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rwasp_structuraltimeseries.wasp

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Structural Time Series Models

Date of computation

Fri, 30 Nov 2012 12:59:30 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/30/t135429862927hhk8dl33h86az.htm/, Retrieved Fri, 03 May 2024 21:09:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195150, Retrieved Fri, 03 May 2024 21:09:16 +0000

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Estimated Impact

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   [Decomposition by Loess] [Unemployment] [2010-11-30 13:30:23] [b98453cac15ba1066b407e146608df68]
- RMPD    [Structural Time Series Models] [] [2012-11-30 15:11:14] [bbed103f50d9b60ea97669d7e6947a11]
- R  D        [Structural Time Series Models] [] [2012-11-30 17:59:30] [d41d8cd98f00b204e9800998ecf8427e] [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	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195150&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195150&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195150&T=0

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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	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	59.8	59.8	0	0	0
2	60.7	60.6573105392772	0.121738274814838	0.042689460722848	0.130357398926475
3	59.7	59.6505114280491	-0.27386917802115	0.0494885719509289	-0.240456466434007
4	60.2	60.1533544502343	0.0309493642993781	0.0466455497657035	0.160519165581433
5	61.3	61.255676905153	0.467828964443153	0.0443230948469783	0.219028026001216
6	59.8	59.7531708224026	-0.34642352543092	0.04682917759743	-0.401421032680154
7	61.2	61.154470737235	0.379279491813664	0.0455292627649831	0.355722602489568
8	59.3	59.2534801903076	-0.569209386694534	0.0465198096924186	-0.464020224736918
9	59.4	59.3536499364252	-0.290591131027721	0.0463500635747914	0.136215163192438
10	63.1	63.054240659176	1.37112664917373	0.0457593408240222	0.812222107794538
11	68	67.9545455003046	2.84066454592857	0.0454544996954169	0.718232145109719
12	69.4	69.3544728754321	2.24071325446606	0.0455271245679602	-0.293216655424375
13	70.2	70.9309471273026	1.97267591158828	-0.730947127302554	-0.154355936252222
14	72.6	72.541389290668	1.83490414854989	0.0586107093320288	-0.0602604281016014
15	72.1	72.0353533302802	0.855202464894941	0.0646466697197915	-0.473936193600129
16	69.7	69.6304516993642	-0.503889478581724	0.0695483006357555	-0.661917831978629
17	71.5	71.4324748831647	0.456391513981297	0.0675251168353482	0.468759890291639
18	75.7	75.6343929063795	2.01586156256364	0.0656070936204553	0.761848376887705
19	76	75.9338799313552	1.30122753440032	0.0661200686448313	-0.349213294776559
20	76.4	76.3337227070563	0.925903052319145	0.0662772929436726	-0.183422802976398
21	83.8	83.7343817939898	3.62203885518289	0.0656182060101619	1.31765464384639
22	86.2	86.1343091952292	3.11312506855283	0.0656908047707982	-0.248718799762137
23	88.5	88.4342810060099	2.77450288439842	0.0657189939901341	-0.165493658872351
24	95.9	95.8343745823159	4.70076809245502	0.0656254176840735	0.941418136870134
25	103.1	103.366246874719	5.86274792292879	-0.266246874718728	0.61624489651933
26	113.5	113.417679880865	7.51017139109959	0.0823201191348368	0.75721285784431
27	115.7	115.608796852591	5.28797322441066	0.0912031474094137	-1.07888285021937
28	113.1	113.001105840762	1.99760852812297	0.0988941592376309	-1.60447133635061
29	112.7	112.599742190837	0.998572039142688	0.100257809162604	-0.487882018809332
30	121.9	121.802463866189	4.41467209884604	0.0975361338111692	1.66910570826413
31	120.3	120.201299149224	1.90972877064972	0.098700850776421	-1.224125683607
32	108.7	108.599772532269	-3.7164534579745	0.100227467731251	-2.74958650180432
33	102.8	102.699628544542	-4.62578702137978	0.10037145545819	-0.444411709123752
34	83.4	83.299060020934	-10.7784474249791	0.100939979066025	-3.00696360970613
35	79.4	79.2992122354373	-7.95559561595392	0.100787764562689	1.37960358289741
36	77.8	77.6992955198821	-5.30883994734974	0.100704480117867	1.29354168488775
37	85.7	85.4399817468506	0.0744784645387823	0.260018253149367	2.77820642557404
38	83.2	83.2467911631548	-0.831263026128509	-0.0467911631547852	-0.424326848379516
39	82	82.0463351303836	-0.985376281699554	-0.046335130383634	-0.0749515356220588
40	86.9	86.9505784655179	1.46857011772991	-0.0505784655179482	1.19731365630942
41	95.7	95.7536621790916	4.52298341949277	-0.0536621790916317	1.49192868383108
42	97.9	97.9530920552098	3.55545120012558	-0.0530920552097409	-0.472768195277239
43	89.3	89.3513512062125	-1.50686904219375	-0.0513512062125019	-2.4739321545622
44	91.5	91.5516610009739	0.0368628695957446	-0.0516610009739112	0.754447288297182
45	86.8	86.8514299872274	-1.93579023298027	-0.0514299872274004	-0.96408240954917
46	91	91.0516046091838	0.619432722172301	-0.0516046091837986	1.24880441446396
47	93.8	93.8516408234394	1.52751926251311	-0.0516408234394077	0.443806448172243
48	96.8	96.8516550940171	2.14072637471866	-0.0516550940170781	0.299691072621692
49	95.7	95.4101763051466	0.659333793276226	0.289823694853396	-0.754174526229767
50	91.4	91.4635494888303	-1.19674491188508	-0.0635494888302573	-0.878333641232694
51	88.7	88.7620749917175	-1.82456116306393	-0.0620749917174577	-0.305641638925975
52	88.2	88.262832607087	-1.27241677001335	-0.0628326070870283	0.269491523666103
53	87.7	87.7630903623266	-0.950641042505346	-0.063090362326637	0.157189840309063
54	89.5	89.5636259574654	0.19497863270953	-0.0636259574653806	0.559809962269748
55	95.6	95.6642969136827	2.65418883501921	-0.0642969136826655	1.20182083242179
56	100.5	100.564445823665	3.58945751899372	-0.0644458236646887	0.457083373486746
57	106.3	106.364531355932	4.51003059351065	-0.0645313559321045	0.449906628918437
58	112	112.064558224738	5.00558794219669	-0.0645582247384428	0.242191991795482
59	117.7	117.764567374538	5.29477239642712	-0.0645673745383824	0.141332288573002
60	125	125.064582792959	6.12983919245462	-0.06458279295914	0.408119988199482
61	132.4	131.660792244689	6.32298103982757	0.739207755311445	0.0975284968720336
62	138.1	138.165983405759	6.39683105731313	-0.0659834057586353	0.0351647033932701
63	134.7	134.758021096714	2.3073066556048	-0.0580210967143124	-1.99224007635448
64	136.7	136.757875432292	2.17922699762378	-0.0578754322925022	-0.0625274837637519
65	134.3	134.35660903386	0.271707080016436	-0.056609033859675	-0.931909547446414
66	131.6	131.656129480333	-0.965960855405112	-0.0561294803332145	-0.604805458643475
67	129.8	129.856050940574	-1.31330321532613	-0.0560509405737011	-0.169748407971652
68	131.9	131.956238507631	0.108164667611019	-0.0562385076309663	0.694700169826487
69	129.8	129.856167697739	-0.811417471661528	-0.0561676977387187	-0.449422800575598
70	119.4	119.455988266347	-4.80453802829208	-0.0559882663470741	-1.9515443876231
71	116.7	116.75601124807	-3.9281136915533	-0.0560112480701938	0.428332402916367
72	112.8	112.856011427224	-3.91640588861882	-0.0560114272238065	0.00572192381956158

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 59.8 & 59.8 & 0 & 0 & 0 \tabularnewline
2 & 60.7 & 60.6573105392772 & 0.121738274814838 & 0.042689460722848 & 0.130357398926475 \tabularnewline
3 & 59.7 & 59.6505114280491 & -0.27386917802115 & 0.0494885719509289 & -0.240456466434007 \tabularnewline
4 & 60.2 & 60.1533544502343 & 0.0309493642993781 & 0.0466455497657035 & 0.160519165581433 \tabularnewline
5 & 61.3 & 61.255676905153 & 0.467828964443153 & 0.0443230948469783 & 0.219028026001216 \tabularnewline
6 & 59.8 & 59.7531708224026 & -0.34642352543092 & 0.04682917759743 & -0.401421032680154 \tabularnewline
7 & 61.2 & 61.154470737235 & 0.379279491813664 & 0.0455292627649831 & 0.355722602489568 \tabularnewline
8 & 59.3 & 59.2534801903076 & -0.569209386694534 & 0.0465198096924186 & -0.464020224736918 \tabularnewline
9 & 59.4 & 59.3536499364252 & -0.290591131027721 & 0.0463500635747914 & 0.136215163192438 \tabularnewline
10 & 63.1 & 63.054240659176 & 1.37112664917373 & 0.0457593408240222 & 0.812222107794538 \tabularnewline
11 & 68 & 67.9545455003046 & 2.84066454592857 & 0.0454544996954169 & 0.718232145109719 \tabularnewline
12 & 69.4 & 69.3544728754321 & 2.24071325446606 & 0.0455271245679602 & -0.293216655424375 \tabularnewline
13 & 70.2 & 70.9309471273026 & 1.97267591158828 & -0.730947127302554 & -0.154355936252222 \tabularnewline
14 & 72.6 & 72.541389290668 & 1.83490414854989 & 0.0586107093320288 & -0.0602604281016014 \tabularnewline
15 & 72.1 & 72.0353533302802 & 0.855202464894941 & 0.0646466697197915 & -0.473936193600129 \tabularnewline
16 & 69.7 & 69.6304516993642 & -0.503889478581724 & 0.0695483006357555 & -0.661917831978629 \tabularnewline
17 & 71.5 & 71.4324748831647 & 0.456391513981297 & 0.0675251168353482 & 0.468759890291639 \tabularnewline
18 & 75.7 & 75.6343929063795 & 2.01586156256364 & 0.0656070936204553 & 0.761848376887705 \tabularnewline
19 & 76 & 75.9338799313552 & 1.30122753440032 & 0.0661200686448313 & -0.349213294776559 \tabularnewline
20 & 76.4 & 76.3337227070563 & 0.925903052319145 & 0.0662772929436726 & -0.183422802976398 \tabularnewline
21 & 83.8 & 83.7343817939898 & 3.62203885518289 & 0.0656182060101619 & 1.31765464384639 \tabularnewline
22 & 86.2 & 86.1343091952292 & 3.11312506855283 & 0.0656908047707982 & -0.248718799762137 \tabularnewline
23 & 88.5 & 88.4342810060099 & 2.77450288439842 & 0.0657189939901341 & -0.165493658872351 \tabularnewline
24 & 95.9 & 95.8343745823159 & 4.70076809245502 & 0.0656254176840735 & 0.941418136870134 \tabularnewline
25 & 103.1 & 103.366246874719 & 5.86274792292879 & -0.266246874718728 & 0.61624489651933 \tabularnewline
26 & 113.5 & 113.417679880865 & 7.51017139109959 & 0.0823201191348368 & 0.75721285784431 \tabularnewline
27 & 115.7 & 115.608796852591 & 5.28797322441066 & 0.0912031474094137 & -1.07888285021937 \tabularnewline
28 & 113.1 & 113.001105840762 & 1.99760852812297 & 0.0988941592376309 & -1.60447133635061 \tabularnewline
29 & 112.7 & 112.599742190837 & 0.998572039142688 & 0.100257809162604 & -0.487882018809332 \tabularnewline
30 & 121.9 & 121.802463866189 & 4.41467209884604 & 0.0975361338111692 & 1.66910570826413 \tabularnewline
31 & 120.3 & 120.201299149224 & 1.90972877064972 & 0.098700850776421 & -1.224125683607 \tabularnewline
32 & 108.7 & 108.599772532269 & -3.7164534579745 & 0.100227467731251 & -2.74958650180432 \tabularnewline
33 & 102.8 & 102.699628544542 & -4.62578702137978 & 0.10037145545819 & -0.444411709123752 \tabularnewline
34 & 83.4 & 83.299060020934 & -10.7784474249791 & 0.100939979066025 & -3.00696360970613 \tabularnewline
35 & 79.4 & 79.2992122354373 & -7.95559561595392 & 0.100787764562689 & 1.37960358289741 \tabularnewline
36 & 77.8 & 77.6992955198821 & -5.30883994734974 & 0.100704480117867 & 1.29354168488775 \tabularnewline
37 & 85.7 & 85.4399817468506 & 0.0744784645387823 & 0.260018253149367 & 2.77820642557404 \tabularnewline
38 & 83.2 & 83.2467911631548 & -0.831263026128509 & -0.0467911631547852 & -0.424326848379516 \tabularnewline
39 & 82 & 82.0463351303836 & -0.985376281699554 & -0.046335130383634 & -0.0749515356220588 \tabularnewline
40 & 86.9 & 86.9505784655179 & 1.46857011772991 & -0.0505784655179482 & 1.19731365630942 \tabularnewline
41 & 95.7 & 95.7536621790916 & 4.52298341949277 & -0.0536621790916317 & 1.49192868383108 \tabularnewline
42 & 97.9 & 97.9530920552098 & 3.55545120012558 & -0.0530920552097409 & -0.472768195277239 \tabularnewline
43 & 89.3 & 89.3513512062125 & -1.50686904219375 & -0.0513512062125019 & -2.4739321545622 \tabularnewline
44 & 91.5 & 91.5516610009739 & 0.0368628695957446 & -0.0516610009739112 & 0.754447288297182 \tabularnewline
45 & 86.8 & 86.8514299872274 & -1.93579023298027 & -0.0514299872274004 & -0.96408240954917 \tabularnewline
46 & 91 & 91.0516046091838 & 0.619432722172301 & -0.0516046091837986 & 1.24880441446396 \tabularnewline
47 & 93.8 & 93.8516408234394 & 1.52751926251311 & -0.0516408234394077 & 0.443806448172243 \tabularnewline
48 & 96.8 & 96.8516550940171 & 2.14072637471866 & -0.0516550940170781 & 0.299691072621692 \tabularnewline
49 & 95.7 & 95.4101763051466 & 0.659333793276226 & 0.289823694853396 & -0.754174526229767 \tabularnewline
50 & 91.4 & 91.4635494888303 & -1.19674491188508 & -0.0635494888302573 & -0.878333641232694 \tabularnewline
51 & 88.7 & 88.7620749917175 & -1.82456116306393 & -0.0620749917174577 & -0.305641638925975 \tabularnewline
52 & 88.2 & 88.262832607087 & -1.27241677001335 & -0.0628326070870283 & 0.269491523666103 \tabularnewline
53 & 87.7 & 87.7630903623266 & -0.950641042505346 & -0.063090362326637 & 0.157189840309063 \tabularnewline
54 & 89.5 & 89.5636259574654 & 0.19497863270953 & -0.0636259574653806 & 0.559809962269748 \tabularnewline
55 & 95.6 & 95.6642969136827 & 2.65418883501921 & -0.0642969136826655 & 1.20182083242179 \tabularnewline
56 & 100.5 & 100.564445823665 & 3.58945751899372 & -0.0644458236646887 & 0.457083373486746 \tabularnewline
57 & 106.3 & 106.364531355932 & 4.51003059351065 & -0.0645313559321045 & 0.449906628918437 \tabularnewline
58 & 112 & 112.064558224738 & 5.00558794219669 & -0.0645582247384428 & 0.242191991795482 \tabularnewline
59 & 117.7 & 117.764567374538 & 5.29477239642712 & -0.0645673745383824 & 0.141332288573002 \tabularnewline
60 & 125 & 125.064582792959 & 6.12983919245462 & -0.06458279295914 & 0.408119988199482 \tabularnewline
61 & 132.4 & 131.660792244689 & 6.32298103982757 & 0.739207755311445 & 0.0975284968720336 \tabularnewline
62 & 138.1 & 138.165983405759 & 6.39683105731313 & -0.0659834057586353 & 0.0351647033932701 \tabularnewline
63 & 134.7 & 134.758021096714 & 2.3073066556048 & -0.0580210967143124 & -1.99224007635448 \tabularnewline
64 & 136.7 & 136.757875432292 & 2.17922699762378 & -0.0578754322925022 & -0.0625274837637519 \tabularnewline
65 & 134.3 & 134.35660903386 & 0.271707080016436 & -0.056609033859675 & -0.931909547446414 \tabularnewline
66 & 131.6 & 131.656129480333 & -0.965960855405112 & -0.0561294803332145 & -0.604805458643475 \tabularnewline
67 & 129.8 & 129.856050940574 & -1.31330321532613 & -0.0560509405737011 & -0.169748407971652 \tabularnewline
68 & 131.9 & 131.956238507631 & 0.108164667611019 & -0.0562385076309663 & 0.694700169826487 \tabularnewline
69 & 129.8 & 129.856167697739 & -0.811417471661528 & -0.0561676977387187 & -0.449422800575598 \tabularnewline
70 & 119.4 & 119.455988266347 & -4.80453802829208 & -0.0559882663470741 & -1.9515443876231 \tabularnewline
71 & 116.7 & 116.75601124807 & -3.9281136915533 & -0.0560112480701938 & 0.428332402916367 \tabularnewline
72 & 112.8 & 112.856011427224 & -3.91640588861882 & -0.0560114272238065 & 0.00572192381956158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195150&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]59.8[/C][C]59.8[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]60.7[/C][C]60.6573105392772[/C][C]0.121738274814838[/C][C]0.042689460722848[/C][C]0.130357398926475[/C][/ROW]
[ROW][C]3[/C][C]59.7[/C][C]59.6505114280491[/C][C]-0.27386917802115[/C][C]0.0494885719509289[/C][C]-0.240456466434007[/C][/ROW]
[ROW][C]4[/C][C]60.2[/C][C]60.1533544502343[/C][C]0.0309493642993781[/C][C]0.0466455497657035[/C][C]0.160519165581433[/C][/ROW]
[ROW][C]5[/C][C]61.3[/C][C]61.255676905153[/C][C]0.467828964443153[/C][C]0.0443230948469783[/C][C]0.219028026001216[/C][/ROW]
[ROW][C]6[/C][C]59.8[/C][C]59.7531708224026[/C][C]-0.34642352543092[/C][C]0.04682917759743[/C][C]-0.401421032680154[/C][/ROW]
[ROW][C]7[/C][C]61.2[/C][C]61.154470737235[/C][C]0.379279491813664[/C][C]0.0455292627649831[/C][C]0.355722602489568[/C][/ROW]
[ROW][C]8[/C][C]59.3[/C][C]59.2534801903076[/C][C]-0.569209386694534[/C][C]0.0465198096924186[/C][C]-0.464020224736918[/C][/ROW]
[ROW][C]9[/C][C]59.4[/C][C]59.3536499364252[/C][C]-0.290591131027721[/C][C]0.0463500635747914[/C][C]0.136215163192438[/C][/ROW]
[ROW][C]10[/C][C]63.1[/C][C]63.054240659176[/C][C]1.37112664917373[/C][C]0.0457593408240222[/C][C]0.812222107794538[/C][/ROW]
[ROW][C]11[/C][C]68[/C][C]67.9545455003046[/C][C]2.84066454592857[/C][C]0.0454544996954169[/C][C]0.718232145109719[/C][/ROW]
[ROW][C]12[/C][C]69.4[/C][C]69.3544728754321[/C][C]2.24071325446606[/C][C]0.0455271245679602[/C][C]-0.293216655424375[/C][/ROW]
[ROW][C]13[/C][C]70.2[/C][C]70.9309471273026[/C][C]1.97267591158828[/C][C]-0.730947127302554[/C][C]-0.154355936252222[/C][/ROW]
[ROW][C]14[/C][C]72.6[/C][C]72.541389290668[/C][C]1.83490414854989[/C][C]0.0586107093320288[/C][C]-0.0602604281016014[/C][/ROW]
[ROW][C]15[/C][C]72.1[/C][C]72.0353533302802[/C][C]0.855202464894941[/C][C]0.0646466697197915[/C][C]-0.473936193600129[/C][/ROW]
[ROW][C]16[/C][C]69.7[/C][C]69.6304516993642[/C][C]-0.503889478581724[/C][C]0.0695483006357555[/C][C]-0.661917831978629[/C][/ROW]
[ROW][C]17[/C][C]71.5[/C][C]71.4324748831647[/C][C]0.456391513981297[/C][C]0.0675251168353482[/C][C]0.468759890291639[/C][/ROW]
[ROW][C]18[/C][C]75.7[/C][C]75.6343929063795[/C][C]2.01586156256364[/C][C]0.0656070936204553[/C][C]0.761848376887705[/C][/ROW]
[ROW][C]19[/C][C]76[/C][C]75.9338799313552[/C][C]1.30122753440032[/C][C]0.0661200686448313[/C][C]-0.349213294776559[/C][/ROW]
[ROW][C]20[/C][C]76.4[/C][C]76.3337227070563[/C][C]0.925903052319145[/C][C]0.0662772929436726[/C][C]-0.183422802976398[/C][/ROW]
[ROW][C]21[/C][C]83.8[/C][C]83.7343817939898[/C][C]3.62203885518289[/C][C]0.0656182060101619[/C][C]1.31765464384639[/C][/ROW]
[ROW][C]22[/C][C]86.2[/C][C]86.1343091952292[/C][C]3.11312506855283[/C][C]0.0656908047707982[/C][C]-0.248718799762137[/C][/ROW]
[ROW][C]23[/C][C]88.5[/C][C]88.4342810060099[/C][C]2.77450288439842[/C][C]0.0657189939901341[/C][C]-0.165493658872351[/C][/ROW]
[ROW][C]24[/C][C]95.9[/C][C]95.8343745823159[/C][C]4.70076809245502[/C][C]0.0656254176840735[/C][C]0.941418136870134[/C][/ROW]
[ROW][C]25[/C][C]103.1[/C][C]103.366246874719[/C][C]5.86274792292879[/C][C]-0.266246874718728[/C][C]0.61624489651933[/C][/ROW]
[ROW][C]26[/C][C]113.5[/C][C]113.417679880865[/C][C]7.51017139109959[/C][C]0.0823201191348368[/C][C]0.75721285784431[/C][/ROW]
[ROW][C]27[/C][C]115.7[/C][C]115.608796852591[/C][C]5.28797322441066[/C][C]0.0912031474094137[/C][C]-1.07888285021937[/C][/ROW]
[ROW][C]28[/C][C]113.1[/C][C]113.001105840762[/C][C]1.99760852812297[/C][C]0.0988941592376309[/C][C]-1.60447133635061[/C][/ROW]
[ROW][C]29[/C][C]112.7[/C][C]112.599742190837[/C][C]0.998572039142688[/C][C]0.100257809162604[/C][C]-0.487882018809332[/C][/ROW]
[ROW][C]30[/C][C]121.9[/C][C]121.802463866189[/C][C]4.41467209884604[/C][C]0.0975361338111692[/C][C]1.66910570826413[/C][/ROW]
[ROW][C]31[/C][C]120.3[/C][C]120.201299149224[/C][C]1.90972877064972[/C][C]0.098700850776421[/C][C]-1.224125683607[/C][/ROW]
[ROW][C]32[/C][C]108.7[/C][C]108.599772532269[/C][C]-3.7164534579745[/C][C]0.100227467731251[/C][C]-2.74958650180432[/C][/ROW]
[ROW][C]33[/C][C]102.8[/C][C]102.699628544542[/C][C]-4.62578702137978[/C][C]0.10037145545819[/C][C]-0.444411709123752[/C][/ROW]
[ROW][C]34[/C][C]83.4[/C][C]83.299060020934[/C][C]-10.7784474249791[/C][C]0.100939979066025[/C][C]-3.00696360970613[/C][/ROW]
[ROW][C]35[/C][C]79.4[/C][C]79.2992122354373[/C][C]-7.95559561595392[/C][C]0.100787764562689[/C][C]1.37960358289741[/C][/ROW]
[ROW][C]36[/C][C]77.8[/C][C]77.6992955198821[/C][C]-5.30883994734974[/C][C]0.100704480117867[/C][C]1.29354168488775[/C][/ROW]
[ROW][C]37[/C][C]85.7[/C][C]85.4399817468506[/C][C]0.0744784645387823[/C][C]0.260018253149367[/C][C]2.77820642557404[/C][/ROW]
[ROW][C]38[/C][C]83.2[/C][C]83.2467911631548[/C][C]-0.831263026128509[/C][C]-0.0467911631547852[/C][C]-0.424326848379516[/C][/ROW]
[ROW][C]39[/C][C]82[/C][C]82.0463351303836[/C][C]-0.985376281699554[/C][C]-0.046335130383634[/C][C]-0.0749515356220588[/C][/ROW]
[ROW][C]40[/C][C]86.9[/C][C]86.9505784655179[/C][C]1.46857011772991[/C][C]-0.0505784655179482[/C][C]1.19731365630942[/C][/ROW]
[ROW][C]41[/C][C]95.7[/C][C]95.7536621790916[/C][C]4.52298341949277[/C][C]-0.0536621790916317[/C][C]1.49192868383108[/C][/ROW]
[ROW][C]42[/C][C]97.9[/C][C]97.9530920552098[/C][C]3.55545120012558[/C][C]-0.0530920552097409[/C][C]-0.472768195277239[/C][/ROW]
[ROW][C]43[/C][C]89.3[/C][C]89.3513512062125[/C][C]-1.50686904219375[/C][C]-0.0513512062125019[/C][C]-2.4739321545622[/C][/ROW]
[ROW][C]44[/C][C]91.5[/C][C]91.5516610009739[/C][C]0.0368628695957446[/C][C]-0.0516610009739112[/C][C]0.754447288297182[/C][/ROW]
[ROW][C]45[/C][C]86.8[/C][C]86.8514299872274[/C][C]-1.93579023298027[/C][C]-0.0514299872274004[/C][C]-0.96408240954917[/C][/ROW]
[ROW][C]46[/C][C]91[/C][C]91.0516046091838[/C][C]0.619432722172301[/C][C]-0.0516046091837986[/C][C]1.24880441446396[/C][/ROW]
[ROW][C]47[/C][C]93.8[/C][C]93.8516408234394[/C][C]1.52751926251311[/C][C]-0.0516408234394077[/C][C]0.443806448172243[/C][/ROW]
[ROW][C]48[/C][C]96.8[/C][C]96.8516550940171[/C][C]2.14072637471866[/C][C]-0.0516550940170781[/C][C]0.299691072621692[/C][/ROW]
[ROW][C]49[/C][C]95.7[/C][C]95.4101763051466[/C][C]0.659333793276226[/C][C]0.289823694853396[/C][C]-0.754174526229767[/C][/ROW]
[ROW][C]50[/C][C]91.4[/C][C]91.4635494888303[/C][C]-1.19674491188508[/C][C]-0.0635494888302573[/C][C]-0.878333641232694[/C][/ROW]
[ROW][C]51[/C][C]88.7[/C][C]88.7620749917175[/C][C]-1.82456116306393[/C][C]-0.0620749917174577[/C][C]-0.305641638925975[/C][/ROW]
[ROW][C]52[/C][C]88.2[/C][C]88.262832607087[/C][C]-1.27241677001335[/C][C]-0.0628326070870283[/C][C]0.269491523666103[/C][/ROW]
[ROW][C]53[/C][C]87.7[/C][C]87.7630903623266[/C][C]-0.950641042505346[/C][C]-0.063090362326637[/C][C]0.157189840309063[/C][/ROW]
[ROW][C]54[/C][C]89.5[/C][C]89.5636259574654[/C][C]0.19497863270953[/C][C]-0.0636259574653806[/C][C]0.559809962269748[/C][/ROW]
[ROW][C]55[/C][C]95.6[/C][C]95.6642969136827[/C][C]2.65418883501921[/C][C]-0.0642969136826655[/C][C]1.20182083242179[/C][/ROW]
[ROW][C]56[/C][C]100.5[/C][C]100.564445823665[/C][C]3.58945751899372[/C][C]-0.0644458236646887[/C][C]0.457083373486746[/C][/ROW]
[ROW][C]57[/C][C]106.3[/C][C]106.364531355932[/C][C]4.51003059351065[/C][C]-0.0645313559321045[/C][C]0.449906628918437[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]112.064558224738[/C][C]5.00558794219669[/C][C]-0.0645582247384428[/C][C]0.242191991795482[/C][/ROW]
[ROW][C]59[/C][C]117.7[/C][C]117.764567374538[/C][C]5.29477239642712[/C][C]-0.0645673745383824[/C][C]0.141332288573002[/C][/ROW]
[ROW][C]60[/C][C]125[/C][C]125.064582792959[/C][C]6.12983919245462[/C][C]-0.06458279295914[/C][C]0.408119988199482[/C][/ROW]
[ROW][C]61[/C][C]132.4[/C][C]131.660792244689[/C][C]6.32298103982757[/C][C]0.739207755311445[/C][C]0.0975284968720336[/C][/ROW]
[ROW][C]62[/C][C]138.1[/C][C]138.165983405759[/C][C]6.39683105731313[/C][C]-0.0659834057586353[/C][C]0.0351647033932701[/C][/ROW]
[ROW][C]63[/C][C]134.7[/C][C]134.758021096714[/C][C]2.3073066556048[/C][C]-0.0580210967143124[/C][C]-1.99224007635448[/C][/ROW]
[ROW][C]64[/C][C]136.7[/C][C]136.757875432292[/C][C]2.17922699762378[/C][C]-0.0578754322925022[/C][C]-0.0625274837637519[/C][/ROW]
[ROW][C]65[/C][C]134.3[/C][C]134.35660903386[/C][C]0.271707080016436[/C][C]-0.056609033859675[/C][C]-0.931909547446414[/C][/ROW]
[ROW][C]66[/C][C]131.6[/C][C]131.656129480333[/C][C]-0.965960855405112[/C][C]-0.0561294803332145[/C][C]-0.604805458643475[/C][/ROW]
[ROW][C]67[/C][C]129.8[/C][C]129.856050940574[/C][C]-1.31330321532613[/C][C]-0.0560509405737011[/C][C]-0.169748407971652[/C][/ROW]
[ROW][C]68[/C][C]131.9[/C][C]131.956238507631[/C][C]0.108164667611019[/C][C]-0.0562385076309663[/C][C]0.694700169826487[/C][/ROW]
[ROW][C]69[/C][C]129.8[/C][C]129.856167697739[/C][C]-0.811417471661528[/C][C]-0.0561676977387187[/C][C]-0.449422800575598[/C][/ROW]
[ROW][C]70[/C][C]119.4[/C][C]119.455988266347[/C][C]-4.80453802829208[/C][C]-0.0559882663470741[/C][C]-1.9515443876231[/C][/ROW]
[ROW][C]71[/C][C]116.7[/C][C]116.75601124807[/C][C]-3.9281136915533[/C][C]-0.0560112480701938[/C][C]0.428332402916367[/C][/ROW]
[ROW][C]72[/C][C]112.8[/C][C]112.856011427224[/C][C]-3.91640588861882[/C][C]-0.0560114272238065[/C][C]0.00572192381956158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195150&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195150&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	59.8	59.8	0	0	0
2	60.7	60.6573105392772	0.121738274814838	0.042689460722848	0.130357398926475
3	59.7	59.6505114280491	-0.27386917802115	0.0494885719509289	-0.240456466434007
4	60.2	60.1533544502343	0.0309493642993781	0.0466455497657035	0.160519165581433
5	61.3	61.255676905153	0.467828964443153	0.0443230948469783	0.219028026001216
6	59.8	59.7531708224026	-0.34642352543092	0.04682917759743	-0.401421032680154
7	61.2	61.154470737235	0.379279491813664	0.0455292627649831	0.355722602489568
8	59.3	59.2534801903076	-0.569209386694534	0.0465198096924186	-0.464020224736918
9	59.4	59.3536499364252	-0.290591131027721	0.0463500635747914	0.136215163192438
10	63.1	63.054240659176	1.37112664917373	0.0457593408240222	0.812222107794538
11	68	67.9545455003046	2.84066454592857	0.0454544996954169	0.718232145109719
12	69.4	69.3544728754321	2.24071325446606	0.0455271245679602	-0.293216655424375
13	70.2	70.9309471273026	1.97267591158828	-0.730947127302554	-0.154355936252222
14	72.6	72.541389290668	1.83490414854989	0.0586107093320288	-0.0602604281016014
15	72.1	72.0353533302802	0.855202464894941	0.0646466697197915	-0.473936193600129
16	69.7	69.6304516993642	-0.503889478581724	0.0695483006357555	-0.661917831978629
17	71.5	71.4324748831647	0.456391513981297	0.0675251168353482	0.468759890291639
18	75.7	75.6343929063795	2.01586156256364	0.0656070936204553	0.761848376887705
19	76	75.9338799313552	1.30122753440032	0.0661200686448313	-0.349213294776559
20	76.4	76.3337227070563	0.925903052319145	0.0662772929436726	-0.183422802976398
21	83.8	83.7343817939898	3.62203885518289	0.0656182060101619	1.31765464384639
22	86.2	86.1343091952292	3.11312506855283	0.0656908047707982	-0.248718799762137
23	88.5	88.4342810060099	2.77450288439842	0.0657189939901341	-0.165493658872351
24	95.9	95.8343745823159	4.70076809245502	0.0656254176840735	0.941418136870134
25	103.1	103.366246874719	5.86274792292879	-0.266246874718728	0.61624489651933
26	113.5	113.417679880865	7.51017139109959	0.0823201191348368	0.75721285784431
27	115.7	115.608796852591	5.28797322441066	0.0912031474094137	-1.07888285021937
28	113.1	113.001105840762	1.99760852812297	0.0988941592376309	-1.60447133635061
29	112.7	112.599742190837	0.998572039142688	0.100257809162604	-0.487882018809332
30	121.9	121.802463866189	4.41467209884604	0.0975361338111692	1.66910570826413
31	120.3	120.201299149224	1.90972877064972	0.098700850776421	-1.224125683607
32	108.7	108.599772532269	-3.7164534579745	0.100227467731251	-2.74958650180432
33	102.8	102.699628544542	-4.62578702137978	0.10037145545819	-0.444411709123752
34	83.4	83.299060020934	-10.7784474249791	0.100939979066025	-3.00696360970613
35	79.4	79.2992122354373	-7.95559561595392	0.100787764562689	1.37960358289741
36	77.8	77.6992955198821	-5.30883994734974	0.100704480117867	1.29354168488775
37	85.7	85.4399817468506	0.0744784645387823	0.260018253149367	2.77820642557404
38	83.2	83.2467911631548	-0.831263026128509	-0.0467911631547852	-0.424326848379516
39	82	82.0463351303836	-0.985376281699554	-0.046335130383634	-0.0749515356220588
40	86.9	86.9505784655179	1.46857011772991	-0.0505784655179482	1.19731365630942
41	95.7	95.7536621790916	4.52298341949277	-0.0536621790916317	1.49192868383108
42	97.9	97.9530920552098	3.55545120012558	-0.0530920552097409	-0.472768195277239
43	89.3	89.3513512062125	-1.50686904219375	-0.0513512062125019	-2.4739321545622
44	91.5	91.5516610009739	0.0368628695957446	-0.0516610009739112	0.754447288297182
45	86.8	86.8514299872274	-1.93579023298027	-0.0514299872274004	-0.96408240954917
46	91	91.0516046091838	0.619432722172301	-0.0516046091837986	1.24880441446396
47	93.8	93.8516408234394	1.52751926251311	-0.0516408234394077	0.443806448172243
48	96.8	96.8516550940171	2.14072637471866	-0.0516550940170781	0.299691072621692
49	95.7	95.4101763051466	0.659333793276226	0.289823694853396	-0.754174526229767
50	91.4	91.4635494888303	-1.19674491188508	-0.0635494888302573	-0.878333641232694
51	88.7	88.7620749917175	-1.82456116306393	-0.0620749917174577	-0.305641638925975
52	88.2	88.262832607087	-1.27241677001335	-0.0628326070870283	0.269491523666103
53	87.7	87.7630903623266	-0.950641042505346	-0.063090362326637	0.157189840309063
54	89.5	89.5636259574654	0.19497863270953	-0.0636259574653806	0.559809962269748
55	95.6	95.6642969136827	2.65418883501921	-0.0642969136826655	1.20182083242179
56	100.5	100.564445823665	3.58945751899372	-0.0644458236646887	0.457083373486746
57	106.3	106.364531355932	4.51003059351065	-0.0645313559321045	0.449906628918437
58	112	112.064558224738	5.00558794219669	-0.0645582247384428	0.242191991795482
59	117.7	117.764567374538	5.29477239642712	-0.0645673745383824	0.141332288573002
60	125	125.064582792959	6.12983919245462	-0.06458279295914	0.408119988199482
61	132.4	131.660792244689	6.32298103982757	0.739207755311445	0.0975284968720336
62	138.1	138.165983405759	6.39683105731313	-0.0659834057586353	0.0351647033932701
63	134.7	134.758021096714	2.3073066556048	-0.0580210967143124	-1.99224007635448
64	136.7	136.757875432292	2.17922699762378	-0.0578754322925022	-0.0625274837637519
65	134.3	134.35660903386	0.271707080016436	-0.056609033859675	-0.931909547446414
66	131.6	131.656129480333	-0.965960855405112	-0.0561294803332145	-0.604805458643475
67	129.8	129.856050940574	-1.31330321532613	-0.0560509405737011	-0.169748407971652
68	131.9	131.956238507631	0.108164667611019	-0.0562385076309663	0.694700169826487
69	129.8	129.856167697739	-0.811417471661528	-0.0561676977387187	-0.449422800575598
70	119.4	119.455988266347	-4.80453802829208	-0.0559882663470741	-1.9515443876231
71	116.7	116.75601124807	-3.9281136915533	-0.0560112480701938	0.428332402916367
72	112.8	112.856011427224	-3.91640588861882	-0.0560114272238065	0.00572192381956158

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