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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

Mon, 20 Dec 2010 18:19:34 +0000

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/2010/Dec/20/t129286944608sym98effrk3al.htm/, Retrieved Fri, 03 May 2024 21:47:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113052, Retrieved Fri, 03 May 2024 21:47:17 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

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] [Paper 'Decomposit...] [2010-12-20 18:19:34] [8d8503577eb9ac26988d64b61a75d95b] [Current]
-    D          [Structural Time Series Models] [Paper] [2010-12-28 17:08:51] [8677c3f87cec9201607d40be65aa9670] 
-               [Structural Time Series Models] [paper (15)] [2010-12-29 19:20:43] [34b8ec63a78ce61b49b6bd4fc5a61e1c] 

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Dataseries X:

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Histogram

Boxplots

9,3
14,2
17,3
23
16,3
18,4
14,2
9,1
5,9
7,2
6,8
8
14,3
14,6
17,5
17,2
17,2
14,1
10,4
6,8
4,1
6,5
6,1
6,3
9,3
16,4
16,1
18
17,6
14
10,5
6,9
2,8
0,7
3,6
6,7
12,5
14,4
16,5
18,7
19,4
15,8
11,3
9,7
2,9
0,1
2,5
6,7
10,3
11,2
17,4
20,5
17
14,2
10,6
6,1

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	'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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113052&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113052&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113052&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	9.3	9.3	0	0	0
2	14.2	13.4736505704315	4.10528827469964	0.0341811489468284	1.68788817435418
3	17.3	17.2954307702691	3.87381902117338	0.0348488777500524	-0.0892422670501881
4	23	22.7953445802416	5.21423320464757	0.0322877236448282	0.509928115872817
5	16.3	17.3813385696288	-3.56701612664088	0.0357082875956243	-3.31928107716536
6	18.4	17.9315460214604	-0.164585710011123	0.0358651880480432	1.28582435110197
7	14.2	14.5068164740025	-2.85875294813151	0.0357222557140473	-1.01816048760667
8	9.1	9.30995685826204	-4.79089331884082	0.0356951289081438	-0.730177046530401
9	5.9	5.73640706114873	-3.78492950094269	0.0356949597100448	0.380164645625416
10	7.2	6.66870415702367	0.113193227848089	0.0356895287162296	1.47314289402519
11	6.8	6.7659825299409	0.100041833914435	0.0356895348691232	-0.00497005451087878
12	8	7.85989162567289	0.921333932602784	0.0356895102183893	0.310375198168052
13	14.3	13.4485867875258	4.72109264248952	0.368312663052871	1.54882453246819
14	14.6	14.9259110002643	2.36626378775062	-0.0829124914284717	-0.849590760451241
15	17.5	17.5563796064935	2.58599970783584	-0.0837173849838232	0.0817094097148589
16	17.2	17.5470406895096	0.445429657382742	-0.0772596839675676	-0.804872088726869
17	17.2	17.3448569191145	-0.0893560378111895	-0.0768856075502051	-0.202078262502383
18	14.1	14.4696843140624	-2.39153556761987	-0.076987354812468	-0.870014716606215
19	10.4	10.6293139453037	-3.58887668960232	-0.0770853519865376	-0.452486321982249
20	6.8	6.89261888343265	-3.71103030858513	-0.0770883107293593	-0.0461631695082386
21	4.1	4.08244132690474	-2.96660127030685	-0.0770878415841244	0.281327813754573
22	6.5	6.05787163699064	1.11728876114332	-0.0770963523468533	1.54334636353314
23	6.1	6.27198608230061	0.370942145418384	-0.0770957674776677	-0.282052486648814
24	6.3	6.40236960764606	0.172154143899226	-0.0770957527653614	-0.0751241433633196
25	9.3	8.13374290892933	1.44892022873946	1.00392927389707	0.505961325380028
26	16.4	15.8956189251827	6.21046591975929	-0.0221772531843799	1.74806730522154
27	16.1	16.6747150620398	1.70140703799051	-0.0102881228118466	-1.68436453918366
28	18	18.0442907361596	1.42757350727018	-0.0096937841099987	-0.103109984803715
29	17.6	17.7859875759373	0.0351368718206689	-0.0089932503773615	-0.526173742409441
30	14	14.3715194464186	-2.81556075867516	-0.00908386898046829	-1.07730608851385
31	10.5	10.6086605345717	-3.59840861191378	-0.00912995371442475	-0.295845814747527
32	6.9	6.9187453757653	-3.67402704265202	-0.0091312710992513	-0.0285770217426683
33	2.8	2.85054458620149	-3.99975656934779	-0.00913141874720444	-0.123096723630126
34	0.7	0.532452665627751	-2.61009794370234	-0.00913350173375578	0.525167076433802
35	3.6	3.06846896338759	1.64244287730242	-0.0091358986383216	1.6070813318533
36	6.7	6.51915607574973	3.13670346047928	-0.00913597818123761	0.564697292667568
37	12.5	11.9879723736224	5.05123823723446	0.26861405482296	0.748990162653571
38	14.4	14.654991988634	3.21514326380093	-0.0447757597081732	-0.679503046031239
39	16.5	16.6679545416293	2.21811792558843	-0.042722230881625	-0.373391843239497
40	18.7	18.756112898119	2.11084037350763	-0.0425404037489694	-0.0404267496904691
41	19.4	19.5775170936669	1.04572260756571	-0.0421220121994161	-0.402493778657041
42	15.8	16.2967721221645	-2.52957745133131	-0.0422107515905544	-1.35114128314369
43	11.3	11.5728472303135	-4.34296811262106	-0.0422941022549466	-0.685298410837876
44	9.7	9.50340232652044	-2.46419852582633	-0.0422685460465063	0.710007341384477
45	2.9	3.33178318700323	-5.52786340039032	-0.0422696303466105	-1.15779220910008
46	0.1	-0.080045471502183	-3.77925868818571	-0.0422716768284112	0.660816698464737
47	2.5	1.93364796522073	1.00780330553977	-0.0422737835600121	1.80908268460161
48	6.7	6.38091307868192	3.8500367587607	-0.0422739016934459	1.07411087077608
49	10.3	9.889864978496	3.56962224557372	0.44578686329263	-0.108894999055899
50	11.2	11.4389686457123	1.99312776352447	-0.0546679883545291	-0.586108574789652
51	17.4	17.0792613359496	5.01593203915044	-0.0597760229065125	1.13390686985301
52	20.5	20.7036617298122	3.86704357078673	-0.0581786994249454	-0.433170802112864
53	17	17.7704874323238	-1.75056447306111	-0.0563687912403605	-2.12284350851554
54	14.2	14.4240643259263	-3.06934250130558	-0.0563956384633632	-0.498379497522009
55	10.6	10.7228080853074	-3.59154720066411	-0.0564153255901948	-0.197346445341313
56	6.1	6.24910627036739	-4.32053114938478	-0.0564234588509501	-0.275490921870606

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 9.3 & 9.3 & 0 & 0 & 0 \tabularnewline
2 & 14.2 & 13.4736505704315 & 4.10528827469964 & 0.0341811489468284 & 1.68788817435418 \tabularnewline
3 & 17.3 & 17.2954307702691 & 3.87381902117338 & 0.0348488777500524 & -0.0892422670501881 \tabularnewline
4 & 23 & 22.7953445802416 & 5.21423320464757 & 0.0322877236448282 & 0.509928115872817 \tabularnewline
5 & 16.3 & 17.3813385696288 & -3.56701612664088 & 0.0357082875956243 & -3.31928107716536 \tabularnewline
6 & 18.4 & 17.9315460214604 & -0.164585710011123 & 0.0358651880480432 & 1.28582435110197 \tabularnewline
7 & 14.2 & 14.5068164740025 & -2.85875294813151 & 0.0357222557140473 & -1.01816048760667 \tabularnewline
8 & 9.1 & 9.30995685826204 & -4.79089331884082 & 0.0356951289081438 & -0.730177046530401 \tabularnewline
9 & 5.9 & 5.73640706114873 & -3.78492950094269 & 0.0356949597100448 & 0.380164645625416 \tabularnewline
10 & 7.2 & 6.66870415702367 & 0.113193227848089 & 0.0356895287162296 & 1.47314289402519 \tabularnewline
11 & 6.8 & 6.7659825299409 & 0.100041833914435 & 0.0356895348691232 & -0.00497005451087878 \tabularnewline
12 & 8 & 7.85989162567289 & 0.921333932602784 & 0.0356895102183893 & 0.310375198168052 \tabularnewline
13 & 14.3 & 13.4485867875258 & 4.72109264248952 & 0.368312663052871 & 1.54882453246819 \tabularnewline
14 & 14.6 & 14.9259110002643 & 2.36626378775062 & -0.0829124914284717 & -0.849590760451241 \tabularnewline
15 & 17.5 & 17.5563796064935 & 2.58599970783584 & -0.0837173849838232 & 0.0817094097148589 \tabularnewline
16 & 17.2 & 17.5470406895096 & 0.445429657382742 & -0.0772596839675676 & -0.804872088726869 \tabularnewline
17 & 17.2 & 17.3448569191145 & -0.0893560378111895 & -0.0768856075502051 & -0.202078262502383 \tabularnewline
18 & 14.1 & 14.4696843140624 & -2.39153556761987 & -0.076987354812468 & -0.870014716606215 \tabularnewline
19 & 10.4 & 10.6293139453037 & -3.58887668960232 & -0.0770853519865376 & -0.452486321982249 \tabularnewline
20 & 6.8 & 6.89261888343265 & -3.71103030858513 & -0.0770883107293593 & -0.0461631695082386 \tabularnewline
21 & 4.1 & 4.08244132690474 & -2.96660127030685 & -0.0770878415841244 & 0.281327813754573 \tabularnewline
22 & 6.5 & 6.05787163699064 & 1.11728876114332 & -0.0770963523468533 & 1.54334636353314 \tabularnewline
23 & 6.1 & 6.27198608230061 & 0.370942145418384 & -0.0770957674776677 & -0.282052486648814 \tabularnewline
24 & 6.3 & 6.40236960764606 & 0.172154143899226 & -0.0770957527653614 & -0.0751241433633196 \tabularnewline
25 & 9.3 & 8.13374290892933 & 1.44892022873946 & 1.00392927389707 & 0.505961325380028 \tabularnewline
26 & 16.4 & 15.8956189251827 & 6.21046591975929 & -0.0221772531843799 & 1.74806730522154 \tabularnewline
27 & 16.1 & 16.6747150620398 & 1.70140703799051 & -0.0102881228118466 & -1.68436453918366 \tabularnewline
28 & 18 & 18.0442907361596 & 1.42757350727018 & -0.0096937841099987 & -0.103109984803715 \tabularnewline
29 & 17.6 & 17.7859875759373 & 0.0351368718206689 & -0.0089932503773615 & -0.526173742409441 \tabularnewline
30 & 14 & 14.3715194464186 & -2.81556075867516 & -0.00908386898046829 & -1.07730608851385 \tabularnewline
31 & 10.5 & 10.6086605345717 & -3.59840861191378 & -0.00912995371442475 & -0.295845814747527 \tabularnewline
32 & 6.9 & 6.9187453757653 & -3.67402704265202 & -0.0091312710992513 & -0.0285770217426683 \tabularnewline
33 & 2.8 & 2.85054458620149 & -3.99975656934779 & -0.00913141874720444 & -0.123096723630126 \tabularnewline
34 & 0.7 & 0.532452665627751 & -2.61009794370234 & -0.00913350173375578 & 0.525167076433802 \tabularnewline
35 & 3.6 & 3.06846896338759 & 1.64244287730242 & -0.0091358986383216 & 1.6070813318533 \tabularnewline
36 & 6.7 & 6.51915607574973 & 3.13670346047928 & -0.00913597818123761 & 0.564697292667568 \tabularnewline
37 & 12.5 & 11.9879723736224 & 5.05123823723446 & 0.26861405482296 & 0.748990162653571 \tabularnewline
38 & 14.4 & 14.654991988634 & 3.21514326380093 & -0.0447757597081732 & -0.679503046031239 \tabularnewline
39 & 16.5 & 16.6679545416293 & 2.21811792558843 & -0.042722230881625 & -0.373391843239497 \tabularnewline
40 & 18.7 & 18.756112898119 & 2.11084037350763 & -0.0425404037489694 & -0.0404267496904691 \tabularnewline
41 & 19.4 & 19.5775170936669 & 1.04572260756571 & -0.0421220121994161 & -0.402493778657041 \tabularnewline
42 & 15.8 & 16.2967721221645 & -2.52957745133131 & -0.0422107515905544 & -1.35114128314369 \tabularnewline
43 & 11.3 & 11.5728472303135 & -4.34296811262106 & -0.0422941022549466 & -0.685298410837876 \tabularnewline
44 & 9.7 & 9.50340232652044 & -2.46419852582633 & -0.0422685460465063 & 0.710007341384477 \tabularnewline
45 & 2.9 & 3.33178318700323 & -5.52786340039032 & -0.0422696303466105 & -1.15779220910008 \tabularnewline
46 & 0.1 & -0.080045471502183 & -3.77925868818571 & -0.0422716768284112 & 0.660816698464737 \tabularnewline
47 & 2.5 & 1.93364796522073 & 1.00780330553977 & -0.0422737835600121 & 1.80908268460161 \tabularnewline
48 & 6.7 & 6.38091307868192 & 3.8500367587607 & -0.0422739016934459 & 1.07411087077608 \tabularnewline
49 & 10.3 & 9.889864978496 & 3.56962224557372 & 0.44578686329263 & -0.108894999055899 \tabularnewline
50 & 11.2 & 11.4389686457123 & 1.99312776352447 & -0.0546679883545291 & -0.586108574789652 \tabularnewline
51 & 17.4 & 17.0792613359496 & 5.01593203915044 & -0.0597760229065125 & 1.13390686985301 \tabularnewline
52 & 20.5 & 20.7036617298122 & 3.86704357078673 & -0.0581786994249454 & -0.433170802112864 \tabularnewline
53 & 17 & 17.7704874323238 & -1.75056447306111 & -0.0563687912403605 & -2.12284350851554 \tabularnewline
54 & 14.2 & 14.4240643259263 & -3.06934250130558 & -0.0563956384633632 & -0.498379497522009 \tabularnewline
55 & 10.6 & 10.7228080853074 & -3.59154720066411 & -0.0564153255901948 & -0.197346445341313 \tabularnewline
56 & 6.1 & 6.24910627036739 & -4.32053114938478 & -0.0564234588509501 & -0.275490921870606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113052&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]9.3[/C][C]9.3[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]14.2[/C][C]13.4736505704315[/C][C]4.10528827469964[/C][C]0.0341811489468284[/C][C]1.68788817435418[/C][/ROW]
[ROW][C]3[/C][C]17.3[/C][C]17.2954307702691[/C][C]3.87381902117338[/C][C]0.0348488777500524[/C][C]-0.0892422670501881[/C][/ROW]
[ROW][C]4[/C][C]23[/C][C]22.7953445802416[/C][C]5.21423320464757[/C][C]0.0322877236448282[/C][C]0.509928115872817[/C][/ROW]
[ROW][C]5[/C][C]16.3[/C][C]17.3813385696288[/C][C]-3.56701612664088[/C][C]0.0357082875956243[/C][C]-3.31928107716536[/C][/ROW]
[ROW][C]6[/C][C]18.4[/C][C]17.9315460214604[/C][C]-0.164585710011123[/C][C]0.0358651880480432[/C][C]1.28582435110197[/C][/ROW]
[ROW][C]7[/C][C]14.2[/C][C]14.5068164740025[/C][C]-2.85875294813151[/C][C]0.0357222557140473[/C][C]-1.01816048760667[/C][/ROW]
[ROW][C]8[/C][C]9.1[/C][C]9.30995685826204[/C][C]-4.79089331884082[/C][C]0.0356951289081438[/C][C]-0.730177046530401[/C][/ROW]
[ROW][C]9[/C][C]5.9[/C][C]5.73640706114873[/C][C]-3.78492950094269[/C][C]0.0356949597100448[/C][C]0.380164645625416[/C][/ROW]
[ROW][C]10[/C][C]7.2[/C][C]6.66870415702367[/C][C]0.113193227848089[/C][C]0.0356895287162296[/C][C]1.47314289402519[/C][/ROW]
[ROW][C]11[/C][C]6.8[/C][C]6.7659825299409[/C][C]0.100041833914435[/C][C]0.0356895348691232[/C][C]-0.00497005451087878[/C][/ROW]
[ROW][C]12[/C][C]8[/C][C]7.85989162567289[/C][C]0.921333932602784[/C][C]0.0356895102183893[/C][C]0.310375198168052[/C][/ROW]
[ROW][C]13[/C][C]14.3[/C][C]13.4485867875258[/C][C]4.72109264248952[/C][C]0.368312663052871[/C][C]1.54882453246819[/C][/ROW]
[ROW][C]14[/C][C]14.6[/C][C]14.9259110002643[/C][C]2.36626378775062[/C][C]-0.0829124914284717[/C][C]-0.849590760451241[/C][/ROW]
[ROW][C]15[/C][C]17.5[/C][C]17.5563796064935[/C][C]2.58599970783584[/C][C]-0.0837173849838232[/C][C]0.0817094097148589[/C][/ROW]
[ROW][C]16[/C][C]17.2[/C][C]17.5470406895096[/C][C]0.445429657382742[/C][C]-0.0772596839675676[/C][C]-0.804872088726869[/C][/ROW]
[ROW][C]17[/C][C]17.2[/C][C]17.3448569191145[/C][C]-0.0893560378111895[/C][C]-0.0768856075502051[/C][C]-0.202078262502383[/C][/ROW]
[ROW][C]18[/C][C]14.1[/C][C]14.4696843140624[/C][C]-2.39153556761987[/C][C]-0.076987354812468[/C][C]-0.870014716606215[/C][/ROW]
[ROW][C]19[/C][C]10.4[/C][C]10.6293139453037[/C][C]-3.58887668960232[/C][C]-0.0770853519865376[/C][C]-0.452486321982249[/C][/ROW]
[ROW][C]20[/C][C]6.8[/C][C]6.89261888343265[/C][C]-3.71103030858513[/C][C]-0.0770883107293593[/C][C]-0.0461631695082386[/C][/ROW]
[ROW][C]21[/C][C]4.1[/C][C]4.08244132690474[/C][C]-2.96660127030685[/C][C]-0.0770878415841244[/C][C]0.281327813754573[/C][/ROW]
[ROW][C]22[/C][C]6.5[/C][C]6.05787163699064[/C][C]1.11728876114332[/C][C]-0.0770963523468533[/C][C]1.54334636353314[/C][/ROW]
[ROW][C]23[/C][C]6.1[/C][C]6.27198608230061[/C][C]0.370942145418384[/C][C]-0.0770957674776677[/C][C]-0.282052486648814[/C][/ROW]
[ROW][C]24[/C][C]6.3[/C][C]6.40236960764606[/C][C]0.172154143899226[/C][C]-0.0770957527653614[/C][C]-0.0751241433633196[/C][/ROW]
[ROW][C]25[/C][C]9.3[/C][C]8.13374290892933[/C][C]1.44892022873946[/C][C]1.00392927389707[/C][C]0.505961325380028[/C][/ROW]
[ROW][C]26[/C][C]16.4[/C][C]15.8956189251827[/C][C]6.21046591975929[/C][C]-0.0221772531843799[/C][C]1.74806730522154[/C][/ROW]
[ROW][C]27[/C][C]16.1[/C][C]16.6747150620398[/C][C]1.70140703799051[/C][C]-0.0102881228118466[/C][C]-1.68436453918366[/C][/ROW]
[ROW][C]28[/C][C]18[/C][C]18.0442907361596[/C][C]1.42757350727018[/C][C]-0.0096937841099987[/C][C]-0.103109984803715[/C][/ROW]
[ROW][C]29[/C][C]17.6[/C][C]17.7859875759373[/C][C]0.0351368718206689[/C][C]-0.0089932503773615[/C][C]-0.526173742409441[/C][/ROW]
[ROW][C]30[/C][C]14[/C][C]14.3715194464186[/C][C]-2.81556075867516[/C][C]-0.00908386898046829[/C][C]-1.07730608851385[/C][/ROW]
[ROW][C]31[/C][C]10.5[/C][C]10.6086605345717[/C][C]-3.59840861191378[/C][C]-0.00912995371442475[/C][C]-0.295845814747527[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]6.9187453757653[/C][C]-3.67402704265202[/C][C]-0.0091312710992513[/C][C]-0.0285770217426683[/C][/ROW]
[ROW][C]33[/C][C]2.8[/C][C]2.85054458620149[/C][C]-3.99975656934779[/C][C]-0.00913141874720444[/C][C]-0.123096723630126[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]0.532452665627751[/C][C]-2.61009794370234[/C][C]-0.00913350173375578[/C][C]0.525167076433802[/C][/ROW]
[ROW][C]35[/C][C]3.6[/C][C]3.06846896338759[/C][C]1.64244287730242[/C][C]-0.0091358986383216[/C][C]1.6070813318533[/C][/ROW]
[ROW][C]36[/C][C]6.7[/C][C]6.51915607574973[/C][C]3.13670346047928[/C][C]-0.00913597818123761[/C][C]0.564697292667568[/C][/ROW]
[ROW][C]37[/C][C]12.5[/C][C]11.9879723736224[/C][C]5.05123823723446[/C][C]0.26861405482296[/C][C]0.748990162653571[/C][/ROW]
[ROW][C]38[/C][C]14.4[/C][C]14.654991988634[/C][C]3.21514326380093[/C][C]-0.0447757597081732[/C][C]-0.679503046031239[/C][/ROW]
[ROW][C]39[/C][C]16.5[/C][C]16.6679545416293[/C][C]2.21811792558843[/C][C]-0.042722230881625[/C][C]-0.373391843239497[/C][/ROW]
[ROW][C]40[/C][C]18.7[/C][C]18.756112898119[/C][C]2.11084037350763[/C][C]-0.0425404037489694[/C][C]-0.0404267496904691[/C][/ROW]
[ROW][C]41[/C][C]19.4[/C][C]19.5775170936669[/C][C]1.04572260756571[/C][C]-0.0421220121994161[/C][C]-0.402493778657041[/C][/ROW]
[ROW][C]42[/C][C]15.8[/C][C]16.2967721221645[/C][C]-2.52957745133131[/C][C]-0.0422107515905544[/C][C]-1.35114128314369[/C][/ROW]
[ROW][C]43[/C][C]11.3[/C][C]11.5728472303135[/C][C]-4.34296811262106[/C][C]-0.0422941022549466[/C][C]-0.685298410837876[/C][/ROW]
[ROW][C]44[/C][C]9.7[/C][C]9.50340232652044[/C][C]-2.46419852582633[/C][C]-0.0422685460465063[/C][C]0.710007341384477[/C][/ROW]
[ROW][C]45[/C][C]2.9[/C][C]3.33178318700323[/C][C]-5.52786340039032[/C][C]-0.0422696303466105[/C][C]-1.15779220910008[/C][/ROW]
[ROW][C]46[/C][C]0.1[/C][C]-0.080045471502183[/C][C]-3.77925868818571[/C][C]-0.0422716768284112[/C][C]0.660816698464737[/C][/ROW]
[ROW][C]47[/C][C]2.5[/C][C]1.93364796522073[/C][C]1.00780330553977[/C][C]-0.0422737835600121[/C][C]1.80908268460161[/C][/ROW]
[ROW][C]48[/C][C]6.7[/C][C]6.38091307868192[/C][C]3.8500367587607[/C][C]-0.0422739016934459[/C][C]1.07411087077608[/C][/ROW]
[ROW][C]49[/C][C]10.3[/C][C]9.889864978496[/C][C]3.56962224557372[/C][C]0.44578686329263[/C][C]-0.108894999055899[/C][/ROW]
[ROW][C]50[/C][C]11.2[/C][C]11.4389686457123[/C][C]1.99312776352447[/C][C]-0.0546679883545291[/C][C]-0.586108574789652[/C][/ROW]
[ROW][C]51[/C][C]17.4[/C][C]17.0792613359496[/C][C]5.01593203915044[/C][C]-0.0597760229065125[/C][C]1.13390686985301[/C][/ROW]
[ROW][C]52[/C][C]20.5[/C][C]20.7036617298122[/C][C]3.86704357078673[/C][C]-0.0581786994249454[/C][C]-0.433170802112864[/C][/ROW]
[ROW][C]53[/C][C]17[/C][C]17.7704874323238[/C][C]-1.75056447306111[/C][C]-0.0563687912403605[/C][C]-2.12284350851554[/C][/ROW]
[ROW][C]54[/C][C]14.2[/C][C]14.4240643259263[/C][C]-3.06934250130558[/C][C]-0.0563956384633632[/C][C]-0.498379497522009[/C][/ROW]
[ROW][C]55[/C][C]10.6[/C][C]10.7228080853074[/C][C]-3.59154720066411[/C][C]-0.0564153255901948[/C][C]-0.197346445341313[/C][/ROW]
[ROW][C]56[/C][C]6.1[/C][C]6.24910627036739[/C][C]-4.32053114938478[/C][C]-0.0564234588509501[/C][C]-0.275490921870606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113052&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113052&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	9.3	9.3	0	0	0
2	14.2	13.4736505704315	4.10528827469964	0.0341811489468284	1.68788817435418
3	17.3	17.2954307702691	3.87381902117338	0.0348488777500524	-0.0892422670501881
4	23	22.7953445802416	5.21423320464757	0.0322877236448282	0.509928115872817
5	16.3	17.3813385696288	-3.56701612664088	0.0357082875956243	-3.31928107716536
6	18.4	17.9315460214604	-0.164585710011123	0.0358651880480432	1.28582435110197
7	14.2	14.5068164740025	-2.85875294813151	0.0357222557140473	-1.01816048760667
8	9.1	9.30995685826204	-4.79089331884082	0.0356951289081438	-0.730177046530401
9	5.9	5.73640706114873	-3.78492950094269	0.0356949597100448	0.380164645625416
10	7.2	6.66870415702367	0.113193227848089	0.0356895287162296	1.47314289402519
11	6.8	6.7659825299409	0.100041833914435	0.0356895348691232	-0.00497005451087878
12	8	7.85989162567289	0.921333932602784	0.0356895102183893	0.310375198168052
13	14.3	13.4485867875258	4.72109264248952	0.368312663052871	1.54882453246819
14	14.6	14.9259110002643	2.36626378775062	-0.0829124914284717	-0.849590760451241
15	17.5	17.5563796064935	2.58599970783584	-0.0837173849838232	0.0817094097148589
16	17.2	17.5470406895096	0.445429657382742	-0.0772596839675676	-0.804872088726869
17	17.2	17.3448569191145	-0.0893560378111895	-0.0768856075502051	-0.202078262502383
18	14.1	14.4696843140624	-2.39153556761987	-0.076987354812468	-0.870014716606215
19	10.4	10.6293139453037	-3.58887668960232	-0.0770853519865376	-0.452486321982249
20	6.8	6.89261888343265	-3.71103030858513	-0.0770883107293593	-0.0461631695082386
21	4.1	4.08244132690474	-2.96660127030685	-0.0770878415841244	0.281327813754573
22	6.5	6.05787163699064	1.11728876114332	-0.0770963523468533	1.54334636353314
23	6.1	6.27198608230061	0.370942145418384	-0.0770957674776677	-0.282052486648814
24	6.3	6.40236960764606	0.172154143899226	-0.0770957527653614	-0.0751241433633196
25	9.3	8.13374290892933	1.44892022873946	1.00392927389707	0.505961325380028
26	16.4	15.8956189251827	6.21046591975929	-0.0221772531843799	1.74806730522154
27	16.1	16.6747150620398	1.70140703799051	-0.0102881228118466	-1.68436453918366
28	18	18.0442907361596	1.42757350727018	-0.0096937841099987	-0.103109984803715
29	17.6	17.7859875759373	0.0351368718206689	-0.0089932503773615	-0.526173742409441
30	14	14.3715194464186	-2.81556075867516	-0.00908386898046829	-1.07730608851385
31	10.5	10.6086605345717	-3.59840861191378	-0.00912995371442475	-0.295845814747527
32	6.9	6.9187453757653	-3.67402704265202	-0.0091312710992513	-0.0285770217426683
33	2.8	2.85054458620149	-3.99975656934779	-0.00913141874720444	-0.123096723630126
34	0.7	0.532452665627751	-2.61009794370234	-0.00913350173375578	0.525167076433802
35	3.6	3.06846896338759	1.64244287730242	-0.0091358986383216	1.6070813318533
36	6.7	6.51915607574973	3.13670346047928	-0.00913597818123761	0.564697292667568
37	12.5	11.9879723736224	5.05123823723446	0.26861405482296	0.748990162653571
38	14.4	14.654991988634	3.21514326380093	-0.0447757597081732	-0.679503046031239
39	16.5	16.6679545416293	2.21811792558843	-0.042722230881625	-0.373391843239497
40	18.7	18.756112898119	2.11084037350763	-0.0425404037489694	-0.0404267496904691
41	19.4	19.5775170936669	1.04572260756571	-0.0421220121994161	-0.402493778657041
42	15.8	16.2967721221645	-2.52957745133131	-0.0422107515905544	-1.35114128314369
43	11.3	11.5728472303135	-4.34296811262106	-0.0422941022549466	-0.685298410837876
44	9.7	9.50340232652044	-2.46419852582633	-0.0422685460465063	0.710007341384477
45	2.9	3.33178318700323	-5.52786340039032	-0.0422696303466105	-1.15779220910008
46	0.1	-0.080045471502183	-3.77925868818571	-0.0422716768284112	0.660816698464737
47	2.5	1.93364796522073	1.00780330553977	-0.0422737835600121	1.80908268460161
48	6.7	6.38091307868192	3.8500367587607	-0.0422739016934459	1.07411087077608
49	10.3	9.889864978496	3.56962224557372	0.44578686329263	-0.108894999055899
50	11.2	11.4389686457123	1.99312776352447	-0.0546679883545291	-0.586108574789652
51	17.4	17.0792613359496	5.01593203915044	-0.0597760229065125	1.13390686985301
52	20.5	20.7036617298122	3.86704357078673	-0.0581786994249454	-0.433170802112864
53	17	17.7704874323238	-1.75056447306111	-0.0563687912403605	-2.12284350851554
54	14.2	14.4240643259263	-3.06934250130558	-0.0563956384633632	-0.498379497522009
55	10.6	10.7228080853074	-3.59154720066411	-0.0564153255901948	-0.197346445341313
56	6.1	6.24910627036739	-4.32053114938478	-0.0564234588509501	-0.275490921870606

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