.4[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]8.6[/C][C]8.59450288184909[/C][C]0.186336498471207[/C][C]0.00549711815091083[/C][C]0.542139808952547[/C][/ROW]
[ROW][C]5[/C][C]8.9[/C][C]8.89818757487719[/C][C]0.298820878666345[/C][C]0.00181242512281285[/C][C]0.327604743032395[/C][/ROW]
[ROW][C]6[/C][C]8.8[/C][C]8.81218879419231[/C][C]-0.0701036903600278[/C][C]-0.0121887941923082[/C][C]-1.0744078602474[/C][/ROW]
[ROW][C]7[/C][C]8.3[/C][C]8.30982820712854[/C][C]-0.484497368791315[/C][C]-0.00982820712853705[/C][C]-1.20682693844648[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]7.50619437027392[/C][C]-0.790443779007934[/C][C]-0.00619437027391512[/C][C]-0.890998953192124[/C][/ROW]
[ROW][C]9[/C][C]7.2[/C][C]7.1841981799698[/C][C]-0.341356654372683[/C][C]0.0158018200302004[/C][C]1.30786355065082[/C][/ROW]
[ROW][C]10[/C][C]7.4[/C][C]7.38783991849545[/C][C]0.181117624453733[/C][C]0.0121600815045500[/C][C]1.52158685435875[/C][/ROW]
[ROW][C]11[/C][C]8.8[/C][C]8.76940313327973[/C][C]1.33195018155721[/C][C]0.0305968667202731[/C][C]3.35153664288356[/C][/ROW]
[ROW][C]12[/C][C]9.3[/C][C]9.33141796858167[/C][C]0.593835381079452[/C][C]-0.0314179685816659[/C][C]-2.14959055962222[/C][/ROW]
[ROW][C]13[/C][C]9.3[/C][C]9.31206024620503[/C][C]0.00614229913265951[/C][C]-0.0120602462050237[/C][C]-1.71219001997661[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.71417121390012[/C][C]-0.573184008276645[/C][C]-0.0141712139001166[/C][C]-1.69423863951449[/C][/ROW]
[ROW][C]15[/C][C]8.2[/C][C]8.19291377757677[/C][C]-0.524590012218204[/C][C]0.00708622242323257[/C][C]0.142937770280577[/C][/ROW]
[ROW][C]16[/C][C]8.3[/C][C]8.27870651858461[/C][C]0.0460847758066103[/C][C]0.0212934814153921[/C][C]1.66000271945657[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.49082657038934[/C][C]0.201233413953079[/C][C]0.00917342961065437[/C][C]0.451892590507891[/C][/ROW]
[ROW][C]18[/C][C]8.6[/C][C]8.61026011305591[/C][C]0.124775165732414[/C][C]-0.0102601130559145[/C][C]-0.222666517111757[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]8.49906162872325[/C][C]-0.0957893751730662[/C][C]0.0009383712767499[/C][C]-0.642344401582395[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]8.22059950369853[/C][C]-0.266530263226196[/C][C]-0.0205995036985341[/C][C]-0.497243774358148[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]8.0671242661379[/C][C]-0.160859902044925[/C][C]0.0328757338620984[/C][C]0.307740764488693[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.9519178929486[/C][C]-0.118188339236399[/C][C]-0.0519178929486033[/C][C]0.124271169664202[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.51974095973871[/C][C]0.523020367497446[/C][C]0.080259040261289[/C][C]1.86737445325227[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]8.7424253381197[/C][C]0.242306274407083[/C][C]-0.0424253381196999[/C][C]-0.8175171896451[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.69797842724487[/C][C]-0.0256417206056453[/C][C]0.00202157275512926[/C][C]-0.780709100960954[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.50132251246483[/C][C]-0.185569562503805[/C][C]-0.00132251246482670[/C][C]-0.466614956822868[/C][/ROW]
[ROW][C]27[/C][C]8.4[/C][C]8.41811469353935[/C][C]-0.0911547063213842[/C][C]-0.0181146935393472[/C][C]0.276352870301122[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.4836511593258[/C][C]0.0535992036847195[/C][C]0.0163488406741942[/C][C]0.421298118657457[/C][/ROW]
[ROW][C]29[/C][C]8.7[/C][C]8.68738617815933[/C][C]0.192128800651334[/C][C]0.0126138218406734[/C][C]0.403448763895573[/C][/ROW]
[ROW][C]30[/C][C]8.7[/C][C]8.71184394878778[/C][C]0.0373675017945224[/C][C]-0.0118439487877778[/C][C]-0.450712780267858[/C][/ROW]
[ROW][C]31[/C][C]8.6[/C][C]8.59304152670997[/C][C]-0.106783563881493[/C][C]0.00695847329002688[/C][C]-0.419806817830184[/C][/ROW]
[ROW][C]32[/C][C]8.5[/C][C]8.52145780871233[/C][C]-0.0742934064926835[/C][C]-0.0214578087123312[/C][C]0.0946201826656657[/C][/ROW]
[ROW][C]33[/C][C]8.3[/C][C]8.25530817586004[/C][C]-0.251378877726735[/C][C]0.0446918241399638[/C][C]-0.515720954263528[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]8.09985758883582[/C][C]-0.162835388833424[/C][C]-0.0998575888358217[/C][C]0.257862671210054[/C][/ROW]
[ROW][C]35[/C][C]8.2[/C][C]8.10177341255155[/C][C]-0.0107652022417415[/C][C]0.0982265874484516[/C][C]0.442870737944124[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]8.12955809375315[/C][C]0.0248150432402895[/C][C]-0.0295580937531451[/C][C]0.103619748756330[/C][/ROW]
[ROW][C]37[/C][C]8.1[/C][C]8.08810141986608[/C][C]-0.0363394533713269[/C][C]0.0118985801339163[/C][C]-0.178202264373939[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]8.00409711361563[/C][C]-0.0803437981701123[/C][C]-0.00409711361562836[/C][C]-0.128225093271845[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.9241028133476[/C][C]-0.080023604231224[/C][C]-0.0241028133476076[/C][C]0.000934916941762015[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.89861201034747[/C][C]-0.0299689247701155[/C][C]0.00138798965252551[/C][C]0.145753330538329[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]7.97379475851115[/C][C]0.0664268345841462[/C][C]0.0262052414888480[/C][C]0.280701723197123[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]8.00277087301101[/C][C]0.0320854763466518[/C][C]-0.00277087301101287[/C][C]-0.100014939197683[/C][/ROW]
[ROW][C]43[/C][C]7.9[/C][C]7.91018055910298[/C][C]-0.0822476986425896[/C][C]-0.0101805591029809[/C][C]-0.332968048500968[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]7.99301301521662[/C][C]0.0691358795899048[/C][C]0.00698698478337603[/C][C]0.440870367703134[/C][/ROW]
[ROW][C]45[/C][C]7.7[/C][C]7.67726132357204[/C][C]-0.283812957491661[/C][C]0.0227386764279626[/C][C]-1.02788278615441[/C][/ROW]
[ROW][C]46[/C][C]7.2[/C][C]7.3141959239161[/C][C]-0.356489541200404[/C][C]-0.114195923916094[/C][C]-0.211653986485931[/C][/ROW]
[ROW][C]47[/C][C]7.5[/C][C]7.38278412037487[/C][C]0.0333207469073576[/C][C]0.117215879625126[/C][C]1.13523790722274[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]7.33239981069436[/C][C]-0.0434311786450603[/C][C]-0.032399810694358[/C][C]-0.223525681529458[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]7.00145157623927[/C][C]-0.307046239928848[/C][C]-0.00145157623927222[/C][C]-0.768172856093289[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]6.98466972743133[/C][C]-0.0409007030036084[/C][C]0.0153302725686740[/C][C]0.77512340161062[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]7.02053972426448[/C][C]0.0291743944877572[/C][C]-0.0205397242644795[/C][C]0.204371834297510[/C][/ROW]
[ROW][C]52[/C][C]7.2[/C][C]7.20162942663088[/C][C]0.168063168540456[/C][C]-0.00162942663088353[/C][C]0.404538839841147[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]7.27829417803854[/C][C]0.0845877803907532[/C][C]0.0217058219614643[/C][C]-0.243056860738686[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]7.10447766873797[/C][C]-0.151449040374118[/C][C]-0.00447766873797478[/C][C]-0.687434972770834[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]6.84491095858611[/C][C]-0.250218854362103[/C][C]-0.044910958586107[/C][C]-0.287643356539499[/C][/ROW]
[ROW][C]56[/C][C]6.4[/C][C]6.37048585356149[/C][C]-0.455039514945662[/C][C]0.0295141464385114[/C][C]-0.596493447011743[/C][/ROW]
[ROW][C]57[/C][C]6.1[/C][C]6.04662841713655[/C][C]-0.335201367206379[/C][C]0.0533715828634461[/C][C]0.349001215668825[/C][/ROW]
[ROW][C]58[/C][C]6.5[/C][C]6.60630158823162[/C][C]0.482295506431774[/C][C]-0.106301588231619[/C][C]2.38077547677439[/C][/ROW]
[ROW][C]59[/C][C]7.7[/C][C]7.56100590096338[/C][C]0.913854115088924[/C][C]0.138994099036624[/C][C]1.25681899661878[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]7.93198033091878[/C][C]0.417984603653717[/C][C]-0.0319803309187814[/C][C]-1.44415926819459[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]7.56674274440778[/C][C]-0.297445557429344[/C][C]-0.06674274440778[/C][C]-2.08462594732407[/C][/ROW]
[ROW][C]62[/C][C]6.9[/C][C]6.90371487086696[/C][C]-0.631307123974338[/C][C]-0.00371487086695706[/C][C]-0.972161148286413[/C][/ROW]
[ROW][C]63[/C][C]6.6[/C][C]6.61464816362608[/C][C]-0.319647774563612[/C][C]-0.0146481636260801[/C][C]0.908425293627625[/C][/ROW]
[ROW][C]64[/C][C]6.9[/C][C]6.86899601328774[/C][C]0.203719304920818[/C][C]0.0310039867122609[/C][C]1.52458534731289[/C][/ROW]
[ROW][C]65[/C][C]7.7[/C][C]7.63511448773715[/C][C]0.716126230078677[/C][C]0.0648855122628517[/C][C]1.49193598767762[/C][/ROW]
[ROW][C]66[/C][C]8[/C][C]8.0266609508785[/C][C]0.420394582704619[/C][C]-0.0266609508785065[/C][C]-0.861286443508214[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]8.03730886785195[/C][C]0.0470167974500614[/C][C]-0.0373088678519463[/C][C]-1.08737666402777[/C][/ROW]
[ROW][C]68[/C][C]7.7[/C][C]7.66381937553885[/C][C]-0.336168985306571[/C][C]0.0361806244611525[/C][C]-1.11593967357225[/C][/ROW]
[ROW][C]69[/C][C]7.3[/C][C]7.30718183205484[/C][C]-0.354820772858166[/C][C]-0.00718183205484464[/C][C]-0.0543190866513019[/C][/ROW]
[ROW][C]70[/C][C]7.4[/C][C]7.53910678983084[/C][C]0.17984804454146[/C][C]-0.139106789830835[/C][C]1.55710462546365[/C][/ROW]
[ROW][C]71[/C][C]8.1[/C][C]7.93571205300436[/C][C]0.377362761122093[/C][C]0.164287946995636[/C][C]0.575216160067762[/C][/ROW]
[ROW][C]72[/C][C]8.3[/C][C]8.28099711948655[/C][C]0.348136768855624[/C][C]0.0190028805134527[/C][C]-0.0851193254992055[/C][/ROW]
[ROW][C]73[/C][C]8.2[/C][C]8.24143453405873[/C][C]-0.00513654574708017[/C][C]-0.0414345340587352[/C][C]-1.02927863813055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62224&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	8.4	8.4	0	0	0
2	8.4	8.4	0	0	0
3	8.4	8.4	0	0	0
4	8.6	8.59450288184909	0.186336498471207	0.00549711815091083	0.542139808952547
5	8.9	8.89818757487719	0.298820878666345	0.00181242512281285	0.327604743032395
6	8.8	8.81218879419231	-0.0701036903600278	-0.0121887941923082	-1.0744078602474
7	8.3	8.30982820712854	-0.484497368791315	-0.00982820712853705	-1.20682693844648
8	7.5	7.50619437027392	-0.790443779007934	-0.00619437027391512	-0.890998953192124
9	7.2	7.1841981799698	-0.341356654372683	0.0158018200302004	1.30786355065082
10	7.4	7.38783991849545	0.181117624453733	0.0121600815045500	1.52158685435875
11	8.8	8.76940313327973	1.33195018155721	0.0305968667202731	3.35153664288356
12	9.3	9.33141796858167	0.593835381079452	-0.0314179685816659	-2.14959055962222
13	9.3	9.31206024620503	0.00614229913265951	-0.0120602462050237	-1.71219001997661
14	8.7	8.71417121390012	-0.573184008276645	-0.0141712139001166	-1.69423863951449
15	8.2	8.19291377757677	-0.524590012218204	0.00708622242323257	0.142937770280577
16	8.3	8.27870651858461	0.0460847758066103	0.0212934814153921	1.66000271945657
17	8.5	8.49082657038934	0.201233413953079	0.00917342961065437	0.451892590507891
18	8.6	8.61026011305591	0.124775165732414	-0.0102601130559145	-0.222666517111757
19	8.5	8.49906162872325	-0.0957893751730662	0.0009383712767499	-0.642344401582395
20	8.2	8.22059950369853	-0.266530263226196	-0.0205995036985341	-0.497243774358148
21	8.1	8.0671242661379	-0.160859902044925	0.0328757338620984	0.307740764488693
22	7.9	7.9519178929486	-0.118188339236399	-0.0519178929486033	0.124271169664202
23	8.6	8.51974095973871	0.523020367497446	0.080259040261289	1.86737445325227
24	8.7	8.7424253381197	0.242306274407083	-0.0424253381196999	-0.8175171896451
25	8.7	8.69797842724487	-0.0256417206056453	0.00202157275512926	-0.780709100960954
26	8.5	8.50132251246483	-0.185569562503805	-0.00132251246482670	-0.466614956822868
27	8.4	8.41811469353935	-0.0911547063213842	-0.0181146935393472	0.276352870301122
28	8.5	8.4836511593258	0.0535992036847195	0.0163488406741942	0.421298118657457
29	8.7	8.68738617815933	0.192128800651334	0.0126138218406734	0.403448763895573
30	8.7	8.71184394878778	0.0373675017945224	-0.0118439487877778	-0.450712780267858
31	8.6	8.59304152670997	-0.106783563881493	0.00695847329002688	-0.419806817830184
32	8.5	8.52145780871233	-0.0742934064926835	-0.0214578087123312	0.0946201826656657
33	8.3	8.25530817586004	-0.251378877726735	0.0446918241399638	-0.515720954263528
34	8	8.09985758883582	-0.162835388833424	-0.0998575888358217	0.257862671210054
35	8.2	8.10177341255155	-0.0107652022417415	0.0982265874484516	0.442870737944124
36	8.1	8.12955809375315	0.0248150432402895	-0.0295580937531451	0.103619748756330
37	8.1	8.08810141986608	-0.0363394533713269	0.0118985801339163	-0.178202264373939
38	8	8.00409711361563	-0.0803437981701123	-0.00409711361562836	-0.128225093271845
39	7.9	7.9241028133476	-0.080023604231224	-0.0241028133476076	0.000934916941762015
40	7.9	7.89861201034747	-0.0299689247701155	0.00138798965252551	0.145753330538329
41	8	7.97379475851115	0.0664268345841462	0.0262052414888480	0.280701723197123
42	8	8.00277087301101	0.0320854763466518	-0.00277087301101287	-0.100014939197683
43	7.9	7.91018055910298	-0.0822476986425896	-0.0101805591029809	-0.332968048500968
44	8	7.99301301521662	0.0691358795899048	0.00698698478337603	0.440870367703134
45	7.7	7.67726132357204	-0.283812957491661	0.0227386764279626	-1.02788278615441
46	7.2	7.3141959239161	-0.356489541200404	-0.114195923916094	-0.211653986485931
47	7.5	7.38278412037487	0.0333207469073576	0.117215879625126	1.13523790722274
48	7.3	7.33239981069436	-0.0434311786450603	-0.032399810694358	-0.223525681529458
49	7	7.00145157623927	-0.307046239928848	-0.00145157623927222	-0.768172856093289
50	7	6.98466972743133	-0.0409007030036084	0.0153302725686740	0.77512340161062
51	7	7.02053972426448	0.0291743944877572	-0.0205397242644795	0.204371834297510
52	7.2	7.20162942663088	0.168063168540456	-0.00162942663088353	0.404538839841147
53	7.3	7.27829417803854	0.0845877803907532	0.0217058219614643	-0.243056860738686
54	7.1	7.10447766873797	-0.151449040374118	-0.00447766873797478	-0.687434972770834
55	6.8	6.84491095858611	-0.250218854362103	-0.044910958586107	-0.287643356539499
56	6.4	6.37048585356149	-0.455039514945662	0.0295141464385114	-0.596493447011743
57	6.1	6.04662841713655	-0.335201367206379	0.0533715828634461	0.349001215668825
58	6.5	6.60630158823162	0.482295506431774	-0.106301588231619	2.38077547677439
59	7.7	7.56100590096338	0.913854115088924	0.138994099036624	1.25681899661878
60	7.9	7.93198033091878	0.417984603653717	-0.0319803309187814	-1.44415926819459
61	7.5	7.56674274440778	-0.297445557429344	-0.06674274440778	-2.08462594732407
62	6.9	6.90371487086696	-0.631307123974338	-0.00371487086695706	-0.972161148286413
63	6.6	6.61464816362608	-0.319647774563612	-0.0146481636260801	0.908425293627625
64	6.9	6.86899601328774	0.203719304920818	0.0310039867122609	1.52458534731289
65	7.7	7.63511448773715	0.716126230078677	0.0648855122628517	1.49193598767762
66	8	8.0266609508785	0.420394582704619	-0.0266609508785065	-0.861286443508214
67	8	8.03730886785195	0.0470167974500614	-0.0373088678519463	-1.08737666402777
68	7.7	7.66381937553885	-0.336168985306571	0.0361806244611525	-1.11593967357225
69	7.3	7.30718183205484	-0.354820772858166	-0.00718183205484464	-0.0543190866513019
70	7.4	7.53910678983084	0.17984804454146	-0.139106789830835	1.55710462546365
71	8.1	7.93571205300436	0.377362761122093	0.164287946995636	0.575216160067762
72	8.3	8.28099711948655	0.348136768855624	0.0190028805134527	-0.0851193254992055
73	8.2	8.24143453405873	-0.00513654574708017	-0.0414345340587352	-1.02927863813055

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