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R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Tue, 07 Dec 2010 19:00:52 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/07/t1291748318k2kn01gb2lrhoes.htm/, Retrieved Fri, 05 Dec 2025 08:05:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106625, Retrieved Fri, 05 Dec 2025 08:05:51 +0000

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Estimated Impact

538

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Structural Time Series Models] [HPC Retail Sales] [2008-03-06 16:52:55] [74be16979710d4c4e7c6647856088456]
- R  D    [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456]
-  M D        [Structural Time Series Models] [] [2010-12-07 19:00:52] [d42b17bf3b3c0d56878eb3f5a4351e6d] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106625&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106625&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	103.48	103.48	0	0	0
2	103.93	103.873915011963	0.0671547068140572	0.0205163683230409	1.05673372968296
3	103.89	103.878658598222	0.0441107069774392	0.0204037216127486	-0.212745217106742
4	104.4	104.328896605387	0.212766643189411	0.018532748645815	1.29441439184492
5	104.79	104.746436345168	0.29987706478355	0.0178085281500633	0.642593675078283
6	104.77	104.784423137891	0.187752274708622	0.0183498153606676	-0.820063166157854
7	105.13	105.096267913576	0.240993750266082	0.0182115452968072	0.388621717198104
8	105.26	105.25235964382	0.204536778405807	0.0182610280463516	-0.265976068843939
9	104.96	104.998903709244	0.00780426151474636	0.0183989511065719	-1.43510339524529
10	104.75	104.762163590399	-0.0972581377454122	0.0184368095504773	-0.766372861116432
11	105.01	104.955252003452	0.0274920658456558	0.0184137520686329	0.909976860503057
12	105.15	105.115035893002	0.0843348039974786	0.0184083678840531	0.41463227353378
13	105.2	105.331371991286	0.138908704581269	-0.147259664919998	0.47449730748307
14	105.77	105.728992794546	0.240710806849184	0.0194658889661998	0.655989540727187
15	105.78	105.783925576531	0.161016128426702	0.0193336915853151	-0.582603370340138
16	106.26	106.20841822986	0.274454159091059	0.0187733441824657	0.822739281923393
17	106.13	106.151963334933	0.132256300814288	0.0193121816321711	-1.03451463989318
18	106.12	106.120936154171	0.0621249776487469	0.0194675510226062	-0.511135457885316
19	106.57	106.509832342419	0.202484848872294	0.0192999243132723	1.02359417310278
20	106.44	106.453065783842	0.0911115333383387	0.0193694853632611	-0.812346035400039
21	106.54	106.523246697419	0.082118914854446	0.0193723871055168	-0.0655943654371804
22	107.1	107.027794431137	0.263621836696443	0.0193422814761452	1.32394345266921
23	108.1	107.992896023293	0.565033073940443	0.0193166370618926	2.19860238118453
24	108.4	108.40039546851	0.497342984325434	0.019319588531805	-0.493756381673127
25	108.84	109.014559614347	0.546622951315751	-0.188909629601856	0.393645454873374
26	109.62	109.59859646102	0.561808997747749	0.0177516252565416	0.103005724369347
27	110.42	110.375253270046	0.654027280557182	0.01785156466381	0.673642701863089
28	110.67	110.693558228224	0.509582608789291	0.0183192319478328	-1.04969404269016
29	111.66	111.593366686826	0.677266744244495	0.0179028983905363	1.22104152281305
30	112.28	112.263041544135	0.674005486869827	0.0179076310698452	-0.0237757695965795
31	112.87	112.861515573975	0.641557894899944	0.0179330122335132	-0.236647995490579
32	112.18	112.311013757318	0.129413430779224	0.0181425174185119	-3.73561412849186
33	112.36	112.352813366424	0.0917694144341112	0.0181504731993205	-0.274586305285415
34	112.16	112.175509953511	-0.0238445254952432	0.0181630331419322	-0.843328331237461
35	111.49	111.547439850187	-0.283470880400788	0.0181775007011105	-1.89380913622189
36	111.25	111.235397803403	-0.295747606376388	0.0181778512986996	-0.0895509590826834
37	111.36	111.433201285786	-0.086226373888755	-0.134216965109667	1.62498585041849
38	111.74	111.688171024441	0.0543345130478958	0.0161280391596024	0.97392945897528
39	111.1	111.15732384563	-0.196911244102784	0.0159258200750152	-1.834638742933
40	111.33	111.275111774956	-0.0615566595291128	0.0155998830405733	0.98458133416731
41	111.25	111.232097947643	-0.0535886858845455	0.0155851718666258	0.0580468408749427
42	111.04	111.041486937155	-0.112453883813694	0.0156486864920975	-0.429209414913862
43	110.97	110.951540990476	-0.10278408806187	0.0156430628196737	0.0705269254169159
44	111.31	111.244845548901	0.0673940003617323	0.0155913052403021	1.24130311966288
45	111.02	111.03863009701	-0.0501671422770438	0.015609777377275	-0.8575273141104
46	111.07	111.047059169843	-0.0249895075574401	0.0156077438104045	0.183654572447691
47	111.36	111.308545394502	0.098105410768704	0.0156026440169899	0.89789931886991
48	111.54	111.511301351241	0.143072776227557	0.0156016892668165	0.328008536002872
49	112.05	112.118054533731	0.340523530686371	-0.125557139606325	1.50853262492872
50	112.52	112.503308664986	0.359112167686081	0.0118244391990438	0.130307665725181
51	112.94	112.920846428869	0.384201157154409	0.011840474552576	0.183163962727882
52	113.33	113.316712157356	0.389217196753956	0.0118308596560312	0.0365078715921515
53	113.78	113.761285223575	0.413003834460183	0.0117959045300156	0.173331500971737
54	113.77	113.804339507651	0.25406549185186	0.0119323906637665	-1.15897875629395
55	113.82	113.835866789549	0.158455743889951	0.0119766431916989	-0.697348796286899
56	113.89	113.890948369518	0.114040384266335	0.0119873938080219	-0.323973999545938
57	114.25	114.212104578002	0.203032499468324	0.0119762653798814	0.649137096645285
58	114.41	114.399926831239	0.196496912928743	0.0119766854838765	-0.0476729010209747

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 103.48 & 103.48 & 0 & 0 & 0 \tabularnewline
2 & 103.93 & 103.873915011963 & 0.0671547068140572 & 0.0205163683230409 & 1.05673372968296 \tabularnewline
3 & 103.89 & 103.878658598222 & 0.0441107069774392 & 0.0204037216127486 & -0.212745217106742 \tabularnewline
4 & 104.4 & 104.328896605387 & 0.212766643189411 & 0.018532748645815 & 1.29441439184492 \tabularnewline
5 & 104.79 & 104.746436345168 & 0.29987706478355 & 0.0178085281500633 & 0.642593675078283 \tabularnewline
6 & 104.77 & 104.784423137891 & 0.187752274708622 & 0.0183498153606676 & -0.820063166157854 \tabularnewline
7 & 105.13 & 105.096267913576 & 0.240993750266082 & 0.0182115452968072 & 0.388621717198104 \tabularnewline
8 & 105.26 & 105.25235964382 & 0.204536778405807 & 0.0182610280463516 & -0.265976068843939 \tabularnewline
9 & 104.96 & 104.998903709244 & 0.00780426151474636 & 0.0183989511065719 & -1.43510339524529 \tabularnewline
10 & 104.75 & 104.762163590399 & -0.0972581377454122 & 0.0184368095504773 & -0.766372861116432 \tabularnewline
11 & 105.01 & 104.955252003452 & 0.0274920658456558 & 0.0184137520686329 & 0.909976860503057 \tabularnewline
12 & 105.15 & 105.115035893002 & 0.0843348039974786 & 0.0184083678840531 & 0.41463227353378 \tabularnewline
13 & 105.2 & 105.331371991286 & 0.138908704581269 & -0.147259664919998 & 0.47449730748307 \tabularnewline
14 & 105.77 & 105.728992794546 & 0.240710806849184 & 0.0194658889661998 & 0.655989540727187 \tabularnewline
15 & 105.78 & 105.783925576531 & 0.161016128426702 & 0.0193336915853151 & -0.582603370340138 \tabularnewline
16 & 106.26 & 106.20841822986 & 0.274454159091059 & 0.0187733441824657 & 0.822739281923393 \tabularnewline
17 & 106.13 & 106.151963334933 & 0.132256300814288 & 0.0193121816321711 & -1.03451463989318 \tabularnewline
18 & 106.12 & 106.120936154171 & 0.0621249776487469 & 0.0194675510226062 & -0.511135457885316 \tabularnewline
19 & 106.57 & 106.509832342419 & 0.202484848872294 & 0.0192999243132723 & 1.02359417310278 \tabularnewline
20 & 106.44 & 106.453065783842 & 0.0911115333383387 & 0.0193694853632611 & -0.812346035400039 \tabularnewline
21 & 106.54 & 106.523246697419 & 0.082118914854446 & 0.0193723871055168 & -0.0655943654371804 \tabularnewline
22 & 107.1 & 107.027794431137 & 0.263621836696443 & 0.0193422814761452 & 1.32394345266921 \tabularnewline
23 & 108.1 & 107.992896023293 & 0.565033073940443 & 0.0193166370618926 & 2.19860238118453 \tabularnewline
24 & 108.4 & 108.40039546851 & 0.497342984325434 & 0.019319588531805 & -0.493756381673127 \tabularnewline
25 & 108.84 & 109.014559614347 & 0.546622951315751 & -0.188909629601856 & 0.393645454873374 \tabularnewline
26 & 109.62 & 109.59859646102 & 0.561808997747749 & 0.0177516252565416 & 0.103005724369347 \tabularnewline
27 & 110.42 & 110.375253270046 & 0.654027280557182 & 0.01785156466381 & 0.673642701863089 \tabularnewline
28 & 110.67 & 110.693558228224 & 0.509582608789291 & 0.0183192319478328 & -1.04969404269016 \tabularnewline
29 & 111.66 & 111.593366686826 & 0.677266744244495 & 0.0179028983905363 & 1.22104152281305 \tabularnewline
30 & 112.28 & 112.263041544135 & 0.674005486869827 & 0.0179076310698452 & -0.0237757695965795 \tabularnewline
31 & 112.87 & 112.861515573975 & 0.641557894899944 & 0.0179330122335132 & -0.236647995490579 \tabularnewline
32 & 112.18 & 112.311013757318 & 0.129413430779224 & 0.0181425174185119 & -3.73561412849186 \tabularnewline
33 & 112.36 & 112.352813366424 & 0.0917694144341112 & 0.0181504731993205 & -0.274586305285415 \tabularnewline
34 & 112.16 & 112.175509953511 & -0.0238445254952432 & 0.0181630331419322 & -0.843328331237461 \tabularnewline
35 & 111.49 & 111.547439850187 & -0.283470880400788 & 0.0181775007011105 & -1.89380913622189 \tabularnewline
36 & 111.25 & 111.235397803403 & -0.295747606376388 & 0.0181778512986996 & -0.0895509590826834 \tabularnewline
37 & 111.36 & 111.433201285786 & -0.086226373888755 & -0.134216965109667 & 1.62498585041849 \tabularnewline
38 & 111.74 & 111.688171024441 & 0.0543345130478958 & 0.0161280391596024 & 0.97392945897528 \tabularnewline
39 & 111.1 & 111.15732384563 & -0.196911244102784 & 0.0159258200750152 & -1.834638742933 \tabularnewline
40 & 111.33 & 111.275111774956 & -0.0615566595291128 & 0.0155998830405733 & 0.98458133416731 \tabularnewline
41 & 111.25 & 111.232097947643 & -0.0535886858845455 & 0.0155851718666258 & 0.0580468408749427 \tabularnewline
42 & 111.04 & 111.041486937155 & -0.112453883813694 & 0.0156486864920975 & -0.429209414913862 \tabularnewline
43 & 110.97 & 110.951540990476 & -0.10278408806187 & 0.0156430628196737 & 0.0705269254169159 \tabularnewline
44 & 111.31 & 111.244845548901 & 0.0673940003617323 & 0.0155913052403021 & 1.24130311966288 \tabularnewline
45 & 111.02 & 111.03863009701 & -0.0501671422770438 & 0.015609777377275 & -0.8575273141104 \tabularnewline
46 & 111.07 & 111.047059169843 & -0.0249895075574401 & 0.0156077438104045 & 0.183654572447691 \tabularnewline
47 & 111.36 & 111.308545394502 & 0.098105410768704 & 0.0156026440169899 & 0.89789931886991 \tabularnewline
48 & 111.54 & 111.511301351241 & 0.143072776227557 & 0.0156016892668165 & 0.328008536002872 \tabularnewline
49 & 112.05 & 112.118054533731 & 0.340523530686371 & -0.125557139606325 & 1.50853262492872 \tabularnewline
50 & 112.52 & 112.503308664986 & 0.359112167686081 & 0.0118244391990438 & 0.130307665725181 \tabularnewline
51 & 112.94 & 112.920846428869 & 0.384201157154409 & 0.011840474552576 & 0.183163962727882 \tabularnewline
52 & 113.33 & 113.316712157356 & 0.389217196753956 & 0.0118308596560312 & 0.0365078715921515 \tabularnewline
53 & 113.78 & 113.761285223575 & 0.413003834460183 & 0.0117959045300156 & 0.173331500971737 \tabularnewline
54 & 113.77 & 113.804339507651 & 0.25406549185186 & 0.0119323906637665 & -1.15897875629395 \tabularnewline
55 & 113.82 & 113.835866789549 & 0.158455743889951 & 0.0119766431916989 & -0.697348796286899 \tabularnewline
56 & 113.89 & 113.890948369518 & 0.114040384266335 & 0.0119873938080219 & -0.323973999545938 \tabularnewline
57 & 114.25 & 114.212104578002 & 0.203032499468324 & 0.0119762653798814 & 0.649137096645285 \tabularnewline
58 & 114.41 & 114.399926831239 & 0.196496912928743 & 0.0119766854838765 & -0.0476729010209747 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106625&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]103.48[/C][C]103.48[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]103.93[/C][C]103.873915011963[/C][C]0.0671547068140572[/C][C]0.0205163683230409[/C][C]1.05673372968296[/C][/ROW]
[ROW][C]3[/C][C]103.89[/C][C]103.878658598222[/C][C]0.0441107069774392[/C][C]0.0204037216127486[/C][C]-0.212745217106742[/C][/ROW]
[ROW][C]4[/C][C]104.4[/C][C]104.328896605387[/C][C]0.212766643189411[/C][C]0.018532748645815[/C][C]1.29441439184492[/C][/ROW]
[ROW][C]5[/C][C]104.79[/C][C]104.746436345168[/C][C]0.29987706478355[/C][C]0.0178085281500633[/C][C]0.642593675078283[/C][/ROW]
[ROW][C]6[/C][C]104.77[/C][C]104.784423137891[/C][C]0.187752274708622[/C][C]0.0183498153606676[/C][C]-0.820063166157854[/C][/ROW]
[ROW][C]7[/C][C]105.13[/C][C]105.096267913576[/C][C]0.240993750266082[/C][C]0.0182115452968072[/C][C]0.388621717198104[/C][/ROW]
[ROW][C]8[/C][C]105.26[/C][C]105.25235964382[/C][C]0.204536778405807[/C][C]0.0182610280463516[/C][C]-0.265976068843939[/C][/ROW]
[ROW][C]9[/C][C]104.96[/C][C]104.998903709244[/C][C]0.00780426151474636[/C][C]0.0183989511065719[/C][C]-1.43510339524529[/C][/ROW]
[ROW][C]10[/C][C]104.75[/C][C]104.762163590399[/C][C]-0.0972581377454122[/C][C]0.0184368095504773[/C][C]-0.766372861116432[/C][/ROW]
[ROW][C]11[/C][C]105.01[/C][C]104.955252003452[/C][C]0.0274920658456558[/C][C]0.0184137520686329[/C][C]0.909976860503057[/C][/ROW]
[ROW][C]12[/C][C]105.15[/C][C]105.115035893002[/C][C]0.0843348039974786[/C][C]0.0184083678840531[/C][C]0.41463227353378[/C][/ROW]
[ROW][C]13[/C][C]105.2[/C][C]105.331371991286[/C][C]0.138908704581269[/C][C]-0.147259664919998[/C][C]0.47449730748307[/C][/ROW]
[ROW][C]14[/C][C]105.77[/C][C]105.728992794546[/C][C]0.240710806849184[/C][C]0.0194658889661998[/C][C]0.655989540727187[/C][/ROW]
[ROW][C]15[/C][C]105.78[/C][C]105.783925576531[/C][C]0.161016128426702[/C][C]0.0193336915853151[/C][C]-0.582603370340138[/C][/ROW]
[ROW][C]16[/C][C]106.26[/C][C]106.20841822986[/C][C]0.274454159091059[/C][C]0.0187733441824657[/C][C]0.822739281923393[/C][/ROW]
[ROW][C]17[/C][C]106.13[/C][C]106.151963334933[/C][C]0.132256300814288[/C][C]0.0193121816321711[/C][C]-1.03451463989318[/C][/ROW]
[ROW][C]18[/C][C]106.12[/C][C]106.120936154171[/C][C]0.0621249776487469[/C][C]0.0194675510226062[/C][C]-0.511135457885316[/C][/ROW]
[ROW][C]19[/C][C]106.57[/C][C]106.509832342419[/C][C]0.202484848872294[/C][C]0.0192999243132723[/C][C]1.02359417310278[/C][/ROW]
[ROW][C]20[/C][C]106.44[/C][C]106.453065783842[/C][C]0.0911115333383387[/C][C]0.0193694853632611[/C][C]-0.812346035400039[/C][/ROW]
[ROW][C]21[/C][C]106.54[/C][C]106.523246697419[/C][C]0.082118914854446[/C][C]0.0193723871055168[/C][C]-0.0655943654371804[/C][/ROW]
[ROW][C]22[/C][C]107.1[/C][C]107.027794431137[/C][C]0.263621836696443[/C][C]0.0193422814761452[/C][C]1.32394345266921[/C][/ROW]
[ROW][C]23[/C][C]108.1[/C][C]107.992896023293[/C][C]0.565033073940443[/C][C]0.0193166370618926[/C][C]2.19860238118453[/C][/ROW]
[ROW][C]24[/C][C]108.4[/C][C]108.40039546851[/C][C]0.497342984325434[/C][C]0.019319588531805[/C][C]-0.493756381673127[/C][/ROW]
[ROW][C]25[/C][C]108.84[/C][C]109.014559614347[/C][C]0.546622951315751[/C][C]-0.188909629601856[/C][C]0.393645454873374[/C][/ROW]
[ROW][C]26[/C][C]109.62[/C][C]109.59859646102[/C][C]0.561808997747749[/C][C]0.0177516252565416[/C][C]0.103005724369347[/C][/ROW]
[ROW][C]27[/C][C]110.42[/C][C]110.375253270046[/C][C]0.654027280557182[/C][C]0.01785156466381[/C][C]0.673642701863089[/C][/ROW]
[ROW][C]28[/C][C]110.67[/C][C]110.693558228224[/C][C]0.509582608789291[/C][C]0.0183192319478328[/C][C]-1.04969404269016[/C][/ROW]
[ROW][C]29[/C][C]111.66[/C][C]111.593366686826[/C][C]0.677266744244495[/C][C]0.0179028983905363[/C][C]1.22104152281305[/C][/ROW]
[ROW][C]30[/C][C]112.28[/C][C]112.263041544135[/C][C]0.674005486869827[/C][C]0.0179076310698452[/C][C]-0.0237757695965795[/C][/ROW]
[ROW][C]31[/C][C]112.87[/C][C]112.861515573975[/C][C]0.641557894899944[/C][C]0.0179330122335132[/C][C]-0.236647995490579[/C][/ROW]
[ROW][C]32[/C][C]112.18[/C][C]112.311013757318[/C][C]0.129413430779224[/C][C]0.0181425174185119[/C][C]-3.73561412849186[/C][/ROW]
[ROW][C]33[/C][C]112.36[/C][C]112.352813366424[/C][C]0.0917694144341112[/C][C]0.0181504731993205[/C][C]-0.274586305285415[/C][/ROW]
[ROW][C]34[/C][C]112.16[/C][C]112.175509953511[/C][C]-0.0238445254952432[/C][C]0.0181630331419322[/C][C]-0.843328331237461[/C][/ROW]
[ROW][C]35[/C][C]111.49[/C][C]111.547439850187[/C][C]-0.283470880400788[/C][C]0.0181775007011105[/C][C]-1.89380913622189[/C][/ROW]
[ROW][C]36[/C][C]111.25[/C][C]111.235397803403[/C][C]-0.295747606376388[/C][C]0.0181778512986996[/C][C]-0.0895509590826834[/C][/ROW]
[ROW][C]37[/C][C]111.36[/C][C]111.433201285786[/C][C]-0.086226373888755[/C][C]-0.134216965109667[/C][C]1.62498585041849[/C][/ROW]
[ROW][C]38[/C][C]111.74[/C][C]111.688171024441[/C][C]0.0543345130478958[/C][C]0.0161280391596024[/C][C]0.97392945897528[/C][/ROW]
[ROW][C]39[/C][C]111.1[/C][C]111.15732384563[/C][C]-0.196911244102784[/C][C]0.0159258200750152[/C][C]-1.834638742933[/C][/ROW]
[ROW][C]40[/C][C]111.33[/C][C]111.275111774956[/C][C]-0.0615566595291128[/C][C]0.0155998830405733[/C][C]0.98458133416731[/C][/ROW]
[ROW][C]41[/C][C]111.25[/C][C]111.232097947643[/C][C]-0.0535886858845455[/C][C]0.0155851718666258[/C][C]0.0580468408749427[/C][/ROW]
[ROW][C]42[/C][C]111.04[/C][C]111.041486937155[/C][C]-0.112453883813694[/C][C]0.0156486864920975[/C][C]-0.429209414913862[/C][/ROW]
[ROW][C]43[/C][C]110.97[/C][C]110.951540990476[/C][C]-0.10278408806187[/C][C]0.0156430628196737[/C][C]0.0705269254169159[/C][/ROW]
[ROW][C]44[/C][C]111.31[/C][C]111.244845548901[/C][C]0.0673940003617323[/C][C]0.0155913052403021[/C][C]1.24130311966288[/C][/ROW]
[ROW][C]45[/C][C]111.02[/C][C]111.03863009701[/C][C]-0.0501671422770438[/C][C]0.015609777377275[/C][C]-0.8575273141104[/C][/ROW]
[ROW][C]46[/C][C]111.07[/C][C]111.047059169843[/C][C]-0.0249895075574401[/C][C]0.0156077438104045[/C][C]0.183654572447691[/C][/ROW]
[ROW][C]47[/C][C]111.36[/C][C]111.308545394502[/C][C]0.098105410768704[/C][C]0.0156026440169899[/C][C]0.89789931886991[/C][/ROW]
[ROW][C]48[/C][C]111.54[/C][C]111.511301351241[/C][C]0.143072776227557[/C][C]0.0156016892668165[/C][C]0.328008536002872[/C][/ROW]
[ROW][C]49[/C][C]112.05[/C][C]112.118054533731[/C][C]0.340523530686371[/C][C]-0.125557139606325[/C][C]1.50853262492872[/C][/ROW]
[ROW][C]50[/C][C]112.52[/C][C]112.503308664986[/C][C]0.359112167686081[/C][C]0.0118244391990438[/C][C]0.130307665725181[/C][/ROW]
[ROW][C]51[/C][C]112.94[/C][C]112.920846428869[/C][C]0.384201157154409[/C][C]0.011840474552576[/C][C]0.183163962727882[/C][/ROW]
[ROW][C]52[/C][C]113.33[/C][C]113.316712157356[/C][C]0.389217196753956[/C][C]0.0118308596560312[/C][C]0.0365078715921515[/C][/ROW]
[ROW][C]53[/C][C]113.78[/C][C]113.761285223575[/C][C]0.413003834460183[/C][C]0.0117959045300156[/C][C]0.173331500971737[/C][/ROW]
[ROW][C]54[/C][C]113.77[/C][C]113.804339507651[/C][C]0.25406549185186[/C][C]0.0119323906637665[/C][C]-1.15897875629395[/C][/ROW]
[ROW][C]55[/C][C]113.82[/C][C]113.835866789549[/C][C]0.158455743889951[/C][C]0.0119766431916989[/C][C]-0.697348796286899[/C][/ROW]
[ROW][C]56[/C][C]113.89[/C][C]113.890948369518[/C][C]0.114040384266335[/C][C]0.0119873938080219[/C][C]-0.323973999545938[/C][/ROW]
[ROW][C]57[/C][C]114.25[/C][C]114.212104578002[/C][C]0.203032499468324[/C][C]0.0119762653798814[/C][C]0.649137096645285[/C][/ROW]
[ROW][C]58[/C][C]114.41[/C][C]114.399926831239[/C][C]0.196496912928743[/C][C]0.0119766854838765[/C][C]-0.0476729010209747[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106625&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	103.48	103.48	0	0	0
2	103.93	103.873915011963	0.0671547068140572	0.0205163683230409	1.05673372968296
3	103.89	103.878658598222	0.0441107069774392	0.0204037216127486	-0.212745217106742
4	104.4	104.328896605387	0.212766643189411	0.018532748645815	1.29441439184492
5	104.79	104.746436345168	0.29987706478355	0.0178085281500633	0.642593675078283
6	104.77	104.784423137891	0.187752274708622	0.0183498153606676	-0.820063166157854
7	105.13	105.096267913576	0.240993750266082	0.0182115452968072	0.388621717198104
8	105.26	105.25235964382	0.204536778405807	0.0182610280463516	-0.265976068843939
9	104.96	104.998903709244	0.00780426151474636	0.0183989511065719	-1.43510339524529
10	104.75	104.762163590399	-0.0972581377454122	0.0184368095504773	-0.766372861116432
11	105.01	104.955252003452	0.0274920658456558	0.0184137520686329	0.909976860503057
12	105.15	105.115035893002	0.0843348039974786	0.0184083678840531	0.41463227353378
13	105.2	105.331371991286	0.138908704581269	-0.147259664919998	0.47449730748307
14	105.77	105.728992794546	0.240710806849184	0.0194658889661998	0.655989540727187
15	105.78	105.783925576531	0.161016128426702	0.0193336915853151	-0.582603370340138
16	106.26	106.20841822986	0.274454159091059	0.0187733441824657	0.822739281923393
17	106.13	106.151963334933	0.132256300814288	0.0193121816321711	-1.03451463989318
18	106.12	106.120936154171	0.0621249776487469	0.0194675510226062	-0.511135457885316
19	106.57	106.509832342419	0.202484848872294	0.0192999243132723	1.02359417310278
20	106.44	106.453065783842	0.0911115333383387	0.0193694853632611	-0.812346035400039
21	106.54	106.523246697419	0.082118914854446	0.0193723871055168	-0.0655943654371804
22	107.1	107.027794431137	0.263621836696443	0.0193422814761452	1.32394345266921
23	108.1	107.992896023293	0.565033073940443	0.0193166370618926	2.19860238118453
24	108.4	108.40039546851	0.497342984325434	0.019319588531805	-0.493756381673127
25	108.84	109.014559614347	0.546622951315751	-0.188909629601856	0.393645454873374
26	109.62	109.59859646102	0.561808997747749	0.0177516252565416	0.103005724369347
27	110.42	110.375253270046	0.654027280557182	0.01785156466381	0.673642701863089
28	110.67	110.693558228224	0.509582608789291	0.0183192319478328	-1.04969404269016
29	111.66	111.593366686826	0.677266744244495	0.0179028983905363	1.22104152281305
30	112.28	112.263041544135	0.674005486869827	0.0179076310698452	-0.0237757695965795
31	112.87	112.861515573975	0.641557894899944	0.0179330122335132	-0.236647995490579
32	112.18	112.311013757318	0.129413430779224	0.0181425174185119	-3.73561412849186
33	112.36	112.352813366424	0.0917694144341112	0.0181504731993205	-0.274586305285415
34	112.16	112.175509953511	-0.0238445254952432	0.0181630331419322	-0.843328331237461
35	111.49	111.547439850187	-0.283470880400788	0.0181775007011105	-1.89380913622189
36	111.25	111.235397803403	-0.295747606376388	0.0181778512986996	-0.0895509590826834
37	111.36	111.433201285786	-0.086226373888755	-0.134216965109667	1.62498585041849
38	111.74	111.688171024441	0.0543345130478958	0.0161280391596024	0.97392945897528
39	111.1	111.15732384563	-0.196911244102784	0.0159258200750152	-1.834638742933
40	111.33	111.275111774956	-0.0615566595291128	0.0155998830405733	0.98458133416731
41	111.25	111.232097947643	-0.0535886858845455	0.0155851718666258	0.0580468408749427
42	111.04	111.041486937155	-0.112453883813694	0.0156486864920975	-0.429209414913862
43	110.97	110.951540990476	-0.10278408806187	0.0156430628196737	0.0705269254169159
44	111.31	111.244845548901	0.0673940003617323	0.0155913052403021	1.24130311966288
45	111.02	111.03863009701	-0.0501671422770438	0.015609777377275	-0.8575273141104
46	111.07	111.047059169843	-0.0249895075574401	0.0156077438104045	0.183654572447691
47	111.36	111.308545394502	0.098105410768704	0.0156026440169899	0.89789931886991
48	111.54	111.511301351241	0.143072776227557	0.0156016892668165	0.328008536002872
49	112.05	112.118054533731	0.340523530686371	-0.125557139606325	1.50853262492872
50	112.52	112.503308664986	0.359112167686081	0.0118244391990438	0.130307665725181
51	112.94	112.920846428869	0.384201157154409	0.011840474552576	0.183163962727882
52	113.33	113.316712157356	0.389217196753956	0.0118308596560312	0.0365078715921515
53	113.78	113.761285223575	0.413003834460183	0.0117959045300156	0.173331500971737
54	113.77	113.804339507651	0.25406549185186	0.0119323906637665	-1.15897875629395
55	113.82	113.835866789549	0.158455743889951	0.0119766431916989	-0.697348796286899
56	113.89	113.890948369518	0.114040384266335	0.0119873938080219	-0.323973999545938
57	114.25	114.212104578002	0.203032499468324	0.0119762653798814	0.649137096645285
58	114.41	114.399926831239	0.196496912928743	0.0119766854838765	-0.0476729010209747

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$resid)
myfit <- mylevel+myseas
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')
grid()
dev.off()
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='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