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R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Fri, 04 Dec 2009 12:54:39 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259956546q4nqzesrcfcbbai.htm/, Retrieved Tue, 10 Feb 2026 19:41:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64111, Retrieved Tue, 10 Feb 2026 19:41:07 +0000

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Estimated Impact

347

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]
- R  D    [Structural Time Series Models] [] [2009-12-03 18:24:15] [fa44bc1b850de3469c0e3e9a5981c418]
-    D        [Structural Time Series Models] [Structural time s...] [2009-12-04 19:54:39] [95bc1f3b1182fbde76c5a24f1f253203] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64111&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]1 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=64111&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64111&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	19	19	0	0	0
2	18	18.1108869988334	-0.051231097300266	-0.0512310975556439	-0.200626530440003
3	19	18.9004944082692	-0.0398278045332988	-0.0398278045332993	0.305317779906727
4	19	19.0130083739769	-0.0387673174784865	-0.0387673174784865	0.0558017298893943
5	22	21.5816274608516	-0.0231613156477001	-0.0231613156477002	0.955488215616181
6	23	22.8048158117019	-0.0159126167790224	-0.0159126167790226	0.456747429571069
7	20	20.4291933373491	-0.0295117081831036	-0.0295117081831038	-0.864754732546442
8	14	14.9787506804773	-0.0605586504685541	-0.0605586504685542	-1.98657023864225
9	14	14.1883374202623	-0.0647146027942089	-0.0647146027942088	-0.267461831052249
10	14	14.0734899979576	-0.0649984508668466	-0.0649984508668466	-0.0183714315332262
11	15	14.9076372112654	-0.0599362284161829	-0.059936228416183	0.329493139930105
12	11	11.6240202077550	-0.0779840534106643	-0.0779840534106638	-1.18130993359118
13	17	14.1818883581347	-0.215206807423069	2.36727488408787	1.18240948626271
14	16	15.9234675080638	-0.163118067413767	-0.163118068548667	0.6029756395653
15	20	19.5104961529234	-0.139743618970718	-0.139743618970719	1.36721031481802
16	24	23.4378945844903	-0.126594440155188	-0.126594440155188	1.48864076745306
17	23	23.1537340304521	-0.127034667374350	-0.127034667374350	-0.0576835873659201
18	20	20.5529785008708	-0.133773463631006	-0.133773463631006	-0.905625815193748
19	21	21.0288148620954	-0.132122767105274	-0.132122767105273	0.223177467762196
20	19	19.3912991965062	-0.136186099490365	-0.136186099490366	-0.551121555475307
21	23	22.5661621676204	-0.127273647106577	-0.127273647106577	1.21216611578203
22	23	23.0261721454294	-0.125697097346314	-0.125697097346314	0.215002437889736
23	23	23.0926204103863	-0.125182669142621	-0.125182669142621	0.0703435644992861
24	23	23.1020166422713	-0.124823324997941	-0.124823324997940	0.0492686224335875
25	27	24.813743856618	-0.170324774837437	1.87357252721930	0.747681575636689
26	26	25.9640351458097	-0.147401698739636	-0.147401702017821	0.434638135554451
27	17	18.4225733035037	-0.177377590719308	-0.177377590719307	-2.69880043671563
28	24	23.3088895353951	-0.166710614046131	-0.166710614046129	1.85296511339913
29	26	25.7243704807678	-0.162004721025879	-0.162004721025879	0.945031693393256
30	24	24.3667736706542	-0.164131260759238	-0.164131260759239	-0.437569293181091
31	27	26.7311014851556	-0.159656812215594	-0.159656812215593	0.925380102187874
32	27	27.0736498418047	-0.158770088205344	-0.158770088205345	0.183799821206169
33	26	26.2693249146466	-0.159907830926560	-0.159907830926559	-0.23626349252131
34	24	24.4449516761456	-0.162836137744504	-0.162836137744503	-0.609169023074157
35	23	23.326487029547	-0.164514427257566	-0.164514427257565	-0.349745143263629
36	23	23.1641427901844	-0.164510622622709	-0.164510622622707	0.000794254146383672
37	24	22.3996663722857	-0.154757675496872	1.70233443029569	-0.235995945432381
38	17	17.8555214912224	-0.211281772688481	-0.211281774705440	-1.48747864115771
39	21	20.6885603225443	-0.202136810370800	-0.202136810370798	1.11177867158714
40	19	19.3896836800057	-0.203850179065471	-0.203850179065470	-0.401286596692104
41	22	21.7634623739253	-0.200364583841613	-0.200364583841614	0.943223462991855
42	22	22.1073863965383	-0.199645920035348	-0.199645920035348	0.199171826098259
43	18	18.7406488578405	-0.203808368649554	-0.203808368649553	-1.15893662772088
44	16	16.5441890055514	-0.206422580280858	-0.206422580280858	-0.729172455501753
45	14	14.5173749489054	-0.208807504442529	-0.208807504442529	-0.666136864396173
46	12	12.5151493740287	-0.211153992432317	-0.211153992432317	-0.656266102712891
47	14	13.9329137669097	-0.209025521960652	-0.209025521960652	0.596070339424432
48	16	15.8464655201049	-0.206255618643653	-0.206255618643651	0.776714571134126
49	8	8.03514433471271	-0.114262851701417	1.25689137184811	-2.93909960858519
50	3	3.78323541200469	-0.156613578762039	-0.156613583824149	-1.42555589150619
51	0	0.663991842963106	-0.163682187017350	-0.163682187017348	-1.08229674760542
52	5	4.48370083080553	-0.158736990329350	-0.158736990329348	1.45738813912598
53	1	1.62013270355226	-0.161644462252316	-0.161644462252317	-0.98968450708988
54	1	1.20489755816989	-0.161910699284411	-0.161910699284411	-0.0927883578614771
55	3	2.85316816971688	-0.160018502727007	-0.160018502727007	0.662342510925763
56	6	5.65487429964198	-0.156927305944377	-0.156927305944378	1.08369020628696
57	7	6.91520497503423	-0.155449737473623	-0.155449737473623	0.518572207386821
58	8	7.95209064425682	-0.154207970164030	-0.15420797016403	0.436273277376316
59	14	13.2280670938837	-0.148558552781648	-0.148558552781648	1.98689353198937
60	14	13.9927947018899	-0.147609382190291	-0.147609382190292	0.334169445813131
61	13	11.9099693457891	-0.128970020093468	1.41867022554141	-0.739898804466961

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 19 & 19 & 0 & 0 & 0 \tabularnewline
2 & 18 & 18.1108869988334 & -0.051231097300266 & -0.0512310975556439 & -0.200626530440003 \tabularnewline
3 & 19 & 18.9004944082692 & -0.0398278045332988 & -0.0398278045332993 & 0.305317779906727 \tabularnewline
4 & 19 & 19.0130083739769 & -0.0387673174784865 & -0.0387673174784865 & 0.0558017298893943 \tabularnewline
5 & 22 & 21.5816274608516 & -0.0231613156477001 & -0.0231613156477002 & 0.955488215616181 \tabularnewline
6 & 23 & 22.8048158117019 & -0.0159126167790224 & -0.0159126167790226 & 0.456747429571069 \tabularnewline
7 & 20 & 20.4291933373491 & -0.0295117081831036 & -0.0295117081831038 & -0.864754732546442 \tabularnewline
8 & 14 & 14.9787506804773 & -0.0605586504685541 & -0.0605586504685542 & -1.98657023864225 \tabularnewline
9 & 14 & 14.1883374202623 & -0.0647146027942089 & -0.0647146027942088 & -0.267461831052249 \tabularnewline
10 & 14 & 14.0734899979576 & -0.0649984508668466 & -0.0649984508668466 & -0.0183714315332262 \tabularnewline
11 & 15 & 14.9076372112654 & -0.0599362284161829 & -0.059936228416183 & 0.329493139930105 \tabularnewline
12 & 11 & 11.6240202077550 & -0.0779840534106643 & -0.0779840534106638 & -1.18130993359118 \tabularnewline
13 & 17 & 14.1818883581347 & -0.215206807423069 & 2.36727488408787 & 1.18240948626271 \tabularnewline
14 & 16 & 15.9234675080638 & -0.163118067413767 & -0.163118068548667 & 0.6029756395653 \tabularnewline
15 & 20 & 19.5104961529234 & -0.139743618970718 & -0.139743618970719 & 1.36721031481802 \tabularnewline
16 & 24 & 23.4378945844903 & -0.126594440155188 & -0.126594440155188 & 1.48864076745306 \tabularnewline
17 & 23 & 23.1537340304521 & -0.127034667374350 & -0.127034667374350 & -0.0576835873659201 \tabularnewline
18 & 20 & 20.5529785008708 & -0.133773463631006 & -0.133773463631006 & -0.905625815193748 \tabularnewline
19 & 21 & 21.0288148620954 & -0.132122767105274 & -0.132122767105273 & 0.223177467762196 \tabularnewline
20 & 19 & 19.3912991965062 & -0.136186099490365 & -0.136186099490366 & -0.551121555475307 \tabularnewline
21 & 23 & 22.5661621676204 & -0.127273647106577 & -0.127273647106577 & 1.21216611578203 \tabularnewline
22 & 23 & 23.0261721454294 & -0.125697097346314 & -0.125697097346314 & 0.215002437889736 \tabularnewline
23 & 23 & 23.0926204103863 & -0.125182669142621 & -0.125182669142621 & 0.0703435644992861 \tabularnewline
24 & 23 & 23.1020166422713 & -0.124823324997941 & -0.124823324997940 & 0.0492686224335875 \tabularnewline
25 & 27 & 24.813743856618 & -0.170324774837437 & 1.87357252721930 & 0.747681575636689 \tabularnewline
26 & 26 & 25.9640351458097 & -0.147401698739636 & -0.147401702017821 & 0.434638135554451 \tabularnewline
27 & 17 & 18.4225733035037 & -0.177377590719308 & -0.177377590719307 & -2.69880043671563 \tabularnewline
28 & 24 & 23.3088895353951 & -0.166710614046131 & -0.166710614046129 & 1.85296511339913 \tabularnewline
29 & 26 & 25.7243704807678 & -0.162004721025879 & -0.162004721025879 & 0.945031693393256 \tabularnewline
30 & 24 & 24.3667736706542 & -0.164131260759238 & -0.164131260759239 & -0.437569293181091 \tabularnewline
31 & 27 & 26.7311014851556 & -0.159656812215594 & -0.159656812215593 & 0.925380102187874 \tabularnewline
32 & 27 & 27.0736498418047 & -0.158770088205344 & -0.158770088205345 & 0.183799821206169 \tabularnewline
33 & 26 & 26.2693249146466 & -0.159907830926560 & -0.159907830926559 & -0.23626349252131 \tabularnewline
34 & 24 & 24.4449516761456 & -0.162836137744504 & -0.162836137744503 & -0.609169023074157 \tabularnewline
35 & 23 & 23.326487029547 & -0.164514427257566 & -0.164514427257565 & -0.349745143263629 \tabularnewline
36 & 23 & 23.1641427901844 & -0.164510622622709 & -0.164510622622707 & 0.000794254146383672 \tabularnewline
37 & 24 & 22.3996663722857 & -0.154757675496872 & 1.70233443029569 & -0.235995945432381 \tabularnewline
38 & 17 & 17.8555214912224 & -0.211281772688481 & -0.211281774705440 & -1.48747864115771 \tabularnewline
39 & 21 & 20.6885603225443 & -0.202136810370800 & -0.202136810370798 & 1.11177867158714 \tabularnewline
40 & 19 & 19.3896836800057 & -0.203850179065471 & -0.203850179065470 & -0.401286596692104 \tabularnewline
41 & 22 & 21.7634623739253 & -0.200364583841613 & -0.200364583841614 & 0.943223462991855 \tabularnewline
42 & 22 & 22.1073863965383 & -0.199645920035348 & -0.199645920035348 & 0.199171826098259 \tabularnewline
43 & 18 & 18.7406488578405 & -0.203808368649554 & -0.203808368649553 & -1.15893662772088 \tabularnewline
44 & 16 & 16.5441890055514 & -0.206422580280858 & -0.206422580280858 & -0.729172455501753 \tabularnewline
45 & 14 & 14.5173749489054 & -0.208807504442529 & -0.208807504442529 & -0.666136864396173 \tabularnewline
46 & 12 & 12.5151493740287 & -0.211153992432317 & -0.211153992432317 & -0.656266102712891 \tabularnewline
47 & 14 & 13.9329137669097 & -0.209025521960652 & -0.209025521960652 & 0.596070339424432 \tabularnewline
48 & 16 & 15.8464655201049 & -0.206255618643653 & -0.206255618643651 & 0.776714571134126 \tabularnewline
49 & 8 & 8.03514433471271 & -0.114262851701417 & 1.25689137184811 & -2.93909960858519 \tabularnewline
50 & 3 & 3.78323541200469 & -0.156613578762039 & -0.156613583824149 & -1.42555589150619 \tabularnewline
51 & 0 & 0.663991842963106 & -0.163682187017350 & -0.163682187017348 & -1.08229674760542 \tabularnewline
52 & 5 & 4.48370083080553 & -0.158736990329350 & -0.158736990329348 & 1.45738813912598 \tabularnewline
53 & 1 & 1.62013270355226 & -0.161644462252316 & -0.161644462252317 & -0.98968450708988 \tabularnewline
54 & 1 & 1.20489755816989 & -0.161910699284411 & -0.161910699284411 & -0.0927883578614771 \tabularnewline
55 & 3 & 2.85316816971688 & -0.160018502727007 & -0.160018502727007 & 0.662342510925763 \tabularnewline
56 & 6 & 5.65487429964198 & -0.156927305944377 & -0.156927305944378 & 1.08369020628696 \tabularnewline
57 & 7 & 6.91520497503423 & -0.155449737473623 & -0.155449737473623 & 0.518572207386821 \tabularnewline
58 & 8 & 7.95209064425682 & -0.154207970164030 & -0.15420797016403 & 0.436273277376316 \tabularnewline
59 & 14 & 13.2280670938837 & -0.148558552781648 & -0.148558552781648 & 1.98689353198937 \tabularnewline
60 & 14 & 13.9927947018899 & -0.147609382190291 & -0.147609382190292 & 0.334169445813131 \tabularnewline
61 & 13 & 11.9099693457891 & -0.128970020093468 & 1.41867022554141 & -0.739898804466961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64111&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]19[/C][C]19[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]18[/C][C]18.1108869988334[/C][C]-0.051231097300266[/C][C]-0.0512310975556439[/C][C]-0.200626530440003[/C][/ROW]
[ROW][C]3[/C][C]19[/C][C]18.9004944082692[/C][C]-0.0398278045332988[/C][C]-0.0398278045332993[/C][C]0.305317779906727[/C][/ROW]
[ROW][C]4[/C][C]19[/C][C]19.0130083739769[/C][C]-0.0387673174784865[/C][C]-0.0387673174784865[/C][C]0.0558017298893943[/C][/ROW]
[ROW][C]5[/C][C]22[/C][C]21.5816274608516[/C][C]-0.0231613156477001[/C][C]-0.0231613156477002[/C][C]0.955488215616181[/C][/ROW]
[ROW][C]6[/C][C]23[/C][C]22.8048158117019[/C][C]-0.0159126167790224[/C][C]-0.0159126167790226[/C][C]0.456747429571069[/C][/ROW]
[ROW][C]7[/C][C]20[/C][C]20.4291933373491[/C][C]-0.0295117081831036[/C][C]-0.0295117081831038[/C][C]-0.864754732546442[/C][/ROW]
[ROW][C]8[/C][C]14[/C][C]14.9787506804773[/C][C]-0.0605586504685541[/C][C]-0.0605586504685542[/C][C]-1.98657023864225[/C][/ROW]
[ROW][C]9[/C][C]14[/C][C]14.1883374202623[/C][C]-0.0647146027942089[/C][C]-0.0647146027942088[/C][C]-0.267461831052249[/C][/ROW]
[ROW][C]10[/C][C]14[/C][C]14.0734899979576[/C][C]-0.0649984508668466[/C][C]-0.0649984508668466[/C][C]-0.0183714315332262[/C][/ROW]
[ROW][C]11[/C][C]15[/C][C]14.9076372112654[/C][C]-0.0599362284161829[/C][C]-0.059936228416183[/C][C]0.329493139930105[/C][/ROW]
[ROW][C]12[/C][C]11[/C][C]11.6240202077550[/C][C]-0.0779840534106643[/C][C]-0.0779840534106638[/C][C]-1.18130993359118[/C][/ROW]
[ROW][C]13[/C][C]17[/C][C]14.1818883581347[/C][C]-0.215206807423069[/C][C]2.36727488408787[/C][C]1.18240948626271[/C][/ROW]
[ROW][C]14[/C][C]16[/C][C]15.9234675080638[/C][C]-0.163118067413767[/C][C]-0.163118068548667[/C][C]0.6029756395653[/C][/ROW]
[ROW][C]15[/C][C]20[/C][C]19.5104961529234[/C][C]-0.139743618970718[/C][C]-0.139743618970719[/C][C]1.36721031481802[/C][/ROW]
[ROW][C]16[/C][C]24[/C][C]23.4378945844903[/C][C]-0.126594440155188[/C][C]-0.126594440155188[/C][C]1.48864076745306[/C][/ROW]
[ROW][C]17[/C][C]23[/C][C]23.1537340304521[/C][C]-0.127034667374350[/C][C]-0.127034667374350[/C][C]-0.0576835873659201[/C][/ROW]
[ROW][C]18[/C][C]20[/C][C]20.5529785008708[/C][C]-0.133773463631006[/C][C]-0.133773463631006[/C][C]-0.905625815193748[/C][/ROW]
[ROW][C]19[/C][C]21[/C][C]21.0288148620954[/C][C]-0.132122767105274[/C][C]-0.132122767105273[/C][C]0.223177467762196[/C][/ROW]
[ROW][C]20[/C][C]19[/C][C]19.3912991965062[/C][C]-0.136186099490365[/C][C]-0.136186099490366[/C][C]-0.551121555475307[/C][/ROW]
[ROW][C]21[/C][C]23[/C][C]22.5661621676204[/C][C]-0.127273647106577[/C][C]-0.127273647106577[/C][C]1.21216611578203[/C][/ROW]
[ROW][C]22[/C][C]23[/C][C]23.0261721454294[/C][C]-0.125697097346314[/C][C]-0.125697097346314[/C][C]0.215002437889736[/C][/ROW]
[ROW][C]23[/C][C]23[/C][C]23.0926204103863[/C][C]-0.125182669142621[/C][C]-0.125182669142621[/C][C]0.0703435644992861[/C][/ROW]
[ROW][C]24[/C][C]23[/C][C]23.1020166422713[/C][C]-0.124823324997941[/C][C]-0.124823324997940[/C][C]0.0492686224335875[/C][/ROW]
[ROW][C]25[/C][C]27[/C][C]24.813743856618[/C][C]-0.170324774837437[/C][C]1.87357252721930[/C][C]0.747681575636689[/C][/ROW]
[ROW][C]26[/C][C]26[/C][C]25.9640351458097[/C][C]-0.147401698739636[/C][C]-0.147401702017821[/C][C]0.434638135554451[/C][/ROW]
[ROW][C]27[/C][C]17[/C][C]18.4225733035037[/C][C]-0.177377590719308[/C][C]-0.177377590719307[/C][C]-2.69880043671563[/C][/ROW]
[ROW][C]28[/C][C]24[/C][C]23.3088895353951[/C][C]-0.166710614046131[/C][C]-0.166710614046129[/C][C]1.85296511339913[/C][/ROW]
[ROW][C]29[/C][C]26[/C][C]25.7243704807678[/C][C]-0.162004721025879[/C][C]-0.162004721025879[/C][C]0.945031693393256[/C][/ROW]
[ROW][C]30[/C][C]24[/C][C]24.3667736706542[/C][C]-0.164131260759238[/C][C]-0.164131260759239[/C][C]-0.437569293181091[/C][/ROW]
[ROW][C]31[/C][C]27[/C][C]26.7311014851556[/C][C]-0.159656812215594[/C][C]-0.159656812215593[/C][C]0.925380102187874[/C][/ROW]
[ROW][C]32[/C][C]27[/C][C]27.0736498418047[/C][C]-0.158770088205344[/C][C]-0.158770088205345[/C][C]0.183799821206169[/C][/ROW]
[ROW][C]33[/C][C]26[/C][C]26.2693249146466[/C][C]-0.159907830926560[/C][C]-0.159907830926559[/C][C]-0.23626349252131[/C][/ROW]
[ROW][C]34[/C][C]24[/C][C]24.4449516761456[/C][C]-0.162836137744504[/C][C]-0.162836137744503[/C][C]-0.609169023074157[/C][/ROW]
[ROW][C]35[/C][C]23[/C][C]23.326487029547[/C][C]-0.164514427257566[/C][C]-0.164514427257565[/C][C]-0.349745143263629[/C][/ROW]
[ROW][C]36[/C][C]23[/C][C]23.1641427901844[/C][C]-0.164510622622709[/C][C]-0.164510622622707[/C][C]0.000794254146383672[/C][/ROW]
[ROW][C]37[/C][C]24[/C][C]22.3996663722857[/C][C]-0.154757675496872[/C][C]1.70233443029569[/C][C]-0.235995945432381[/C][/ROW]
[ROW][C]38[/C][C]17[/C][C]17.8555214912224[/C][C]-0.211281772688481[/C][C]-0.211281774705440[/C][C]-1.48747864115771[/C][/ROW]
[ROW][C]39[/C][C]21[/C][C]20.6885603225443[/C][C]-0.202136810370800[/C][C]-0.202136810370798[/C][C]1.11177867158714[/C][/ROW]
[ROW][C]40[/C][C]19[/C][C]19.3896836800057[/C][C]-0.203850179065471[/C][C]-0.203850179065470[/C][C]-0.401286596692104[/C][/ROW]
[ROW][C]41[/C][C]22[/C][C]21.7634623739253[/C][C]-0.200364583841613[/C][C]-0.200364583841614[/C][C]0.943223462991855[/C][/ROW]
[ROW][C]42[/C][C]22[/C][C]22.1073863965383[/C][C]-0.199645920035348[/C][C]-0.199645920035348[/C][C]0.199171826098259[/C][/ROW]
[ROW][C]43[/C][C]18[/C][C]18.7406488578405[/C][C]-0.203808368649554[/C][C]-0.203808368649553[/C][C]-1.15893662772088[/C][/ROW]
[ROW][C]44[/C][C]16[/C][C]16.5441890055514[/C][C]-0.206422580280858[/C][C]-0.206422580280858[/C][C]-0.729172455501753[/C][/ROW]
[ROW][C]45[/C][C]14[/C][C]14.5173749489054[/C][C]-0.208807504442529[/C][C]-0.208807504442529[/C][C]-0.666136864396173[/C][/ROW]
[ROW][C]46[/C][C]12[/C][C]12.5151493740287[/C][C]-0.211153992432317[/C][C]-0.211153992432317[/C][C]-0.656266102712891[/C][/ROW]
[ROW][C]47[/C][C]14[/C][C]13.9329137669097[/C][C]-0.209025521960652[/C][C]-0.209025521960652[/C][C]0.596070339424432[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]15.8464655201049[/C][C]-0.206255618643653[/C][C]-0.206255618643651[/C][C]0.776714571134126[/C][/ROW]
[ROW][C]49[/C][C]8[/C][C]8.03514433471271[/C][C]-0.114262851701417[/C][C]1.25689137184811[/C][C]-2.93909960858519[/C][/ROW]
[ROW][C]50[/C][C]3[/C][C]3.78323541200469[/C][C]-0.156613578762039[/C][C]-0.156613583824149[/C][C]-1.42555589150619[/C][/ROW]
[ROW][C]51[/C][C]0[/C][C]0.663991842963106[/C][C]-0.163682187017350[/C][C]-0.163682187017348[/C][C]-1.08229674760542[/C][/ROW]
[ROW][C]52[/C][C]5[/C][C]4.48370083080553[/C][C]-0.158736990329350[/C][C]-0.158736990329348[/C][C]1.45738813912598[/C][/ROW]
[ROW][C]53[/C][C]1[/C][C]1.62013270355226[/C][C]-0.161644462252316[/C][C]-0.161644462252317[/C][C]-0.98968450708988[/C][/ROW]
[ROW][C]54[/C][C]1[/C][C]1.20489755816989[/C][C]-0.161910699284411[/C][C]-0.161910699284411[/C][C]-0.0927883578614771[/C][/ROW]
[ROW][C]55[/C][C]3[/C][C]2.85316816971688[/C][C]-0.160018502727007[/C][C]-0.160018502727007[/C][C]0.662342510925763[/C][/ROW]
[ROW][C]56[/C][C]6[/C][C]5.65487429964198[/C][C]-0.156927305944377[/C][C]-0.156927305944378[/C][C]1.08369020628696[/C][/ROW]
[ROW][C]57[/C][C]7[/C][C]6.91520497503423[/C][C]-0.155449737473623[/C][C]-0.155449737473623[/C][C]0.518572207386821[/C][/ROW]
[ROW][C]58[/C][C]8[/C][C]7.95209064425682[/C][C]-0.154207970164030[/C][C]-0.15420797016403[/C][C]0.436273277376316[/C][/ROW]
[ROW][C]59[/C][C]14[/C][C]13.2280670938837[/C][C]-0.148558552781648[/C][C]-0.148558552781648[/C][C]1.98689353198937[/C][/ROW]
[ROW][C]60[/C][C]14[/C][C]13.9927947018899[/C][C]-0.147609382190291[/C][C]-0.147609382190292[/C][C]0.334169445813131[/C][/ROW]
[ROW][C]61[/C][C]13[/C][C]11.9099693457891[/C][C]-0.128970020093468[/C][C]1.41867022554141[/C][C]-0.739898804466961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64111&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64111&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	19	19	0	0	0
2	18	18.1108869988334	-0.051231097300266	-0.0512310975556439	-0.200626530440003
3	19	18.9004944082692	-0.0398278045332988	-0.0398278045332993	0.305317779906727
4	19	19.0130083739769	-0.0387673174784865	-0.0387673174784865	0.0558017298893943
5	22	21.5816274608516	-0.0231613156477001	-0.0231613156477002	0.955488215616181
6	23	22.8048158117019	-0.0159126167790224	-0.0159126167790226	0.456747429571069
7	20	20.4291933373491	-0.0295117081831036	-0.0295117081831038	-0.864754732546442
8	14	14.9787506804773	-0.0605586504685541	-0.0605586504685542	-1.98657023864225
9	14	14.1883374202623	-0.0647146027942089	-0.0647146027942088	-0.267461831052249
10	14	14.0734899979576	-0.0649984508668466	-0.0649984508668466	-0.0183714315332262
11	15	14.9076372112654	-0.0599362284161829	-0.059936228416183	0.329493139930105
12	11	11.6240202077550	-0.0779840534106643	-0.0779840534106638	-1.18130993359118
13	17	14.1818883581347	-0.215206807423069	2.36727488408787	1.18240948626271
14	16	15.9234675080638	-0.163118067413767	-0.163118068548667	0.6029756395653
15	20	19.5104961529234	-0.139743618970718	-0.139743618970719	1.36721031481802
16	24	23.4378945844903	-0.126594440155188	-0.126594440155188	1.48864076745306
17	23	23.1537340304521	-0.127034667374350	-0.127034667374350	-0.0576835873659201
18	20	20.5529785008708	-0.133773463631006	-0.133773463631006	-0.905625815193748
19	21	21.0288148620954	-0.132122767105274	-0.132122767105273	0.223177467762196
20	19	19.3912991965062	-0.136186099490365	-0.136186099490366	-0.551121555475307
21	23	22.5661621676204	-0.127273647106577	-0.127273647106577	1.21216611578203
22	23	23.0261721454294	-0.125697097346314	-0.125697097346314	0.215002437889736
23	23	23.0926204103863	-0.125182669142621	-0.125182669142621	0.0703435644992861
24	23	23.1020166422713	-0.124823324997941	-0.124823324997940	0.0492686224335875
25	27	24.813743856618	-0.170324774837437	1.87357252721930	0.747681575636689
26	26	25.9640351458097	-0.147401698739636	-0.147401702017821	0.434638135554451
27	17	18.4225733035037	-0.177377590719308	-0.177377590719307	-2.69880043671563
28	24	23.3088895353951	-0.166710614046131	-0.166710614046129	1.85296511339913
29	26	25.7243704807678	-0.162004721025879	-0.162004721025879	0.945031693393256
30	24	24.3667736706542	-0.164131260759238	-0.164131260759239	-0.437569293181091
31	27	26.7311014851556	-0.159656812215594	-0.159656812215593	0.925380102187874
32	27	27.0736498418047	-0.158770088205344	-0.158770088205345	0.183799821206169
33	26	26.2693249146466	-0.159907830926560	-0.159907830926559	-0.23626349252131
34	24	24.4449516761456	-0.162836137744504	-0.162836137744503	-0.609169023074157
35	23	23.326487029547	-0.164514427257566	-0.164514427257565	-0.349745143263629
36	23	23.1641427901844	-0.164510622622709	-0.164510622622707	0.000794254146383672
37	24	22.3996663722857	-0.154757675496872	1.70233443029569	-0.235995945432381
38	17	17.8555214912224	-0.211281772688481	-0.211281774705440	-1.48747864115771
39	21	20.6885603225443	-0.202136810370800	-0.202136810370798	1.11177867158714
40	19	19.3896836800057	-0.203850179065471	-0.203850179065470	-0.401286596692104
41	22	21.7634623739253	-0.200364583841613	-0.200364583841614	0.943223462991855
42	22	22.1073863965383	-0.199645920035348	-0.199645920035348	0.199171826098259
43	18	18.7406488578405	-0.203808368649554	-0.203808368649553	-1.15893662772088
44	16	16.5441890055514	-0.206422580280858	-0.206422580280858	-0.729172455501753
45	14	14.5173749489054	-0.208807504442529	-0.208807504442529	-0.666136864396173
46	12	12.5151493740287	-0.211153992432317	-0.211153992432317	-0.656266102712891
47	14	13.9329137669097	-0.209025521960652	-0.209025521960652	0.596070339424432
48	16	15.8464655201049	-0.206255618643653	-0.206255618643651	0.776714571134126
49	8	8.03514433471271	-0.114262851701417	1.25689137184811	-2.93909960858519
50	3	3.78323541200469	-0.156613578762039	-0.156613583824149	-1.42555589150619
51	0	0.663991842963106	-0.163682187017350	-0.163682187017348	-1.08229674760542
52	5	4.48370083080553	-0.158736990329350	-0.158736990329348	1.45738813912598
53	1	1.62013270355226	-0.161644462252316	-0.161644462252317	-0.98968450708988
54	1	1.20489755816989	-0.161910699284411	-0.161910699284411	-0.0927883578614771
55	3	2.85316816971688	-0.160018502727007	-0.160018502727007	0.662342510925763
56	6	5.65487429964198	-0.156927305944377	-0.156927305944378	1.08369020628696
57	7	6.91520497503423	-0.155449737473623	-0.155449737473623	0.518572207386821
58	8	7.95209064425682	-0.154207970164030	-0.15420797016403	0.436273277376316
59	14	13.2280670938837	-0.148558552781648	-0.148558552781648	1.98689353198937
60	14	13.9927947018899	-0.147609382190291	-0.147609382190292	0.334169445813131
61	13	11.9099693457891	-0.128970020093468	1.41867022554141	-0.739898804466961

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