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*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

Fri, 04 Dec 2009 10:22:48 -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/04/t1259947466269v1fcs9fqls3e.htm/, Retrieved Sun, 28 Apr 2024 18:27:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63936, Retrieved Sun, 28 Apr 2024 18:27:16 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

128

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]
-   PD    [Structural Time Series Models] [ws 8 Ad hoc forec...] [2009-12-02 20:13:08] [616e2df490b611f6cb7080068870ecbd]
-   PD        [Structural Time Series Models] [ws9: decomposition 3] [2009-12-04 17:22:48] [a315839f8c359622c3a1e6ed387dd5cd] [Current]

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Dataseries X:

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Histogram

Boxplots

6,3
6,2
6,1
6,3
6,5
6,6
6,5
6,2
6,2
5,9
6,1
6,1
6,1
6,1
6,1
6,4
6,7
6,9
7
7
6,8
6,4
5,9
5,5
5,5
5,6
5,8
5,9
6,1
6,1
6
6
5,9
5,5
5,6
5,4
5,2
5,2
5,2
5,5
5,8
5,8
5,5
5,3
5,1
5,2
5,8
5,8
5,5
5
4,9
5,3
6,1
6,5
6,8
6,6
6,4
6,4
6,6

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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63936&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63936&T=0

As an alternative you can also use a QR Code:

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

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

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	6.3	6.3	0	0	0
2	6.2	6.20033875634969	-0.0996892400546821	-0.000338756349693864	-0.413526898000771
3	6.1	6.09976744827461	-0.100562515222695	0.000232551725384802	-0.00363474764207676
4	6.3	6.2974530563921	0.193771042443022	0.00254694360790351	1.21883612320128
5	6.5	6.50062828204771	0.203054049444421	-0.000628282047714086	0.0384449021976258
6	6.6	6.60097171365893	0.101665299403964	-0.000971713658931074	-0.419893279294913
7	6.5	6.50158266492297	-0.0968007826560898	-0.00158266492297389	-0.821931126823448
8	6.2	6.20138698065123	-0.2975773150637	-0.00138698065122801	-0.831499669577698
9	6.2	6.19705230530992	-0.0081096582559993	0.00294769469008469	1.19880674346806
10	5.9	5.90319097012336	-0.290182783260372	-0.00319097012336136	-1.16818289178009
11	6.1	6.09522394922025	0.185825295955012	0.00477605077974664	1.9713487220021
12	6.1	6.10267012692514	0.00974249630433024	-0.00267012692514542	-0.729232584938666
13	6.1	6.09961056619894	-0.00289373740588862	0.000389433801055103	-0.0523382102394348
14	6.1	6.09785093585783	-0.00177405910085651	0.00214906414216770	0.00464350935965628
15	6.1	6.10327734927333	0.00527074334871684	-0.00327734927332607	0.0292998277865995
16	6.4	6.39355779297442	0.283524727495623	0.00644220702558011	1.15208749848241
17	6.7	6.70141704898546	0.307286599264358	-0.00141704898545800	0.098409103018933
18	6.9	6.90239308024715	0.203474052341428	-0.00239308024714992	-0.429931209766651
19	7	6.99751842689687	0.0976719463955992	0.00248157310312842	-0.438170815007838
20	7	7.00932280684428	0.0138226543213788	-0.00932280684427659	-0.347255019452226
21	6.8	6.79247267854197	-0.211428359410104	0.00752732145802524	-0.932858742203005
22	6.4	6.41270405860088	-0.375811908003098	-0.0127040586008774	-0.680781089097793
23	5.9	5.89467502498198	-0.514686465598539	0.00532497501802364	-0.575137684607805
24	5.5	5.50016070165732	-0.397338999364159	-0.000160701657324725	0.485985066471323
25	5.5	5.49399960026595	-0.0153873066090311	0.00600039973404482	1.58202586966257
26	5.6	5.59298140995175	0.0963144004655587	0.00701859004825286	0.463081881057796
27	5.8	5.80749816570284	0.210931531069805	-0.00749816570284082	0.476226005450853
28	5.9	5.89843543212545	0.0947024869909643	0.00156456787455183	-0.481200501660963
29	6.1	6.09747947505157	0.195774205083794	0.00252052494842619	0.41859107594146
30	6.1	6.10474415012635	0.0131619052041264	-0.00474415012635025	-0.756273520089822
31	6	6.00004468809009	-0.101011726964120	-4.46880900908772e-05	-0.472840848662802
32	6	6.00321778512485	-8.70050724529753e-05	-0.00321778512485429	0.417971520913078
33	5.9	5.89378461292126	-0.106011607387369	0.00621538707874165	-0.438678120515491
34	5.5	5.51396360252218	-0.37125323279174	-0.0139636025221789	-1.09847660896160
35	5.6	5.58173306876045	0.0540330601232895	0.0182669312395535	1.76128872590351
36	5.4	5.41421378592133	-0.160585822070662	-0.0142137859213330	-0.888827211245181
37	5.2	5.19562301857758	-0.216770702132943	0.0043769814224184	-0.232720492953543
38	5.2	5.19360557190027	-0.0086987165242462	0.00639442809972834	0.862275194198476
39	5.2	5.20190747552098	0.0076847069001057	-0.0019074755209796	0.068010706536208
40	5.5	5.49850417747576	0.286015370002777	0.00149582252424102	1.15232777236473
41	5.8	5.79469937014512	0.295821345738657	0.00530062985488497	0.0406118825422641
42	5.8	5.80582243223237	0.0215580799705882	-0.00582243223236669	-1.13583787026343
43	5.5	5.51191357179922	-0.282345598274516	-0.0119135717992181	-1.25859262625289
44	5.3	5.30200515969737	-0.212563904753882	-0.00200515969737416	0.288995201556250
45	5.1	5.07691512668202	-0.224630833187949	0.0230848733179795	-0.0499742023660053
46	5.2	5.22309337936363	0.132584926646026	-0.023093379363633	1.47938000429862
47	5.8	5.76785510696308	0.52965338684852	0.0321448930369196	1.64442727565032
48	5.8	5.82250193702928	0.072064157359714	-0.0225019370292789	-1.89507026558255
49	5.5	5.51027369316912	-0.298106915018495	-0.010273693169116	-1.53330788173242
50	5	4.99125394428652	-0.510949537531044	0.00874605571347878	-0.881785297819474
51	4.9	4.89885467575368	-0.109261599430379	0.00114532424631634	1.66634087652492
52	5.3	5.29238487599785	0.373323917032699	0.00761512400215245	1.99808449014423
53	6.1	6.08227568793519	0.773063685238924	0.0177243120648116	1.65552840689468
54	6.5	6.50481287239076	0.436667506505551	-0.00481287239075659	-1.39315722914169
55	6.8	6.81867230351617	0.318809639292635	-0.0186723035161743	-0.488098869759394
56	6.6	6.60604110816872	-0.191206426526746	-0.00604110816871922	-2.11219003005265
57	6.4	6.37966157589264	-0.224961508823594	0.0203384241073565	-0.139793928781406
58	6.4	6.43870483881188	0.047593964335382	-0.0387048388118812	1.12876631249156
59	6.6	6.55781274595347	0.116225189273000	0.0421872540465295	0.284230857820430

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 6.3 & 6.3 & 0 & 0 & 0 \tabularnewline
2 & 6.2 & 6.20033875634969 & -0.0996892400546821 & -0.000338756349693864 & -0.413526898000771 \tabularnewline
3 & 6.1 & 6.09976744827461 & -0.100562515222695 & 0.000232551725384802 & -0.00363474764207676 \tabularnewline
4 & 6.3 & 6.2974530563921 & 0.193771042443022 & 0.00254694360790351 & 1.21883612320128 \tabularnewline
5 & 6.5 & 6.50062828204771 & 0.203054049444421 & -0.000628282047714086 & 0.0384449021976258 \tabularnewline
6 & 6.6 & 6.60097171365893 & 0.101665299403964 & -0.000971713658931074 & -0.419893279294913 \tabularnewline
7 & 6.5 & 6.50158266492297 & -0.0968007826560898 & -0.00158266492297389 & -0.821931126823448 \tabularnewline
8 & 6.2 & 6.20138698065123 & -0.2975773150637 & -0.00138698065122801 & -0.831499669577698 \tabularnewline
9 & 6.2 & 6.19705230530992 & -0.0081096582559993 & 0.00294769469008469 & 1.19880674346806 \tabularnewline
10 & 5.9 & 5.90319097012336 & -0.290182783260372 & -0.00319097012336136 & -1.16818289178009 \tabularnewline
11 & 6.1 & 6.09522394922025 & 0.185825295955012 & 0.00477605077974664 & 1.9713487220021 \tabularnewline
12 & 6.1 & 6.10267012692514 & 0.00974249630433024 & -0.00267012692514542 & -0.729232584938666 \tabularnewline
13 & 6.1 & 6.09961056619894 & -0.00289373740588862 & 0.000389433801055103 & -0.0523382102394348 \tabularnewline
14 & 6.1 & 6.09785093585783 & -0.00177405910085651 & 0.00214906414216770 & 0.00464350935965628 \tabularnewline
15 & 6.1 & 6.10327734927333 & 0.00527074334871684 & -0.00327734927332607 & 0.0292998277865995 \tabularnewline
16 & 6.4 & 6.39355779297442 & 0.283524727495623 & 0.00644220702558011 & 1.15208749848241 \tabularnewline
17 & 6.7 & 6.70141704898546 & 0.307286599264358 & -0.00141704898545800 & 0.098409103018933 \tabularnewline
18 & 6.9 & 6.90239308024715 & 0.203474052341428 & -0.00239308024714992 & -0.429931209766651 \tabularnewline
19 & 7 & 6.99751842689687 & 0.0976719463955992 & 0.00248157310312842 & -0.438170815007838 \tabularnewline
20 & 7 & 7.00932280684428 & 0.0138226543213788 & -0.00932280684427659 & -0.347255019452226 \tabularnewline
21 & 6.8 & 6.79247267854197 & -0.211428359410104 & 0.00752732145802524 & -0.932858742203005 \tabularnewline
22 & 6.4 & 6.41270405860088 & -0.375811908003098 & -0.0127040586008774 & -0.680781089097793 \tabularnewline
23 & 5.9 & 5.89467502498198 & -0.514686465598539 & 0.00532497501802364 & -0.575137684607805 \tabularnewline
24 & 5.5 & 5.50016070165732 & -0.397338999364159 & -0.000160701657324725 & 0.485985066471323 \tabularnewline
25 & 5.5 & 5.49399960026595 & -0.0153873066090311 & 0.00600039973404482 & 1.58202586966257 \tabularnewline
26 & 5.6 & 5.59298140995175 & 0.0963144004655587 & 0.00701859004825286 & 0.463081881057796 \tabularnewline
27 & 5.8 & 5.80749816570284 & 0.210931531069805 & -0.00749816570284082 & 0.476226005450853 \tabularnewline
28 & 5.9 & 5.89843543212545 & 0.0947024869909643 & 0.00156456787455183 & -0.481200501660963 \tabularnewline
29 & 6.1 & 6.09747947505157 & 0.195774205083794 & 0.00252052494842619 & 0.41859107594146 \tabularnewline
30 & 6.1 & 6.10474415012635 & 0.0131619052041264 & -0.00474415012635025 & -0.756273520089822 \tabularnewline
31 & 6 & 6.00004468809009 & -0.101011726964120 & -4.46880900908772e-05 & -0.472840848662802 \tabularnewline
32 & 6 & 6.00321778512485 & -8.70050724529753e-05 & -0.00321778512485429 & 0.417971520913078 \tabularnewline
33 & 5.9 & 5.89378461292126 & -0.106011607387369 & 0.00621538707874165 & -0.438678120515491 \tabularnewline
34 & 5.5 & 5.51396360252218 & -0.37125323279174 & -0.0139636025221789 & -1.09847660896160 \tabularnewline
35 & 5.6 & 5.58173306876045 & 0.0540330601232895 & 0.0182669312395535 & 1.76128872590351 \tabularnewline
36 & 5.4 & 5.41421378592133 & -0.160585822070662 & -0.0142137859213330 & -0.888827211245181 \tabularnewline
37 & 5.2 & 5.19562301857758 & -0.216770702132943 & 0.0043769814224184 & -0.232720492953543 \tabularnewline
38 & 5.2 & 5.19360557190027 & -0.0086987165242462 & 0.00639442809972834 & 0.862275194198476 \tabularnewline
39 & 5.2 & 5.20190747552098 & 0.0076847069001057 & -0.0019074755209796 & 0.068010706536208 \tabularnewline
40 & 5.5 & 5.49850417747576 & 0.286015370002777 & 0.00149582252424102 & 1.15232777236473 \tabularnewline
41 & 5.8 & 5.79469937014512 & 0.295821345738657 & 0.00530062985488497 & 0.0406118825422641 \tabularnewline
42 & 5.8 & 5.80582243223237 & 0.0215580799705882 & -0.00582243223236669 & -1.13583787026343 \tabularnewline
43 & 5.5 & 5.51191357179922 & -0.282345598274516 & -0.0119135717992181 & -1.25859262625289 \tabularnewline
44 & 5.3 & 5.30200515969737 & -0.212563904753882 & -0.00200515969737416 & 0.288995201556250 \tabularnewline
45 & 5.1 & 5.07691512668202 & -0.224630833187949 & 0.0230848733179795 & -0.0499742023660053 \tabularnewline
46 & 5.2 & 5.22309337936363 & 0.132584926646026 & -0.023093379363633 & 1.47938000429862 \tabularnewline
47 & 5.8 & 5.76785510696308 & 0.52965338684852 & 0.0321448930369196 & 1.64442727565032 \tabularnewline
48 & 5.8 & 5.82250193702928 & 0.072064157359714 & -0.0225019370292789 & -1.89507026558255 \tabularnewline
49 & 5.5 & 5.51027369316912 & -0.298106915018495 & -0.010273693169116 & -1.53330788173242 \tabularnewline
50 & 5 & 4.99125394428652 & -0.510949537531044 & 0.00874605571347878 & -0.881785297819474 \tabularnewline
51 & 4.9 & 4.89885467575368 & -0.109261599430379 & 0.00114532424631634 & 1.66634087652492 \tabularnewline
52 & 5.3 & 5.29238487599785 & 0.373323917032699 & 0.00761512400215245 & 1.99808449014423 \tabularnewline
53 & 6.1 & 6.08227568793519 & 0.773063685238924 & 0.0177243120648116 & 1.65552840689468 \tabularnewline
54 & 6.5 & 6.50481287239076 & 0.436667506505551 & -0.00481287239075659 & -1.39315722914169 \tabularnewline
55 & 6.8 & 6.81867230351617 & 0.318809639292635 & -0.0186723035161743 & -0.488098869759394 \tabularnewline
56 & 6.6 & 6.60604110816872 & -0.191206426526746 & -0.00604110816871922 & -2.11219003005265 \tabularnewline
57 & 6.4 & 6.37966157589264 & -0.224961508823594 & 0.0203384241073565 & -0.139793928781406 \tabularnewline
58 & 6.4 & 6.43870483881188 & 0.047593964335382 & -0.0387048388118812 & 1.12876631249156 \tabularnewline
59 & 6.6 & 6.55781274595347 & 0.116225189273000 & 0.0421872540465295 & 0.284230857820430 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63936&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]6.3[/C][C]6.3[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]6.2[/C][C]6.20033875634969[/C][C]-0.0996892400546821[/C][C]-0.000338756349693864[/C][C]-0.413526898000771[/C][/ROW]
[ROW][C]3[/C][C]6.1[/C][C]6.09976744827461[/C][C]-0.100562515222695[/C][C]0.000232551725384802[/C][C]-0.00363474764207676[/C][/ROW]
[ROW][C]4[/C][C]6.3[/C][C]6.2974530563921[/C][C]0.193771042443022[/C][C]0.00254694360790351[/C][C]1.21883612320128[/C][/ROW]
[ROW][C]5[/C][C]6.5[/C][C]6.50062828204771[/C][C]0.203054049444421[/C][C]-0.000628282047714086[/C][C]0.0384449021976258[/C][/ROW]
[ROW][C]6[/C][C]6.6[/C][C]6.60097171365893[/C][C]0.101665299403964[/C][C]-0.000971713658931074[/C][C]-0.419893279294913[/C][/ROW]
[ROW][C]7[/C][C]6.5[/C][C]6.50158266492297[/C][C]-0.0968007826560898[/C][C]-0.00158266492297389[/C][C]-0.821931126823448[/C][/ROW]
[ROW][C]8[/C][C]6.2[/C][C]6.20138698065123[/C][C]-0.2975773150637[/C][C]-0.00138698065122801[/C][C]-0.831499669577698[/C][/ROW]
[ROW][C]9[/C][C]6.2[/C][C]6.19705230530992[/C][C]-0.0081096582559993[/C][C]0.00294769469008469[/C][C]1.19880674346806[/C][/ROW]
[ROW][C]10[/C][C]5.9[/C][C]5.90319097012336[/C][C]-0.290182783260372[/C][C]-0.00319097012336136[/C][C]-1.16818289178009[/C][/ROW]
[ROW][C]11[/C][C]6.1[/C][C]6.09522394922025[/C][C]0.185825295955012[/C][C]0.00477605077974664[/C][C]1.9713487220021[/C][/ROW]
[ROW][C]12[/C][C]6.1[/C][C]6.10267012692514[/C][C]0.00974249630433024[/C][C]-0.00267012692514542[/C][C]-0.729232584938666[/C][/ROW]
[ROW][C]13[/C][C]6.1[/C][C]6.09961056619894[/C][C]-0.00289373740588862[/C][C]0.000389433801055103[/C][C]-0.0523382102394348[/C][/ROW]
[ROW][C]14[/C][C]6.1[/C][C]6.09785093585783[/C][C]-0.00177405910085651[/C][C]0.00214906414216770[/C][C]0.00464350935965628[/C][/ROW]
[ROW][C]15[/C][C]6.1[/C][C]6.10327734927333[/C][C]0.00527074334871684[/C][C]-0.00327734927332607[/C][C]0.0292998277865995[/C][/ROW]
[ROW][C]16[/C][C]6.4[/C][C]6.39355779297442[/C][C]0.283524727495623[/C][C]0.00644220702558011[/C][C]1.15208749848241[/C][/ROW]
[ROW][C]17[/C][C]6.7[/C][C]6.70141704898546[/C][C]0.307286599264358[/C][C]-0.00141704898545800[/C][C]0.098409103018933[/C][/ROW]
[ROW][C]18[/C][C]6.9[/C][C]6.90239308024715[/C][C]0.203474052341428[/C][C]-0.00239308024714992[/C][C]-0.429931209766651[/C][/ROW]
[ROW][C]19[/C][C]7[/C][C]6.99751842689687[/C][C]0.0976719463955992[/C][C]0.00248157310312842[/C][C]-0.438170815007838[/C][/ROW]
[ROW][C]20[/C][C]7[/C][C]7.00932280684428[/C][C]0.0138226543213788[/C][C]-0.00932280684427659[/C][C]-0.347255019452226[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]6.79247267854197[/C][C]-0.211428359410104[/C][C]0.00752732145802524[/C][C]-0.932858742203005[/C][/ROW]
[ROW][C]22[/C][C]6.4[/C][C]6.41270405860088[/C][C]-0.375811908003098[/C][C]-0.0127040586008774[/C][C]-0.680781089097793[/C][/ROW]
[ROW][C]23[/C][C]5.9[/C][C]5.89467502498198[/C][C]-0.514686465598539[/C][C]0.00532497501802364[/C][C]-0.575137684607805[/C][/ROW]
[ROW][C]24[/C][C]5.5[/C][C]5.50016070165732[/C][C]-0.397338999364159[/C][C]-0.000160701657324725[/C][C]0.485985066471323[/C][/ROW]
[ROW][C]25[/C][C]5.5[/C][C]5.49399960026595[/C][C]-0.0153873066090311[/C][C]0.00600039973404482[/C][C]1.58202586966257[/C][/ROW]
[ROW][C]26[/C][C]5.6[/C][C]5.59298140995175[/C][C]0.0963144004655587[/C][C]0.00701859004825286[/C][C]0.463081881057796[/C][/ROW]
[ROW][C]27[/C][C]5.8[/C][C]5.80749816570284[/C][C]0.210931531069805[/C][C]-0.00749816570284082[/C][C]0.476226005450853[/C][/ROW]
[ROW][C]28[/C][C]5.9[/C][C]5.89843543212545[/C][C]0.0947024869909643[/C][C]0.00156456787455183[/C][C]-0.481200501660963[/C][/ROW]
[ROW][C]29[/C][C]6.1[/C][C]6.09747947505157[/C][C]0.195774205083794[/C][C]0.00252052494842619[/C][C]0.41859107594146[/C][/ROW]
[ROW][C]30[/C][C]6.1[/C][C]6.10474415012635[/C][C]0.0131619052041264[/C][C]-0.00474415012635025[/C][C]-0.756273520089822[/C][/ROW]
[ROW][C]31[/C][C]6[/C][C]6.00004468809009[/C][C]-0.101011726964120[/C][C]-4.46880900908772e-05[/C][C]-0.472840848662802[/C][/ROW]
[ROW][C]32[/C][C]6[/C][C]6.00321778512485[/C][C]-8.70050724529753e-05[/C][C]-0.00321778512485429[/C][C]0.417971520913078[/C][/ROW]
[ROW][C]33[/C][C]5.9[/C][C]5.89378461292126[/C][C]-0.106011607387369[/C][C]0.00621538707874165[/C][C]-0.438678120515491[/C][/ROW]
[ROW][C]34[/C][C]5.5[/C][C]5.51396360252218[/C][C]-0.37125323279174[/C][C]-0.0139636025221789[/C][C]-1.09847660896160[/C][/ROW]
[ROW][C]35[/C][C]5.6[/C][C]5.58173306876045[/C][C]0.0540330601232895[/C][C]0.0182669312395535[/C][C]1.76128872590351[/C][/ROW]
[ROW][C]36[/C][C]5.4[/C][C]5.41421378592133[/C][C]-0.160585822070662[/C][C]-0.0142137859213330[/C][C]-0.888827211245181[/C][/ROW]
[ROW][C]37[/C][C]5.2[/C][C]5.19562301857758[/C][C]-0.216770702132943[/C][C]0.0043769814224184[/C][C]-0.232720492953543[/C][/ROW]
[ROW][C]38[/C][C]5.2[/C][C]5.19360557190027[/C][C]-0.0086987165242462[/C][C]0.00639442809972834[/C][C]0.862275194198476[/C][/ROW]
[ROW][C]39[/C][C]5.2[/C][C]5.20190747552098[/C][C]0.0076847069001057[/C][C]-0.0019074755209796[/C][C]0.068010706536208[/C][/ROW]
[ROW][C]40[/C][C]5.5[/C][C]5.49850417747576[/C][C]0.286015370002777[/C][C]0.00149582252424102[/C][C]1.15232777236473[/C][/ROW]
[ROW][C]41[/C][C]5.8[/C][C]5.79469937014512[/C][C]0.295821345738657[/C][C]0.00530062985488497[/C][C]0.0406118825422641[/C][/ROW]
[ROW][C]42[/C][C]5.8[/C][C]5.80582243223237[/C][C]0.0215580799705882[/C][C]-0.00582243223236669[/C][C]-1.13583787026343[/C][/ROW]
[ROW][C]43[/C][C]5.5[/C][C]5.51191357179922[/C][C]-0.282345598274516[/C][C]-0.0119135717992181[/C][C]-1.25859262625289[/C][/ROW]
[ROW][C]44[/C][C]5.3[/C][C]5.30200515969737[/C][C]-0.212563904753882[/C][C]-0.00200515969737416[/C][C]0.288995201556250[/C][/ROW]
[ROW][C]45[/C][C]5.1[/C][C]5.07691512668202[/C][C]-0.224630833187949[/C][C]0.0230848733179795[/C][C]-0.0499742023660053[/C][/ROW]
[ROW][C]46[/C][C]5.2[/C][C]5.22309337936363[/C][C]0.132584926646026[/C][C]-0.023093379363633[/C][C]1.47938000429862[/C][/ROW]
[ROW][C]47[/C][C]5.8[/C][C]5.76785510696308[/C][C]0.52965338684852[/C][C]0.0321448930369196[/C][C]1.64442727565032[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.82250193702928[/C][C]0.072064157359714[/C][C]-0.0225019370292789[/C][C]-1.89507026558255[/C][/ROW]
[ROW][C]49[/C][C]5.5[/C][C]5.51027369316912[/C][C]-0.298106915018495[/C][C]-0.010273693169116[/C][C]-1.53330788173242[/C][/ROW]
[ROW][C]50[/C][C]5[/C][C]4.99125394428652[/C][C]-0.510949537531044[/C][C]0.00874605571347878[/C][C]-0.881785297819474[/C][/ROW]
[ROW][C]51[/C][C]4.9[/C][C]4.89885467575368[/C][C]-0.109261599430379[/C][C]0.00114532424631634[/C][C]1.66634087652492[/C][/ROW]
[ROW][C]52[/C][C]5.3[/C][C]5.29238487599785[/C][C]0.373323917032699[/C][C]0.00761512400215245[/C][C]1.99808449014423[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]6.08227568793519[/C][C]0.773063685238924[/C][C]0.0177243120648116[/C][C]1.65552840689468[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]6.50481287239076[/C][C]0.436667506505551[/C][C]-0.00481287239075659[/C][C]-1.39315722914169[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]6.81867230351617[/C][C]0.318809639292635[/C][C]-0.0186723035161743[/C][C]-0.488098869759394[/C][/ROW]
[ROW][C]56[/C][C]6.6[/C][C]6.60604110816872[/C][C]-0.191206426526746[/C][C]-0.00604110816871922[/C][C]-2.11219003005265[/C][/ROW]
[ROW][C]57[/C][C]6.4[/C][C]6.37966157589264[/C][C]-0.224961508823594[/C][C]0.0203384241073565[/C][C]-0.139793928781406[/C][/ROW]
[ROW][C]58[/C][C]6.4[/C][C]6.43870483881188[/C][C]0.047593964335382[/C][C]-0.0387048388118812[/C][C]1.12876631249156[/C][/ROW]
[ROW][C]59[/C][C]6.6[/C][C]6.55781274595347[/C][C]0.116225189273000[/C][C]0.0421872540465295[/C][C]0.284230857820430[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63936&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	6.3	6.3	0	0	0
2	6.2	6.20033875634969	-0.0996892400546821	-0.000338756349693864	-0.413526898000771
3	6.1	6.09976744827461	-0.100562515222695	0.000232551725384802	-0.00363474764207676
4	6.3	6.2974530563921	0.193771042443022	0.00254694360790351	1.21883612320128
5	6.5	6.50062828204771	0.203054049444421	-0.000628282047714086	0.0384449021976258
6	6.6	6.60097171365893	0.101665299403964	-0.000971713658931074	-0.419893279294913
7	6.5	6.50158266492297	-0.0968007826560898	-0.00158266492297389	-0.821931126823448
8	6.2	6.20138698065123	-0.2975773150637	-0.00138698065122801	-0.831499669577698
9	6.2	6.19705230530992	-0.0081096582559993	0.00294769469008469	1.19880674346806
10	5.9	5.90319097012336	-0.290182783260372	-0.00319097012336136	-1.16818289178009
11	6.1	6.09522394922025	0.185825295955012	0.00477605077974664	1.9713487220021
12	6.1	6.10267012692514	0.00974249630433024	-0.00267012692514542	-0.729232584938666
13	6.1	6.09961056619894	-0.00289373740588862	0.000389433801055103	-0.0523382102394348
14	6.1	6.09785093585783	-0.00177405910085651	0.00214906414216770	0.00464350935965628
15	6.1	6.10327734927333	0.00527074334871684	-0.00327734927332607	0.0292998277865995
16	6.4	6.39355779297442	0.283524727495623	0.00644220702558011	1.15208749848241
17	6.7	6.70141704898546	0.307286599264358	-0.00141704898545800	0.098409103018933
18	6.9	6.90239308024715	0.203474052341428	-0.00239308024714992	-0.429931209766651
19	7	6.99751842689687	0.0976719463955992	0.00248157310312842	-0.438170815007838
20	7	7.00932280684428	0.0138226543213788	-0.00932280684427659	-0.347255019452226
21	6.8	6.79247267854197	-0.211428359410104	0.00752732145802524	-0.932858742203005
22	6.4	6.41270405860088	-0.375811908003098	-0.0127040586008774	-0.680781089097793
23	5.9	5.89467502498198	-0.514686465598539	0.00532497501802364	-0.575137684607805
24	5.5	5.50016070165732	-0.397338999364159	-0.000160701657324725	0.485985066471323
25	5.5	5.49399960026595	-0.0153873066090311	0.00600039973404482	1.58202586966257
26	5.6	5.59298140995175	0.0963144004655587	0.00701859004825286	0.463081881057796
27	5.8	5.80749816570284	0.210931531069805	-0.00749816570284082	0.476226005450853
28	5.9	5.89843543212545	0.0947024869909643	0.00156456787455183	-0.481200501660963
29	6.1	6.09747947505157	0.195774205083794	0.00252052494842619	0.41859107594146
30	6.1	6.10474415012635	0.0131619052041264	-0.00474415012635025	-0.756273520089822
31	6	6.00004468809009	-0.101011726964120	-4.46880900908772e-05	-0.472840848662802
32	6	6.00321778512485	-8.70050724529753e-05	-0.00321778512485429	0.417971520913078
33	5.9	5.89378461292126	-0.106011607387369	0.00621538707874165	-0.438678120515491
34	5.5	5.51396360252218	-0.37125323279174	-0.0139636025221789	-1.09847660896160
35	5.6	5.58173306876045	0.0540330601232895	0.0182669312395535	1.76128872590351
36	5.4	5.41421378592133	-0.160585822070662	-0.0142137859213330	-0.888827211245181
37	5.2	5.19562301857758	-0.216770702132943	0.0043769814224184	-0.232720492953543
38	5.2	5.19360557190027	-0.0086987165242462	0.00639442809972834	0.862275194198476
39	5.2	5.20190747552098	0.0076847069001057	-0.0019074755209796	0.068010706536208
40	5.5	5.49850417747576	0.286015370002777	0.00149582252424102	1.15232777236473
41	5.8	5.79469937014512	0.295821345738657	0.00530062985488497	0.0406118825422641
42	5.8	5.80582243223237	0.0215580799705882	-0.00582243223236669	-1.13583787026343
43	5.5	5.51191357179922	-0.282345598274516	-0.0119135717992181	-1.25859262625289
44	5.3	5.30200515969737	-0.212563904753882	-0.00200515969737416	0.288995201556250
45	5.1	5.07691512668202	-0.224630833187949	0.0230848733179795	-0.0499742023660053
46	5.2	5.22309337936363	0.132584926646026	-0.023093379363633	1.47938000429862
47	5.8	5.76785510696308	0.52965338684852	0.0321448930369196	1.64442727565032
48	5.8	5.82250193702928	0.072064157359714	-0.0225019370292789	-1.89507026558255
49	5.5	5.51027369316912	-0.298106915018495	-0.010273693169116	-1.53330788173242
50	5	4.99125394428652	-0.510949537531044	0.00874605571347878	-0.881785297819474
51	4.9	4.89885467575368	-0.109261599430379	0.00114532424631634	1.66634087652492
52	5.3	5.29238487599785	0.373323917032699	0.00761512400215245	1.99808449014423
53	6.1	6.08227568793519	0.773063685238924	0.0177243120648116	1.65552840689468
54	6.5	6.50481287239076	0.436667506505551	-0.00481287239075659	-1.39315722914169
55	6.8	6.81867230351617	0.318809639292635	-0.0186723035161743	-0.488098869759394
56	6.6	6.60604110816872	-0.191206426526746	-0.00604110816871922	-2.11219003005265
57	6.4	6.37966157589264	-0.224961508823594	0.0203384241073565	-0.139793928781406
58	6.4	6.43870483881188	0.047593964335382	-0.0387048388118812	1.12876631249156
59	6.6	6.55781274595347	0.116225189273000	0.0421872540465295	0.284230857820430

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 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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