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Structural Time Series Models

Date of computation

Wed, 27 Nov 2013 21:35:31 -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/2013/Nov/27/t13856061386y5f6djsqevlklx.htm/, Retrieved Mon, 29 Apr 2024 13:53:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229178, Retrieved Mon, 29 Apr 2024 13:53:47 +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 Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Structural Time Series Models] [WS8: Structural T...] [2012-11-22 13:01:13] [73586a5ad7cb70bd9d8f219d68ef24b6]
- RM              [Structural Time Series Models] [] [2013-11-28 02:35:31] [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	6 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 & 6 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229178&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]6 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=229178&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229178&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	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	9700	9700	0	0	0
2	9081	9420.75534855199	-4.57309005414925	-334.809656133766	-1.94834233353035
3	9084	9148.23681304996	-22.2228324194573	-61.4764080168714	-1.35941202912031
4	9743	9343.34042237475	-8.81343040478239	396.803719095776	1.35792559118875
5	8587	9095.71794577328	-19.3897705437256	-504.932085873077	-1.70068213258547
6	9731	9271.80935357071	-13.6789053189743	455.876241551857	1.44995449824689
7	9563	9434.34157101725	-10.0335119070046	125.613538466011	1.31903979241334
8	9998	9698.05277455607	-5.32867042515834	295.196383339666	2.05149723799353
9	9437	9674.89359265038	-5.61978426565983	-237.584207961196	-0.133510804104988
10	10038	9807.960002383	-3.34211104374617	227.636926357699	1.03724835423323
11	9918	9889.11187295499	-1.93643006689646	27.4257592995891	0.631428495803008
12	9252	9667.92206288852	-5.59561438263755	-412.129455298054	-1.63791153123622
13	9737	9552.09673292144	-3.60291303249015	186.867331298579	-0.867997288966891
14	9035	9409.6045308197	-2.67799038622164	-372.146323972933	-1.07958715017294
15	9133	9311.8674637109	-4.16388138199647	-177.363932784747	-0.6726683722269
16	9487	9154.70496438778	-8.33649044199379	334.583963876599	-1.05065569779451
17	8700	9193.58274363402	-6.97662342798474	-494.306224323897	0.333376762510389
18	9627	9253.45665240867	-5.30611167093077	372.477532026236	0.487313610465123
19	8947	9171.22219856989	-6.84882860641563	-222.964132266305	-0.570818059094276
20	9283	9097.54352347646	-7.92757697731067	186.562692239169	-0.499540958550639
21	8829	9104.99860546162	-7.71999509924839	-276.254518045126	0.115256926625467
22	9947	9330.40069558411	-5.08062386483179	612.713319368563	1.74690713405446
23	9628	9424.00699823351	-4.2336892260828	202.346011438165	0.739031113053178
24	9318	9518.23324934119	-3.76366410957429	-201.880863482011	0.7382399880221
25	9605	9459.67948873172	-3.82804163094699	146.242487498528	-0.412981271781821
26	8640	9244.05590108533	-4.56140678988308	-600.523068786789	-1.58335183799335
27	9214	9214.62764831041	-4.81013763273581	-0.22515935018059	-0.181374415632695
28	9567	9224.51717058538	-4.57394589305237	342.251052549569	0.105410581675466
29	8547	9155.49409583326	-5.80533754699979	-607.480765171361	-0.46355025092837
30	9185	8982.9437561199	-8.98964452579239	204.714442181488	-1.21612599593983
31	9470	9195.94977937513	-5.17610189679198	270.453401315822	1.64058374074186
32	9123	9183.67779650025	-5.2791774802775	-60.561492393887	-0.0528642176675717
33	9278	9382.19716370664	-2.87322832073637	-107.558997854042	1.52367746099457
34	10170	9524.09425203613	-1.54031564780128	643.510338439346	1.08334430820871
35	9434	9459.82994469404	-1.9669842794927	-24.7905173912511	-0.469403201143593
36	9655	9554.21052078832	-1.4917129194757	99.1913630748823	0.721116780711331
37	9429	9426.440204917	-2.04138555861924	4.6521079656469	-0.943904509669429
38	8739	9354.04525919485	-2.44735856468092	-613.887819499368	-0.522575332519961
39	9552	9400.49139347728	-2.02040768316172	150.714845172622	0.359345888005635
40	9687	9364.4698354374	-2.42462995986503	323.075417816691	-0.247865995620457
41	9019	9439.24094949365	-1.3410766139186	-421.474088615306	0.562504783072611
42	9672	9526.31259608928	-0.0428002528425941	144.268145783405	0.648149669107271
43	9206	9354.37081022107	-2.4455498595861	-145.586898822481	-1.27010286256063
44	9069	9291.78891478252	-3.18980847698942	-221.807051628344	-0.447039881234846
45	9788	9527.26866330024	-0.715850576423168	256.812943299528	1.78023393246572
46	10312	9624.42016437485	0.100211470240847	685.968105301338	0.730999497915097
47	10105	9836.11998038803	1.50198135202239	265.390069156292	1.58105540804935
48	9863	9824.44228430115	1.42878010730025	38.7751318297001	-0.0984370525435768
49	9656	9747.28651317558	1.00264192344492	-89.9925765903169	-0.585804217448706
50	9295	9801.81345733772	1.34093348364258	-507.690452077037	0.397304413484031
51	9946	9816.20288749432	1.44481250339541	129.584849916699	0.0963131193449886
52	9701	9677.00381169591	0.0715148368080913	26.2692338677064	-1.03365616798114
53	9049	9569.03854557257	-1.13197880359327	-518.297126868695	-0.793457167449151
54	10190	9686.25385828471	0.255674060646229	501.834845757328	0.871658921327052
55	9706	9795.08410156763	1.49973165828775	-90.8459645319912	0.803260153597851
56	9765	9964.84995753557	3.26812001201982	-202.594702366161	1.24994535825273
57	9893	9928.37955837887	2.90361450815234	-34.7286819282486	-0.295991666012637
58	9994	9736.87346512086	1.39319797853729	260.319105141993	-1.45005711655378
59	10433	9841.16895698433	2.07215315380453	590.138997072426	0.767852769841204
60	10073	9924.92239245375	2.55432679567888	146.734459291319	0.609239136706893
61	10112	10052.7993802873	3.28504223935974	57.1429537393578	0.933304756870176
62	9266	9964.62360809379	2.70214316368767	-697.12671581134	-0.679264140205079
63	9820	9805.68390166276	1.51499737223014	16.9504547895107	-1.19658314756813
64	10097	9863.91322081197	1.99311293280302	232.165913083476	0.418810387330148
65	9115	9841.34228057075	1.76460062796137	-725.944114781722	-0.181294601987163
66	10411	9901.66168165606	2.33422209816352	508.388405775682	0.432782826087989
67	9678	9895.09611809772	2.2485731162224	-216.951356335166	-0.0659480734311708
68	10408	10131.5181975542	4.36915097090551	272.660375807678	1.73978727386636
69	10153	10180.0044874449	4.73067642711336	-27.7264850760512	0.328414258657286
70	10368	10200.9384737923	4.84832577837536	166.795820249956	0.120758991815425
71	10581	10156.2673868467	4.5279059047316	425.545495861981	-0.369206053880769
72	10597	10266.9784821143	5.16440960309164	328.278390516174	0.791435108005612
73	10680	10388.5759024032	5.85385733423934	289.514681065728	0.866900055495605
74	9738	10404.3990842246	5.91603110056213	-666.562241209605	0.0740972194248406
75	9556	10104.9951589431	3.8332477035943	-544.011075258887	-2.26486245203599

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 9700 & 9700 & 0 & 0 & 0 \tabularnewline
2 & 9081 & 9420.75534855199 & -4.57309005414925 & -334.809656133766 & -1.94834233353035 \tabularnewline
3 & 9084 & 9148.23681304996 & -22.2228324194573 & -61.4764080168714 & -1.35941202912031 \tabularnewline
4 & 9743 & 9343.34042237475 & -8.81343040478239 & 396.803719095776 & 1.35792559118875 \tabularnewline
5 & 8587 & 9095.71794577328 & -19.3897705437256 & -504.932085873077 & -1.70068213258547 \tabularnewline
6 & 9731 & 9271.80935357071 & -13.6789053189743 & 455.876241551857 & 1.44995449824689 \tabularnewline
7 & 9563 & 9434.34157101725 & -10.0335119070046 & 125.613538466011 & 1.31903979241334 \tabularnewline
8 & 9998 & 9698.05277455607 & -5.32867042515834 & 295.196383339666 & 2.05149723799353 \tabularnewline
9 & 9437 & 9674.89359265038 & -5.61978426565983 & -237.584207961196 & -0.133510804104988 \tabularnewline
10 & 10038 & 9807.960002383 & -3.34211104374617 & 227.636926357699 & 1.03724835423323 \tabularnewline
11 & 9918 & 9889.11187295499 & -1.93643006689646 & 27.4257592995891 & 0.631428495803008 \tabularnewline
12 & 9252 & 9667.92206288852 & -5.59561438263755 & -412.129455298054 & -1.63791153123622 \tabularnewline
13 & 9737 & 9552.09673292144 & -3.60291303249015 & 186.867331298579 & -0.867997288966891 \tabularnewline
14 & 9035 & 9409.6045308197 & -2.67799038622164 & -372.146323972933 & -1.07958715017294 \tabularnewline
15 & 9133 & 9311.8674637109 & -4.16388138199647 & -177.363932784747 & -0.6726683722269 \tabularnewline
16 & 9487 & 9154.70496438778 & -8.33649044199379 & 334.583963876599 & -1.05065569779451 \tabularnewline
17 & 8700 & 9193.58274363402 & -6.97662342798474 & -494.306224323897 & 0.333376762510389 \tabularnewline
18 & 9627 & 9253.45665240867 & -5.30611167093077 & 372.477532026236 & 0.487313610465123 \tabularnewline
19 & 8947 & 9171.22219856989 & -6.84882860641563 & -222.964132266305 & -0.570818059094276 \tabularnewline
20 & 9283 & 9097.54352347646 & -7.92757697731067 & 186.562692239169 & -0.499540958550639 \tabularnewline
21 & 8829 & 9104.99860546162 & -7.71999509924839 & -276.254518045126 & 0.115256926625467 \tabularnewline
22 & 9947 & 9330.40069558411 & -5.08062386483179 & 612.713319368563 & 1.74690713405446 \tabularnewline
23 & 9628 & 9424.00699823351 & -4.2336892260828 & 202.346011438165 & 0.739031113053178 \tabularnewline
24 & 9318 & 9518.23324934119 & -3.76366410957429 & -201.880863482011 & 0.7382399880221 \tabularnewline
25 & 9605 & 9459.67948873172 & -3.82804163094699 & 146.242487498528 & -0.412981271781821 \tabularnewline
26 & 8640 & 9244.05590108533 & -4.56140678988308 & -600.523068786789 & -1.58335183799335 \tabularnewline
27 & 9214 & 9214.62764831041 & -4.81013763273581 & -0.22515935018059 & -0.181374415632695 \tabularnewline
28 & 9567 & 9224.51717058538 & -4.57394589305237 & 342.251052549569 & 0.105410581675466 \tabularnewline
29 & 8547 & 9155.49409583326 & -5.80533754699979 & -607.480765171361 & -0.46355025092837 \tabularnewline
30 & 9185 & 8982.9437561199 & -8.98964452579239 & 204.714442181488 & -1.21612599593983 \tabularnewline
31 & 9470 & 9195.94977937513 & -5.17610189679198 & 270.453401315822 & 1.64058374074186 \tabularnewline
32 & 9123 & 9183.67779650025 & -5.2791774802775 & -60.561492393887 & -0.0528642176675717 \tabularnewline
33 & 9278 & 9382.19716370664 & -2.87322832073637 & -107.558997854042 & 1.52367746099457 \tabularnewline
34 & 10170 & 9524.09425203613 & -1.54031564780128 & 643.510338439346 & 1.08334430820871 \tabularnewline
35 & 9434 & 9459.82994469404 & -1.9669842794927 & -24.7905173912511 & -0.469403201143593 \tabularnewline
36 & 9655 & 9554.21052078832 & -1.4917129194757 & 99.1913630748823 & 0.721116780711331 \tabularnewline
37 & 9429 & 9426.440204917 & -2.04138555861924 & 4.6521079656469 & -0.943904509669429 \tabularnewline
38 & 8739 & 9354.04525919485 & -2.44735856468092 & -613.887819499368 & -0.522575332519961 \tabularnewline
39 & 9552 & 9400.49139347728 & -2.02040768316172 & 150.714845172622 & 0.359345888005635 \tabularnewline
40 & 9687 & 9364.4698354374 & -2.42462995986503 & 323.075417816691 & -0.247865995620457 \tabularnewline
41 & 9019 & 9439.24094949365 & -1.3410766139186 & -421.474088615306 & 0.562504783072611 \tabularnewline
42 & 9672 & 9526.31259608928 & -0.0428002528425941 & 144.268145783405 & 0.648149669107271 \tabularnewline
43 & 9206 & 9354.37081022107 & -2.4455498595861 & -145.586898822481 & -1.27010286256063 \tabularnewline
44 & 9069 & 9291.78891478252 & -3.18980847698942 & -221.807051628344 & -0.447039881234846 \tabularnewline
45 & 9788 & 9527.26866330024 & -0.715850576423168 & 256.812943299528 & 1.78023393246572 \tabularnewline
46 & 10312 & 9624.42016437485 & 0.100211470240847 & 685.968105301338 & 0.730999497915097 \tabularnewline
47 & 10105 & 9836.11998038803 & 1.50198135202239 & 265.390069156292 & 1.58105540804935 \tabularnewline
48 & 9863 & 9824.44228430115 & 1.42878010730025 & 38.7751318297001 & -0.0984370525435768 \tabularnewline
49 & 9656 & 9747.28651317558 & 1.00264192344492 & -89.9925765903169 & -0.585804217448706 \tabularnewline
50 & 9295 & 9801.81345733772 & 1.34093348364258 & -507.690452077037 & 0.397304413484031 \tabularnewline
51 & 9946 & 9816.20288749432 & 1.44481250339541 & 129.584849916699 & 0.0963131193449886 \tabularnewline
52 & 9701 & 9677.00381169591 & 0.0715148368080913 & 26.2692338677064 & -1.03365616798114 \tabularnewline
53 & 9049 & 9569.03854557257 & -1.13197880359327 & -518.297126868695 & -0.793457167449151 \tabularnewline
54 & 10190 & 9686.25385828471 & 0.255674060646229 & 501.834845757328 & 0.871658921327052 \tabularnewline
55 & 9706 & 9795.08410156763 & 1.49973165828775 & -90.8459645319912 & 0.803260153597851 \tabularnewline
56 & 9765 & 9964.84995753557 & 3.26812001201982 & -202.594702366161 & 1.24994535825273 \tabularnewline
57 & 9893 & 9928.37955837887 & 2.90361450815234 & -34.7286819282486 & -0.295991666012637 \tabularnewline
58 & 9994 & 9736.87346512086 & 1.39319797853729 & 260.319105141993 & -1.45005711655378 \tabularnewline
59 & 10433 & 9841.16895698433 & 2.07215315380453 & 590.138997072426 & 0.767852769841204 \tabularnewline
60 & 10073 & 9924.92239245375 & 2.55432679567888 & 146.734459291319 & 0.609239136706893 \tabularnewline
61 & 10112 & 10052.7993802873 & 3.28504223935974 & 57.1429537393578 & 0.933304756870176 \tabularnewline
62 & 9266 & 9964.62360809379 & 2.70214316368767 & -697.12671581134 & -0.679264140205079 \tabularnewline
63 & 9820 & 9805.68390166276 & 1.51499737223014 & 16.9504547895107 & -1.19658314756813 \tabularnewline
64 & 10097 & 9863.91322081197 & 1.99311293280302 & 232.165913083476 & 0.418810387330148 \tabularnewline
65 & 9115 & 9841.34228057075 & 1.76460062796137 & -725.944114781722 & -0.181294601987163 \tabularnewline
66 & 10411 & 9901.66168165606 & 2.33422209816352 & 508.388405775682 & 0.432782826087989 \tabularnewline
67 & 9678 & 9895.09611809772 & 2.2485731162224 & -216.951356335166 & -0.0659480734311708 \tabularnewline
68 & 10408 & 10131.5181975542 & 4.36915097090551 & 272.660375807678 & 1.73978727386636 \tabularnewline
69 & 10153 & 10180.0044874449 & 4.73067642711336 & -27.7264850760512 & 0.328414258657286 \tabularnewline
70 & 10368 & 10200.9384737923 & 4.84832577837536 & 166.795820249956 & 0.120758991815425 \tabularnewline
71 & 10581 & 10156.2673868467 & 4.5279059047316 & 425.545495861981 & -0.369206053880769 \tabularnewline
72 & 10597 & 10266.9784821143 & 5.16440960309164 & 328.278390516174 & 0.791435108005612 \tabularnewline
73 & 10680 & 10388.5759024032 & 5.85385733423934 & 289.514681065728 & 0.866900055495605 \tabularnewline
74 & 9738 & 10404.3990842246 & 5.91603110056213 & -666.562241209605 & 0.0740972194248406 \tabularnewline
75 & 9556 & 10104.9951589431 & 3.8332477035943 & -544.011075258887 & -2.26486245203599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229178&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]9700[/C][C]9700[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]9081[/C][C]9420.75534855199[/C][C]-4.57309005414925[/C][C]-334.809656133766[/C][C]-1.94834233353035[/C][/ROW]
[ROW][C]3[/C][C]9084[/C][C]9148.23681304996[/C][C]-22.2228324194573[/C][C]-61.4764080168714[/C][C]-1.35941202912031[/C][/ROW]
[ROW][C]4[/C][C]9743[/C][C]9343.34042237475[/C][C]-8.81343040478239[/C][C]396.803719095776[/C][C]1.35792559118875[/C][/ROW]
[ROW][C]5[/C][C]8587[/C][C]9095.71794577328[/C][C]-19.3897705437256[/C][C]-504.932085873077[/C][C]-1.70068213258547[/C][/ROW]
[ROW][C]6[/C][C]9731[/C][C]9271.80935357071[/C][C]-13.6789053189743[/C][C]455.876241551857[/C][C]1.44995449824689[/C][/ROW]
[ROW][C]7[/C][C]9563[/C][C]9434.34157101725[/C][C]-10.0335119070046[/C][C]125.613538466011[/C][C]1.31903979241334[/C][/ROW]
[ROW][C]8[/C][C]9998[/C][C]9698.05277455607[/C][C]-5.32867042515834[/C][C]295.196383339666[/C][C]2.05149723799353[/C][/ROW]
[ROW][C]9[/C][C]9437[/C][C]9674.89359265038[/C][C]-5.61978426565983[/C][C]-237.584207961196[/C][C]-0.133510804104988[/C][/ROW]
[ROW][C]10[/C][C]10038[/C][C]9807.960002383[/C][C]-3.34211104374617[/C][C]227.636926357699[/C][C]1.03724835423323[/C][/ROW]
[ROW][C]11[/C][C]9918[/C][C]9889.11187295499[/C][C]-1.93643006689646[/C][C]27.4257592995891[/C][C]0.631428495803008[/C][/ROW]
[ROW][C]12[/C][C]9252[/C][C]9667.92206288852[/C][C]-5.59561438263755[/C][C]-412.129455298054[/C][C]-1.63791153123622[/C][/ROW]
[ROW][C]13[/C][C]9737[/C][C]9552.09673292144[/C][C]-3.60291303249015[/C][C]186.867331298579[/C][C]-0.867997288966891[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9409.6045308197[/C][C]-2.67799038622164[/C][C]-372.146323972933[/C][C]-1.07958715017294[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9311.8674637109[/C][C]-4.16388138199647[/C][C]-177.363932784747[/C][C]-0.6726683722269[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9154.70496438778[/C][C]-8.33649044199379[/C][C]334.583963876599[/C][C]-1.05065569779451[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]9193.58274363402[/C][C]-6.97662342798474[/C][C]-494.306224323897[/C][C]0.333376762510389[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9253.45665240867[/C][C]-5.30611167093077[/C][C]372.477532026236[/C][C]0.487313610465123[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9171.22219856989[/C][C]-6.84882860641563[/C][C]-222.964132266305[/C][C]-0.570818059094276[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9097.54352347646[/C][C]-7.92757697731067[/C][C]186.562692239169[/C][C]-0.499540958550639[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9104.99860546162[/C][C]-7.71999509924839[/C][C]-276.254518045126[/C][C]0.115256926625467[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9330.40069558411[/C][C]-5.08062386483179[/C][C]612.713319368563[/C][C]1.74690713405446[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9424.00699823351[/C][C]-4.2336892260828[/C][C]202.346011438165[/C][C]0.739031113053178[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]9518.23324934119[/C][C]-3.76366410957429[/C][C]-201.880863482011[/C][C]0.7382399880221[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9459.67948873172[/C][C]-3.82804163094699[/C][C]146.242487498528[/C][C]-0.412981271781821[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]9244.05590108533[/C][C]-4.56140678988308[/C][C]-600.523068786789[/C][C]-1.58335183799335[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]9214.62764831041[/C][C]-4.81013763273581[/C][C]-0.22515935018059[/C][C]-0.181374415632695[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9224.51717058538[/C][C]-4.57394589305237[/C][C]342.251052549569[/C][C]0.105410581675466[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]9155.49409583326[/C][C]-5.80533754699979[/C][C]-607.480765171361[/C][C]-0.46355025092837[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]8982.9437561199[/C][C]-8.98964452579239[/C][C]204.714442181488[/C][C]-1.21612599593983[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]9195.94977937513[/C][C]-5.17610189679198[/C][C]270.453401315822[/C][C]1.64058374074186[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9183.67779650025[/C][C]-5.2791774802775[/C][C]-60.561492393887[/C][C]-0.0528642176675717[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]9382.19716370664[/C][C]-2.87322832073637[/C][C]-107.558997854042[/C][C]1.52367746099457[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9524.09425203613[/C][C]-1.54031564780128[/C][C]643.510338439346[/C][C]1.08334430820871[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9459.82994469404[/C][C]-1.9669842794927[/C][C]-24.7905173912511[/C][C]-0.469403201143593[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9554.21052078832[/C][C]-1.4917129194757[/C][C]99.1913630748823[/C][C]0.721116780711331[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9426.440204917[/C][C]-2.04138555861924[/C][C]4.6521079656469[/C][C]-0.943904509669429[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]9354.04525919485[/C][C]-2.44735856468092[/C][C]-613.887819499368[/C][C]-0.522575332519961[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9400.49139347728[/C][C]-2.02040768316172[/C][C]150.714845172622[/C][C]0.359345888005635[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9364.4698354374[/C][C]-2.42462995986503[/C][C]323.075417816691[/C][C]-0.247865995620457[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]9439.24094949365[/C][C]-1.3410766139186[/C][C]-421.474088615306[/C][C]0.562504783072611[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9526.31259608928[/C][C]-0.0428002528425941[/C][C]144.268145783405[/C][C]0.648149669107271[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9354.37081022107[/C][C]-2.4455498595861[/C][C]-145.586898822481[/C][C]-1.27010286256063[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9291.78891478252[/C][C]-3.18980847698942[/C][C]-221.807051628344[/C][C]-0.447039881234846[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9527.26866330024[/C][C]-0.715850576423168[/C][C]256.812943299528[/C][C]1.78023393246572[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]9624.42016437485[/C][C]0.100211470240847[/C][C]685.968105301338[/C][C]0.730999497915097[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9836.11998038803[/C][C]1.50198135202239[/C][C]265.390069156292[/C][C]1.58105540804935[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9824.44228430115[/C][C]1.42878010730025[/C][C]38.7751318297001[/C][C]-0.0984370525435768[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9747.28651317558[/C][C]1.00264192344492[/C][C]-89.9925765903169[/C][C]-0.585804217448706[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9801.81345733772[/C][C]1.34093348364258[/C][C]-507.690452077037[/C][C]0.397304413484031[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9816.20288749432[/C][C]1.44481250339541[/C][C]129.584849916699[/C][C]0.0963131193449886[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]9677.00381169591[/C][C]0.0715148368080913[/C][C]26.2692338677064[/C][C]-1.03365616798114[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9569.03854557257[/C][C]-1.13197880359327[/C][C]-518.297126868695[/C][C]-0.793457167449151[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9686.25385828471[/C][C]0.255674060646229[/C][C]501.834845757328[/C][C]0.871658921327052[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9795.08410156763[/C][C]1.49973165828775[/C][C]-90.8459645319912[/C][C]0.803260153597851[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9964.84995753557[/C][C]3.26812001201982[/C][C]-202.594702366161[/C][C]1.24994535825273[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]9928.37955837887[/C][C]2.90361450815234[/C][C]-34.7286819282486[/C][C]-0.295991666012637[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]9736.87346512086[/C][C]1.39319797853729[/C][C]260.319105141993[/C][C]-1.45005711655378[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]9841.16895698433[/C][C]2.07215315380453[/C][C]590.138997072426[/C][C]0.767852769841204[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]9924.92239245375[/C][C]2.55432679567888[/C][C]146.734459291319[/C][C]0.609239136706893[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]10052.7993802873[/C][C]3.28504223935974[/C][C]57.1429537393578[/C][C]0.933304756870176[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9964.62360809379[/C][C]2.70214316368767[/C][C]-697.12671581134[/C][C]-0.679264140205079[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]9805.68390166276[/C][C]1.51499737223014[/C][C]16.9504547895107[/C][C]-1.19658314756813[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9863.91322081197[/C][C]1.99311293280302[/C][C]232.165913083476[/C][C]0.418810387330148[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9841.34228057075[/C][C]1.76460062796137[/C][C]-725.944114781722[/C][C]-0.181294601987163[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]9901.66168165606[/C][C]2.33422209816352[/C][C]508.388405775682[/C][C]0.432782826087989[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9895.09611809772[/C][C]2.2485731162224[/C][C]-216.951356335166[/C][C]-0.0659480734311708[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]10131.5181975542[/C][C]4.36915097090551[/C][C]272.660375807678[/C][C]1.73978727386636[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10180.0044874449[/C][C]4.73067642711336[/C][C]-27.7264850760512[/C][C]0.328414258657286[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10200.9384737923[/C][C]4.84832577837536[/C][C]166.795820249956[/C][C]0.120758991815425[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10156.2673868467[/C][C]4.5279059047316[/C][C]425.545495861981[/C][C]-0.369206053880769[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10266.9784821143[/C][C]5.16440960309164[/C][C]328.278390516174[/C][C]0.791435108005612[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10388.5759024032[/C][C]5.85385733423934[/C][C]289.514681065728[/C][C]0.866900055495605[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]10404.3990842246[/C][C]5.91603110056213[/C][C]-666.562241209605[/C][C]0.0740972194248406[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10104.9951589431[/C][C]3.8332477035943[/C][C]-544.011075258887[/C][C]-2.26486245203599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229178&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229178&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	9700	9700	0	0	0
2	9081	9420.75534855199	-4.57309005414925	-334.809656133766	-1.94834233353035
3	9084	9148.23681304996	-22.2228324194573	-61.4764080168714	-1.35941202912031
4	9743	9343.34042237475	-8.81343040478239	396.803719095776	1.35792559118875
5	8587	9095.71794577328	-19.3897705437256	-504.932085873077	-1.70068213258547
6	9731	9271.80935357071	-13.6789053189743	455.876241551857	1.44995449824689
7	9563	9434.34157101725	-10.0335119070046	125.613538466011	1.31903979241334
8	9998	9698.05277455607	-5.32867042515834	295.196383339666	2.05149723799353
9	9437	9674.89359265038	-5.61978426565983	-237.584207961196	-0.133510804104988
10	10038	9807.960002383	-3.34211104374617	227.636926357699	1.03724835423323
11	9918	9889.11187295499	-1.93643006689646	27.4257592995891	0.631428495803008
12	9252	9667.92206288852	-5.59561438263755	-412.129455298054	-1.63791153123622
13	9737	9552.09673292144	-3.60291303249015	186.867331298579	-0.867997288966891
14	9035	9409.6045308197	-2.67799038622164	-372.146323972933	-1.07958715017294
15	9133	9311.8674637109	-4.16388138199647	-177.363932784747	-0.6726683722269
16	9487	9154.70496438778	-8.33649044199379	334.583963876599	-1.05065569779451
17	8700	9193.58274363402	-6.97662342798474	-494.306224323897	0.333376762510389
18	9627	9253.45665240867	-5.30611167093077	372.477532026236	0.487313610465123
19	8947	9171.22219856989	-6.84882860641563	-222.964132266305	-0.570818059094276
20	9283	9097.54352347646	-7.92757697731067	186.562692239169	-0.499540958550639
21	8829	9104.99860546162	-7.71999509924839	-276.254518045126	0.115256926625467
22	9947	9330.40069558411	-5.08062386483179	612.713319368563	1.74690713405446
23	9628	9424.00699823351	-4.2336892260828	202.346011438165	0.739031113053178
24	9318	9518.23324934119	-3.76366410957429	-201.880863482011	0.7382399880221
25	9605	9459.67948873172	-3.82804163094699	146.242487498528	-0.412981271781821
26	8640	9244.05590108533	-4.56140678988308	-600.523068786789	-1.58335183799335
27	9214	9214.62764831041	-4.81013763273581	-0.22515935018059	-0.181374415632695
28	9567	9224.51717058538	-4.57394589305237	342.251052549569	0.105410581675466
29	8547	9155.49409583326	-5.80533754699979	-607.480765171361	-0.46355025092837
30	9185	8982.9437561199	-8.98964452579239	204.714442181488	-1.21612599593983
31	9470	9195.94977937513	-5.17610189679198	270.453401315822	1.64058374074186
32	9123	9183.67779650025	-5.2791774802775	-60.561492393887	-0.0528642176675717
33	9278	9382.19716370664	-2.87322832073637	-107.558997854042	1.52367746099457
34	10170	9524.09425203613	-1.54031564780128	643.510338439346	1.08334430820871
35	9434	9459.82994469404	-1.9669842794927	-24.7905173912511	-0.469403201143593
36	9655	9554.21052078832	-1.4917129194757	99.1913630748823	0.721116780711331
37	9429	9426.440204917	-2.04138555861924	4.6521079656469	-0.943904509669429
38	8739	9354.04525919485	-2.44735856468092	-613.887819499368	-0.522575332519961
39	9552	9400.49139347728	-2.02040768316172	150.714845172622	0.359345888005635
40	9687	9364.4698354374	-2.42462995986503	323.075417816691	-0.247865995620457
41	9019	9439.24094949365	-1.3410766139186	-421.474088615306	0.562504783072611
42	9672	9526.31259608928	-0.0428002528425941	144.268145783405	0.648149669107271
43	9206	9354.37081022107	-2.4455498595861	-145.586898822481	-1.27010286256063
44	9069	9291.78891478252	-3.18980847698942	-221.807051628344	-0.447039881234846
45	9788	9527.26866330024	-0.715850576423168	256.812943299528	1.78023393246572
46	10312	9624.42016437485	0.100211470240847	685.968105301338	0.730999497915097
47	10105	9836.11998038803	1.50198135202239	265.390069156292	1.58105540804935
48	9863	9824.44228430115	1.42878010730025	38.7751318297001	-0.0984370525435768
49	9656	9747.28651317558	1.00264192344492	-89.9925765903169	-0.585804217448706
50	9295	9801.81345733772	1.34093348364258	-507.690452077037	0.397304413484031
51	9946	9816.20288749432	1.44481250339541	129.584849916699	0.0963131193449886
52	9701	9677.00381169591	0.0715148368080913	26.2692338677064	-1.03365616798114
53	9049	9569.03854557257	-1.13197880359327	-518.297126868695	-0.793457167449151
54	10190	9686.25385828471	0.255674060646229	501.834845757328	0.871658921327052
55	9706	9795.08410156763	1.49973165828775	-90.8459645319912	0.803260153597851
56	9765	9964.84995753557	3.26812001201982	-202.594702366161	1.24994535825273
57	9893	9928.37955837887	2.90361450815234	-34.7286819282486	-0.295991666012637
58	9994	9736.87346512086	1.39319797853729	260.319105141993	-1.45005711655378
59	10433	9841.16895698433	2.07215315380453	590.138997072426	0.767852769841204
60	10073	9924.92239245375	2.55432679567888	146.734459291319	0.609239136706893
61	10112	10052.7993802873	3.28504223935974	57.1429537393578	0.933304756870176
62	9266	9964.62360809379	2.70214316368767	-697.12671581134	-0.679264140205079
63	9820	9805.68390166276	1.51499737223014	16.9504547895107	-1.19658314756813
64	10097	9863.91322081197	1.99311293280302	232.165913083476	0.418810387330148
65	9115	9841.34228057075	1.76460062796137	-725.944114781722	-0.181294601987163
66	10411	9901.66168165606	2.33422209816352	508.388405775682	0.432782826087989
67	9678	9895.09611809772	2.2485731162224	-216.951356335166	-0.0659480734311708
68	10408	10131.5181975542	4.36915097090551	272.660375807678	1.73978727386636
69	10153	10180.0044874449	4.73067642711336	-27.7264850760512	0.328414258657286
70	10368	10200.9384737923	4.84832577837536	166.795820249956	0.120758991815425
71	10581	10156.2673868467	4.5279059047316	425.545495861981	-0.369206053880769
72	10597	10266.9784821143	5.16440960309164	328.278390516174	0.791435108005612
73	10680	10388.5759024032	5.85385733423934	289.514681065728	0.866900055495605
74	9738	10404.3990842246	5.91603110056213	-666.562241209605	0.0740972194248406
75	9556	10104.9951589431	3.8332477035943	-544.011075258887	-2.26486245203599

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 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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