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Author

*The author of this computation has been verified*

R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Fri, 11 Dec 2009 05:10:52 -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/11/t1260533524e55pxnlogqf9coh.htm/, Retrieved Sat, 02 May 2026 05:40:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66061, Retrieved Sat, 02 May 2026 05:40:28 +0000

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User-defined keywords

Estimated Impact

396

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Structural Time Series Models] [] [2009-11-27 15:02:30] [b98453cac15ba1066b407e146608df68]
-    D    [Structural Time Series Models] [workshop 9 - ad h...] [2009-12-04 10:30:46] [f1a50df816abcbb519e7637ff6b72fa0]
-    D        [Structural Time Series Models] [workshop 9 - revi...] [2009-12-11 12:10:52] [a18540c86166a2b66550d1fef0503cc2] [Current]

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Dataseries X:

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Histogram

Boxplots

5.4
5.4
5.6
5.7
5.8
5.8
5.8
5.9
6.1
6.4
6.4
6.3
6.2
6.2
6.3
6.4
6.5
6.6
6.6
6.6
6.8
7
7.2
7.3
7.5
7.6
7.6
7.7
7.7
7.7
7.7
7.6
7.7
7.9
7.9
7.9
7.8
7.6
7.4
7
7
7.2
7.5
7.8
7.8
7.7
7.6
7.6
7.5
7.5
7.6
7.6
7.9
7.6
7.5
7.5
7.6
7.7
7.8
7.9
7.9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66061&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]4 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=66061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66061&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	5.4	5.4	0	0	0
2	5.4	5.4	0	0	0
3	5.6	5.59492906224467	0.186778243748734	0.00221427715431012	1.42458337469500
4	5.7	5.70252607853967	0.111016827213531	-0.00139554471429272	-0.570862247186259
5	5.8	5.80008927511991	0.0981409066347055	0.000102955835649726	-0.0970457396502012
6	5.8	5.80235207494681	0.00637655182629163	-0.000982115106944923	-0.69161815226378
7	5.8	5.79992580436382	-0.0020485221601655	0.000199974492124871	-0.0634988920090417
8	5.9	5.89743696070077	0.0932387481502883	0.00114048519531547	0.7181700750304
9	6.1	6.09755551667313	0.195532040049441	0.000917335558287218	0.770973718620297
10	6.4	6.39763481100681	0.295592877760667	0.000871369777945345	0.754147947587207
11	6.4	6.40747016793218	0.0220980170669061	-0.00338713317532346	-2.06130182982399
12	6.3	6.30237985010868	-0.099632308005343	-0.000562524741128899	-0.917468581237651
13	6.2	6.19902993875199	-0.103182513573111	0.00102306265612186	-0.0270898119053488
14	6.2	6.20013575468071	-0.00702524368577775	-0.00150880414386178	0.723733395498135
15	6.3	6.29335051725193	0.0879427323860012	0.00526691770730597	0.713000940592935
16	6.4	6.40165290372803	0.107185462175953	-0.00193407170385801	0.144935730386198
17	6.5	6.49884986214798	0.0977396072453852	0.00128834281056557	-0.0711934804822539
18	6.6	6.5996970274486	0.100678456729547	0.000259974724853204	0.0221497777472345
19	6.6	6.60338484512448	0.00895520589438013	-0.00204285472685143	-0.691308465887857
20	6.6	6.59881426253884	-0.00383599856638569	0.00137288381643899	-0.0964059544292592
21	6.8	6.79609425770665	0.186357444232509	0.00112304813995894	1.43346786040070
22	7	6.99611219313887	0.199276059584364	0.00369879637410487	0.09736623693722
23	7.2	7.20123040203931	0.204801056751968	-0.00131123751204656	0.0416413826691433
24	7.3	7.30297255889833	0.107350482078810	-0.00154679298410702	-0.734488431525079
25	7.5	7.49742654516942	0.189629100090806	0.00136866908338301	0.625796016197485
26	7.6	7.60703199949395	0.116016038872831	-0.00598900387268696	-0.553974498406099
27	7.6	7.60014948336185	0.000630647335701798	0.00151138029593659	-0.867864757490339
28	7.7	7.697293118246	0.0910610194924145	0.00140463339607679	0.680954470032129
29	7.7	7.70464141272945	0.0125802444187983	-0.00350924567481978	-0.591513393392292
30	7.7	7.69826377207266	-0.00519432183834172	0.00199263523332874	-0.133964660063898
31	7.7	7.69842050660236	-0.000177414621978083	0.00150712154214752	0.037811903148499
32	7.6	7.6079138855999	-0.0848654138004662	-0.00669221133973031	-0.638284477413956
33	7.7	7.69233302868732	0.0738470560132779	0.00537745036201355	1.19619912826708
34	7.9	7.89430433410102	0.193970989304979	0.00396280759871149	0.905361423552947
35	7.9	7.90518505650615	0.0223077825633996	-0.00270871075913092	-1.29381480943853
36	7.9	7.90538476002576	0.00158615846250746	-0.00508585652124643	-0.156192584076223
37	7.8	7.80163330806544	-0.0971475180939086	-0.000206986290705274	-0.748851785082806
38	7.6	7.60293755832055	-0.190476204578409	-0.00162045759966602	-0.702411224447467
39	7.4	7.40363111443934	-0.198714039820923	-0.00351341290785465	-0.062039334267044
40	7	7.00404497532107	-0.385837040293015	-0.00137521949952675	-1.40884139874126
41	7	6.98630874439361	-0.0427767195160832	0.0087870800554346	2.58566111656610
42	7.2	7.19129158744361	0.188163429262786	0.00540711354479786	1.74056265310308
43	7.5	7.48853574444534	0.289835947444405	0.0100108306524826	0.766295107050017
44	7.8	7.80985414041975	0.319179828001152	-0.0102736158529113	0.221161713028408
45	7.8	7.81647675151408	0.0278539810744289	-0.0123122017393184	-2.19569223430684
46	7.7	7.69431319402758	-0.111976366329345	0.00768570205743901	-1.05388731292599
47	7.6	7.60183556242515	-0.0938014117586268	-0.00209537713186450	0.136983655418038
48	7.6	7.59872646065476	-0.00930513963389062	6.57712675868477e-05	0.636988803157634
49	7.5	7.50101968344662	-0.0917198423608942	0.000160284299135285	-0.623779211866528
50	7.5	7.5022558913517	-0.00631540265347379	-0.00345880529299559	0.642892908591166
51	7.6	7.58286193807387	0.0744182522217325	0.0159900833287319	0.608485940145603
52	7.6	7.61388978368848	0.0341521149609615	-0.0133185409214909	-0.303144393414934
53	7.9	7.88781710451507	0.256725468936608	0.0090192529231363	1.67752712011016
54	7.6	7.62245678993505	-0.228009411016664	-0.0155666882137413	-3.65337255024858
55	7.5	7.4922631519282	-0.137193784208280	0.0064459696577424	0.684467621822883
56	7.5	7.49330159412482	-0.00885709677260038	0.00487419117958781	0.96725999751738
57	7.6	7.60037912811503	0.0987785429623711	-0.00190909233294563	0.81123846432232
58	7.7	7.6923737559083	0.0924800394378096	0.0077157727802329	-0.0474712782275398
59	7.8	7.80706340727148	0.113100172953108	-0.00735650833255159	0.155412221241903
60	7.9	7.89542768843735	0.0901464748783864	0.00489855096200324	-0.173063731784843
61	7.9	7.90713747032916	0.0172968737823766	-0.00610054118703283	-0.550585766746228

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 5.4 & 5.4 & 0 & 0 & 0 \tabularnewline
2 & 5.4 & 5.4 & 0 & 0 & 0 \tabularnewline
3 & 5.6 & 5.59492906224467 & 0.186778243748734 & 0.00221427715431012 & 1.42458337469500 \tabularnewline
4 & 5.7 & 5.70252607853967 & 0.111016827213531 & -0.00139554471429272 & -0.570862247186259 \tabularnewline
5 & 5.8 & 5.80008927511991 & 0.0981409066347055 & 0.000102955835649726 & -0.0970457396502012 \tabularnewline
6 & 5.8 & 5.80235207494681 & 0.00637655182629163 & -0.000982115106944923 & -0.69161815226378 \tabularnewline
7 & 5.8 & 5.79992580436382 & -0.0020485221601655 & 0.000199974492124871 & -0.0634988920090417 \tabularnewline
8 & 5.9 & 5.89743696070077 & 0.0932387481502883 & 0.00114048519531547 & 0.7181700750304 \tabularnewline
9 & 6.1 & 6.09755551667313 & 0.195532040049441 & 0.000917335558287218 & 0.770973718620297 \tabularnewline
10 & 6.4 & 6.39763481100681 & 0.295592877760667 & 0.000871369777945345 & 0.754147947587207 \tabularnewline
11 & 6.4 & 6.40747016793218 & 0.0220980170669061 & -0.00338713317532346 & -2.06130182982399 \tabularnewline
12 & 6.3 & 6.30237985010868 & -0.099632308005343 & -0.000562524741128899 & -0.917468581237651 \tabularnewline
13 & 6.2 & 6.19902993875199 & -0.103182513573111 & 0.00102306265612186 & -0.0270898119053488 \tabularnewline
14 & 6.2 & 6.20013575468071 & -0.00702524368577775 & -0.00150880414386178 & 0.723733395498135 \tabularnewline
15 & 6.3 & 6.29335051725193 & 0.0879427323860012 & 0.00526691770730597 & 0.713000940592935 \tabularnewline
16 & 6.4 & 6.40165290372803 & 0.107185462175953 & -0.00193407170385801 & 0.144935730386198 \tabularnewline
17 & 6.5 & 6.49884986214798 & 0.0977396072453852 & 0.00128834281056557 & -0.0711934804822539 \tabularnewline
18 & 6.6 & 6.5996970274486 & 0.100678456729547 & 0.000259974724853204 & 0.0221497777472345 \tabularnewline
19 & 6.6 & 6.60338484512448 & 0.00895520589438013 & -0.00204285472685143 & -0.691308465887857 \tabularnewline
20 & 6.6 & 6.59881426253884 & -0.00383599856638569 & 0.00137288381643899 & -0.0964059544292592 \tabularnewline
21 & 6.8 & 6.79609425770665 & 0.186357444232509 & 0.00112304813995894 & 1.43346786040070 \tabularnewline
22 & 7 & 6.99611219313887 & 0.199276059584364 & 0.00369879637410487 & 0.09736623693722 \tabularnewline
23 & 7.2 & 7.20123040203931 & 0.204801056751968 & -0.00131123751204656 & 0.0416413826691433 \tabularnewline
24 & 7.3 & 7.30297255889833 & 0.107350482078810 & -0.00154679298410702 & -0.734488431525079 \tabularnewline
25 & 7.5 & 7.49742654516942 & 0.189629100090806 & 0.00136866908338301 & 0.625796016197485 \tabularnewline
26 & 7.6 & 7.60703199949395 & 0.116016038872831 & -0.00598900387268696 & -0.553974498406099 \tabularnewline
27 & 7.6 & 7.60014948336185 & 0.000630647335701798 & 0.00151138029593659 & -0.867864757490339 \tabularnewline
28 & 7.7 & 7.697293118246 & 0.0910610194924145 & 0.00140463339607679 & 0.680954470032129 \tabularnewline
29 & 7.7 & 7.70464141272945 & 0.0125802444187983 & -0.00350924567481978 & -0.591513393392292 \tabularnewline
30 & 7.7 & 7.69826377207266 & -0.00519432183834172 & 0.00199263523332874 & -0.133964660063898 \tabularnewline
31 & 7.7 & 7.69842050660236 & -0.000177414621978083 & 0.00150712154214752 & 0.037811903148499 \tabularnewline
32 & 7.6 & 7.6079138855999 & -0.0848654138004662 & -0.00669221133973031 & -0.638284477413956 \tabularnewline
33 & 7.7 & 7.69233302868732 & 0.0738470560132779 & 0.00537745036201355 & 1.19619912826708 \tabularnewline
34 & 7.9 & 7.89430433410102 & 0.193970989304979 & 0.00396280759871149 & 0.905361423552947 \tabularnewline
35 & 7.9 & 7.90518505650615 & 0.0223077825633996 & -0.00270871075913092 & -1.29381480943853 \tabularnewline
36 & 7.9 & 7.90538476002576 & 0.00158615846250746 & -0.00508585652124643 & -0.156192584076223 \tabularnewline
37 & 7.8 & 7.80163330806544 & -0.0971475180939086 & -0.000206986290705274 & -0.748851785082806 \tabularnewline
38 & 7.6 & 7.60293755832055 & -0.190476204578409 & -0.00162045759966602 & -0.702411224447467 \tabularnewline
39 & 7.4 & 7.40363111443934 & -0.198714039820923 & -0.00351341290785465 & -0.062039334267044 \tabularnewline
40 & 7 & 7.00404497532107 & -0.385837040293015 & -0.00137521949952675 & -1.40884139874126 \tabularnewline
41 & 7 & 6.98630874439361 & -0.0427767195160832 & 0.0087870800554346 & 2.58566111656610 \tabularnewline
42 & 7.2 & 7.19129158744361 & 0.188163429262786 & 0.00540711354479786 & 1.74056265310308 \tabularnewline
43 & 7.5 & 7.48853574444534 & 0.289835947444405 & 0.0100108306524826 & 0.766295107050017 \tabularnewline
44 & 7.8 & 7.80985414041975 & 0.319179828001152 & -0.0102736158529113 & 0.221161713028408 \tabularnewline
45 & 7.8 & 7.81647675151408 & 0.0278539810744289 & -0.0123122017393184 & -2.19569223430684 \tabularnewline
46 & 7.7 & 7.69431319402758 & -0.111976366329345 & 0.00768570205743901 & -1.05388731292599 \tabularnewline
47 & 7.6 & 7.60183556242515 & -0.0938014117586268 & -0.00209537713186450 & 0.136983655418038 \tabularnewline
48 & 7.6 & 7.59872646065476 & -0.00930513963389062 & 6.57712675868477e-05 & 0.636988803157634 \tabularnewline
49 & 7.5 & 7.50101968344662 & -0.0917198423608942 & 0.000160284299135285 & -0.623779211866528 \tabularnewline
50 & 7.5 & 7.5022558913517 & -0.00631540265347379 & -0.00345880529299559 & 0.642892908591166 \tabularnewline
51 & 7.6 & 7.58286193807387 & 0.0744182522217325 & 0.0159900833287319 & 0.608485940145603 \tabularnewline
52 & 7.6 & 7.61388978368848 & 0.0341521149609615 & -0.0133185409214909 & -0.303144393414934 \tabularnewline
53 & 7.9 & 7.88781710451507 & 0.256725468936608 & 0.0090192529231363 & 1.67752712011016 \tabularnewline
54 & 7.6 & 7.62245678993505 & -0.228009411016664 & -0.0155666882137413 & -3.65337255024858 \tabularnewline
55 & 7.5 & 7.4922631519282 & -0.137193784208280 & 0.0064459696577424 & 0.684467621822883 \tabularnewline
56 & 7.5 & 7.49330159412482 & -0.00885709677260038 & 0.00487419117958781 & 0.96725999751738 \tabularnewline
57 & 7.6 & 7.60037912811503 & 0.0987785429623711 & -0.00190909233294563 & 0.81123846432232 \tabularnewline
58 & 7.7 & 7.6923737559083 & 0.0924800394378096 & 0.0077157727802329 & -0.0474712782275398 \tabularnewline
59 & 7.8 & 7.80706340727148 & 0.113100172953108 & -0.00735650833255159 & 0.155412221241903 \tabularnewline
60 & 7.9 & 7.89542768843735 & 0.0901464748783864 & 0.00489855096200324 & -0.173063731784843 \tabularnewline
61 & 7.9 & 7.90713747032916 & 0.0172968737823766 & -0.00610054118703283 & -0.550585766746228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66061&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]5.4[/C][C]5.4[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]5.4[/C][C]5.4[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]5.6[/C][C]5.59492906224467[/C][C]0.186778243748734[/C][C]0.00221427715431012[/C][C]1.42458337469500[/C][/ROW]
[ROW][C]4[/C][C]5.7[/C][C]5.70252607853967[/C][C]0.111016827213531[/C][C]-0.00139554471429272[/C][C]-0.570862247186259[/C][/ROW]
[ROW][C]5[/C][C]5.8[/C][C]5.80008927511991[/C][C]0.0981409066347055[/C][C]0.000102955835649726[/C][C]-0.0970457396502012[/C][/ROW]
[ROW][C]6[/C][C]5.8[/C][C]5.80235207494681[/C][C]0.00637655182629163[/C][C]-0.000982115106944923[/C][C]-0.69161815226378[/C][/ROW]
[ROW][C]7[/C][C]5.8[/C][C]5.79992580436382[/C][C]-0.0020485221601655[/C][C]0.000199974492124871[/C][C]-0.0634988920090417[/C][/ROW]
[ROW][C]8[/C][C]5.9[/C][C]5.89743696070077[/C][C]0.0932387481502883[/C][C]0.00114048519531547[/C][C]0.7181700750304[/C][/ROW]
[ROW][C]9[/C][C]6.1[/C][C]6.09755551667313[/C][C]0.195532040049441[/C][C]0.000917335558287218[/C][C]0.770973718620297[/C][/ROW]
[ROW][C]10[/C][C]6.4[/C][C]6.39763481100681[/C][C]0.295592877760667[/C][C]0.000871369777945345[/C][C]0.754147947587207[/C][/ROW]
[ROW][C]11[/C][C]6.4[/C][C]6.40747016793218[/C][C]0.0220980170669061[/C][C]-0.00338713317532346[/C][C]-2.06130182982399[/C][/ROW]
[ROW][C]12[/C][C]6.3[/C][C]6.30237985010868[/C][C]-0.099632308005343[/C][C]-0.000562524741128899[/C][C]-0.917468581237651[/C][/ROW]
[ROW][C]13[/C][C]6.2[/C][C]6.19902993875199[/C][C]-0.103182513573111[/C][C]0.00102306265612186[/C][C]-0.0270898119053488[/C][/ROW]
[ROW][C]14[/C][C]6.2[/C][C]6.20013575468071[/C][C]-0.00702524368577775[/C][C]-0.00150880414386178[/C][C]0.723733395498135[/C][/ROW]
[ROW][C]15[/C][C]6.3[/C][C]6.29335051725193[/C][C]0.0879427323860012[/C][C]0.00526691770730597[/C][C]0.713000940592935[/C][/ROW]
[ROW][C]16[/C][C]6.4[/C][C]6.40165290372803[/C][C]0.107185462175953[/C][C]-0.00193407170385801[/C][C]0.144935730386198[/C][/ROW]
[ROW][C]17[/C][C]6.5[/C][C]6.49884986214798[/C][C]0.0977396072453852[/C][C]0.00128834281056557[/C][C]-0.0711934804822539[/C][/ROW]
[ROW][C]18[/C][C]6.6[/C][C]6.5996970274486[/C][C]0.100678456729547[/C][C]0.000259974724853204[/C][C]0.0221497777472345[/C][/ROW]
[ROW][C]19[/C][C]6.6[/C][C]6.60338484512448[/C][C]0.00895520589438013[/C][C]-0.00204285472685143[/C][C]-0.691308465887857[/C][/ROW]
[ROW][C]20[/C][C]6.6[/C][C]6.59881426253884[/C][C]-0.00383599856638569[/C][C]0.00137288381643899[/C][C]-0.0964059544292592[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]6.79609425770665[/C][C]0.186357444232509[/C][C]0.00112304813995894[/C][C]1.43346786040070[/C][/ROW]
[ROW][C]22[/C][C]7[/C][C]6.99611219313887[/C][C]0.199276059584364[/C][C]0.00369879637410487[/C][C]0.09736623693722[/C][/ROW]
[ROW][C]23[/C][C]7.2[/C][C]7.20123040203931[/C][C]0.204801056751968[/C][C]-0.00131123751204656[/C][C]0.0416413826691433[/C][/ROW]
[ROW][C]24[/C][C]7.3[/C][C]7.30297255889833[/C][C]0.107350482078810[/C][C]-0.00154679298410702[/C][C]-0.734488431525079[/C][/ROW]
[ROW][C]25[/C][C]7.5[/C][C]7.49742654516942[/C][C]0.189629100090806[/C][C]0.00136866908338301[/C][C]0.625796016197485[/C][/ROW]
[ROW][C]26[/C][C]7.6[/C][C]7.60703199949395[/C][C]0.116016038872831[/C][C]-0.00598900387268696[/C][C]-0.553974498406099[/C][/ROW]
[ROW][C]27[/C][C]7.6[/C][C]7.60014948336185[/C][C]0.000630647335701798[/C][C]0.00151138029593659[/C][C]-0.867864757490339[/C][/ROW]
[ROW][C]28[/C][C]7.7[/C][C]7.697293118246[/C][C]0.0910610194924145[/C][C]0.00140463339607679[/C][C]0.680954470032129[/C][/ROW]
[ROW][C]29[/C][C]7.7[/C][C]7.70464141272945[/C][C]0.0125802444187983[/C][C]-0.00350924567481978[/C][C]-0.591513393392292[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.69826377207266[/C][C]-0.00519432183834172[/C][C]0.00199263523332874[/C][C]-0.133964660063898[/C][/ROW]
[ROW][C]31[/C][C]7.7[/C][C]7.69842050660236[/C][C]-0.000177414621978083[/C][C]0.00150712154214752[/C][C]0.037811903148499[/C][/ROW]
[ROW][C]32[/C][C]7.6[/C][C]7.6079138855999[/C][C]-0.0848654138004662[/C][C]-0.00669221133973031[/C][C]-0.638284477413956[/C][/ROW]
[ROW][C]33[/C][C]7.7[/C][C]7.69233302868732[/C][C]0.0738470560132779[/C][C]0.00537745036201355[/C][C]1.19619912826708[/C][/ROW]
[ROW][C]34[/C][C]7.9[/C][C]7.89430433410102[/C][C]0.193970989304979[/C][C]0.00396280759871149[/C][C]0.905361423552947[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.90518505650615[/C][C]0.0223077825633996[/C][C]-0.00270871075913092[/C][C]-1.29381480943853[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.90538476002576[/C][C]0.00158615846250746[/C][C]-0.00508585652124643[/C][C]-0.156192584076223[/C][/ROW]
[ROW][C]37[/C][C]7.8[/C][C]7.80163330806544[/C][C]-0.0971475180939086[/C][C]-0.000206986290705274[/C][C]-0.748851785082806[/C][/ROW]
[ROW][C]38[/C][C]7.6[/C][C]7.60293755832055[/C][C]-0.190476204578409[/C][C]-0.00162045759966602[/C][C]-0.702411224447467[/C][/ROW]
[ROW][C]39[/C][C]7.4[/C][C]7.40363111443934[/C][C]-0.198714039820923[/C][C]-0.00351341290785465[/C][C]-0.062039334267044[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]7.00404497532107[/C][C]-0.385837040293015[/C][C]-0.00137521949952675[/C][C]-1.40884139874126[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]6.98630874439361[/C][C]-0.0427767195160832[/C][C]0.0087870800554346[/C][C]2.58566111656610[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]7.19129158744361[/C][C]0.188163429262786[/C][C]0.00540711354479786[/C][C]1.74056265310308[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]7.48853574444534[/C][C]0.289835947444405[/C][C]0.0100108306524826[/C][C]0.766295107050017[/C][/ROW]
[ROW][C]44[/C][C]7.8[/C][C]7.80985414041975[/C][C]0.319179828001152[/C][C]-0.0102736158529113[/C][C]0.221161713028408[/C][/ROW]
[ROW][C]45[/C][C]7.8[/C][C]7.81647675151408[/C][C]0.0278539810744289[/C][C]-0.0123122017393184[/C][C]-2.19569223430684[/C][/ROW]
[ROW][C]46[/C][C]7.7[/C][C]7.69431319402758[/C][C]-0.111976366329345[/C][C]0.00768570205743901[/C][C]-1.05388731292599[/C][/ROW]
[ROW][C]47[/C][C]7.6[/C][C]7.60183556242515[/C][C]-0.0938014117586268[/C][C]-0.00209537713186450[/C][C]0.136983655418038[/C][/ROW]
[ROW][C]48[/C][C]7.6[/C][C]7.59872646065476[/C][C]-0.00930513963389062[/C][C]6.57712675868477e-05[/C][C]0.636988803157634[/C][/ROW]
[ROW][C]49[/C][C]7.5[/C][C]7.50101968344662[/C][C]-0.0917198423608942[/C][C]0.000160284299135285[/C][C]-0.623779211866528[/C][/ROW]
[ROW][C]50[/C][C]7.5[/C][C]7.5022558913517[/C][C]-0.00631540265347379[/C][C]-0.00345880529299559[/C][C]0.642892908591166[/C][/ROW]
[ROW][C]51[/C][C]7.6[/C][C]7.58286193807387[/C][C]0.0744182522217325[/C][C]0.0159900833287319[/C][C]0.608485940145603[/C][/ROW]
[ROW][C]52[/C][C]7.6[/C][C]7.61388978368848[/C][C]0.0341521149609615[/C][C]-0.0133185409214909[/C][C]-0.303144393414934[/C][/ROW]
[ROW][C]53[/C][C]7.9[/C][C]7.88781710451507[/C][C]0.256725468936608[/C][C]0.0090192529231363[/C][C]1.67752712011016[/C][/ROW]
[ROW][C]54[/C][C]7.6[/C][C]7.62245678993505[/C][C]-0.228009411016664[/C][C]-0.0155666882137413[/C][C]-3.65337255024858[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]7.4922631519282[/C][C]-0.137193784208280[/C][C]0.0064459696577424[/C][C]0.684467621822883[/C][/ROW]
[ROW][C]56[/C][C]7.5[/C][C]7.49330159412482[/C][C]-0.00885709677260038[/C][C]0.00487419117958781[/C][C]0.96725999751738[/C][/ROW]
[ROW][C]57[/C][C]7.6[/C][C]7.60037912811503[/C][C]0.0987785429623711[/C][C]-0.00190909233294563[/C][C]0.81123846432232[/C][/ROW]
[ROW][C]58[/C][C]7.7[/C][C]7.6923737559083[/C][C]0.0924800394378096[/C][C]0.0077157727802329[/C][C]-0.0474712782275398[/C][/ROW]
[ROW][C]59[/C][C]7.8[/C][C]7.80706340727148[/C][C]0.113100172953108[/C][C]-0.00735650833255159[/C][C]0.155412221241903[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]7.89542768843735[/C][C]0.0901464748783864[/C][C]0.00489855096200324[/C][C]-0.173063731784843[/C][/ROW]
[ROW][C]61[/C][C]7.9[/C][C]7.90713747032916[/C][C]0.0172968737823766[/C][C]-0.00610054118703283[/C][C]-0.550585766746228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66061&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	5.4	5.4	0	0	0
2	5.4	5.4	0	0	0
3	5.6	5.59492906224467	0.186778243748734	0.00221427715431012	1.42458337469500
4	5.7	5.70252607853967	0.111016827213531	-0.00139554471429272	-0.570862247186259
5	5.8	5.80008927511991	0.0981409066347055	0.000102955835649726	-0.0970457396502012
6	5.8	5.80235207494681	0.00637655182629163	-0.000982115106944923	-0.69161815226378
7	5.8	5.79992580436382	-0.0020485221601655	0.000199974492124871	-0.0634988920090417
8	5.9	5.89743696070077	0.0932387481502883	0.00114048519531547	0.7181700750304
9	6.1	6.09755551667313	0.195532040049441	0.000917335558287218	0.770973718620297
10	6.4	6.39763481100681	0.295592877760667	0.000871369777945345	0.754147947587207
11	6.4	6.40747016793218	0.0220980170669061	-0.00338713317532346	-2.06130182982399
12	6.3	6.30237985010868	-0.099632308005343	-0.000562524741128899	-0.917468581237651
13	6.2	6.19902993875199	-0.103182513573111	0.00102306265612186	-0.0270898119053488
14	6.2	6.20013575468071	-0.00702524368577775	-0.00150880414386178	0.723733395498135
15	6.3	6.29335051725193	0.0879427323860012	0.00526691770730597	0.713000940592935
16	6.4	6.40165290372803	0.107185462175953	-0.00193407170385801	0.144935730386198
17	6.5	6.49884986214798	0.0977396072453852	0.00128834281056557	-0.0711934804822539
18	6.6	6.5996970274486	0.100678456729547	0.000259974724853204	0.0221497777472345
19	6.6	6.60338484512448	0.00895520589438013	-0.00204285472685143	-0.691308465887857
20	6.6	6.59881426253884	-0.00383599856638569	0.00137288381643899	-0.0964059544292592
21	6.8	6.79609425770665	0.186357444232509	0.00112304813995894	1.43346786040070
22	7	6.99611219313887	0.199276059584364	0.00369879637410487	0.09736623693722
23	7.2	7.20123040203931	0.204801056751968	-0.00131123751204656	0.0416413826691433
24	7.3	7.30297255889833	0.107350482078810	-0.00154679298410702	-0.734488431525079
25	7.5	7.49742654516942	0.189629100090806	0.00136866908338301	0.625796016197485
26	7.6	7.60703199949395	0.116016038872831	-0.00598900387268696	-0.553974498406099
27	7.6	7.60014948336185	0.000630647335701798	0.00151138029593659	-0.867864757490339
28	7.7	7.697293118246	0.0910610194924145	0.00140463339607679	0.680954470032129
29	7.7	7.70464141272945	0.0125802444187983	-0.00350924567481978	-0.591513393392292
30	7.7	7.69826377207266	-0.00519432183834172	0.00199263523332874	-0.133964660063898
31	7.7	7.69842050660236	-0.000177414621978083	0.00150712154214752	0.037811903148499
32	7.6	7.6079138855999	-0.0848654138004662	-0.00669221133973031	-0.638284477413956
33	7.7	7.69233302868732	0.0738470560132779	0.00537745036201355	1.19619912826708
34	7.9	7.89430433410102	0.193970989304979	0.00396280759871149	0.905361423552947
35	7.9	7.90518505650615	0.0223077825633996	-0.00270871075913092	-1.29381480943853
36	7.9	7.90538476002576	0.00158615846250746	-0.00508585652124643	-0.156192584076223
37	7.8	7.80163330806544	-0.0971475180939086	-0.000206986290705274	-0.748851785082806
38	7.6	7.60293755832055	-0.190476204578409	-0.00162045759966602	-0.702411224447467
39	7.4	7.40363111443934	-0.198714039820923	-0.00351341290785465	-0.062039334267044
40	7	7.00404497532107	-0.385837040293015	-0.00137521949952675	-1.40884139874126
41	7	6.98630874439361	-0.0427767195160832	0.0087870800554346	2.58566111656610
42	7.2	7.19129158744361	0.188163429262786	0.00540711354479786	1.74056265310308
43	7.5	7.48853574444534	0.289835947444405	0.0100108306524826	0.766295107050017
44	7.8	7.80985414041975	0.319179828001152	-0.0102736158529113	0.221161713028408
45	7.8	7.81647675151408	0.0278539810744289	-0.0123122017393184	-2.19569223430684
46	7.7	7.69431319402758	-0.111976366329345	0.00768570205743901	-1.05388731292599
47	7.6	7.60183556242515	-0.0938014117586268	-0.00209537713186450	0.136983655418038
48	7.6	7.59872646065476	-0.00930513963389062	6.57712675868477e-05	0.636988803157634
49	7.5	7.50101968344662	-0.0917198423608942	0.000160284299135285	-0.623779211866528
50	7.5	7.5022558913517	-0.00631540265347379	-0.00345880529299559	0.642892908591166
51	7.6	7.58286193807387	0.0744182522217325	0.0159900833287319	0.608485940145603
52	7.6	7.61388978368848	0.0341521149609615	-0.0133185409214909	-0.303144393414934
53	7.9	7.88781710451507	0.256725468936608	0.0090192529231363	1.67752712011016
54	7.6	7.62245678993505	-0.228009411016664	-0.0155666882137413	-3.65337255024858
55	7.5	7.4922631519282	-0.137193784208280	0.0064459696577424	0.684467621822883
56	7.5	7.49330159412482	-0.00885709677260038	0.00487419117958781	0.96725999751738
57	7.6	7.60037912811503	0.0987785429623711	-0.00190909233294563	0.81123846432232
58	7.7	7.6923737559083	0.0924800394378096	0.0077157727802329	-0.0474712782275398
59	7.8	7.80706340727148	0.113100172953108	-0.00735650833255159	0.155412221241903
60	7.9	7.89542768843735	0.0901464748783864	0.00489855096200324	-0.173063731784843
61	7.9	7.90713747032916	0.0172968737823766	-0.00610054118703283	-0.550585766746228

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