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R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Mon, 12 Nov 2012 20:29:14 -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/12/t1352770219l92ntalaabvwchw.htm/, Retrieved Sat, 07 Feb 2026 01:55:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=188524, Retrieved Sat, 07 Feb 2026 01:55:35 +0000

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IsPrivate?

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Estimated Impact

303

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]
- R P         [Univariate Data Series] [] [2012-11-13 01:01:47] [7ba0816b78c58edd3dfdcc950c417269]
- RMP             [Structural Time Series Models] [] [2012-11-13 01:29:14] [f2337e058d7973ced5b4608d8602e1f8] [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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=188524&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=188524&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=188524&T=0

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	9700	9700	0	0	0
2	9081	9420.72572088135	-4.57650590562583	-334.77068502008	-1.94832687028407
3	9084	9148.22896222675	-22.2243875445831	-61.4635790451628	-1.35926283014435
4	9743	9343.35355583652	-8.81461752562042	396.784788453786	1.35805752508255
5	8587	9095.71396620184	-19.3902960412747	-504.920651031314	-1.70074936554354
6	9731	9271.82128915795	-13.6798179021033	455.857775217391	1.45002004532437
7	9563	9434.35676669054	-10.0348186806924	125.592546987779	1.31901459662823
8	9998	9698.07258538314	-5.33029079398532	295.167550090146	2.05145162030975
9	9437	9674.89508662169	-5.62166049542184	-237.584831043575	-0.133629936115216
10	10038	9807.96467915003	-3.34401391015703	227.627651635858	1.03724069661718
11	9918	9889.11518580483	-1.93839485651972	27.4196919882493	0.631405014655373
12	9252	9667.90745025653	-5.59764314597327	-412.107445483491	-1.63795975603681
13	9737	9552.08375903964	-3.60454864393269	186.883929022552	-0.867939210236263
14	9035	9409.58737849509	-2.67974580145488	-372.124540115769	-1.07955414058433
15	9133	9311.85260831709	-4.16578471700865	-177.346353697658	-0.67260262783964
16	9487	9154.69504412586	-8.33829473764172	334.598059687382	-1.05056490127207
17	8700	9193.57731081212	-6.97830915198858	-494.30224905625	0.333409728930745
18	9627	9253.45730004762	-5.3077628287418	372.474755364865	0.48735258280257
19	8947	9171.22093233486	-6.85029544798299	-222.960500206711	-0.570797213653731
20	9283	9097.5457827484	-7.92883151314275	186.562423078578	-0.499482497733582
21	8829	9105.0035157116	-7.72121733031172	-276.259972475282	0.11528118429673
22	9947	9330.4210576024	-5.0818419303781	612.685407331218	1.74695555872627
23	9628	9424.02459976685	-4.23497529720333	202.325354263228	0.738987074020824
24	9318	9518.24229039398	-3.76506232719794	-201.892865568379	0.738153151287752
25	9605	9459.67413326003	-3.82937372764132	146.249788945676	-0.413062021293639
26	8640	9244.03549954723	-4.56264527965705	-600.495828111361	-1.58338539719983
27	9214	9214.61328985033	-4.8113126915217	-0.210167812057477	-0.181312783575778
28	9567	9224.50668800261	-4.57503226375296	342.261022635839	0.105442009715022
29	8547	9155.48462432579	-5.80637815883035	-607.469429877878	-0.463515977768877
30	9185	8982.93319758843	-8.99054792563163	204.729986011092	-1.21607829142995
31	9470	9195.95738085327	-5.1769613828464	270.438745464098	1.64065882867935
32	9123	9183.67709105827	-5.28013567594385	-60.5604467156372	-0.0529175082976271
33	9278	9382.20732402294	-2.87427936202179	-107.575648890438	1.52370115173463
34	10170	9524.11187032098	-1.54142129368911	643.48809553436	1.08336129684396
35	9434	9459.8408060871	-1.96807599454922	-24.7993398517645	-0.469425120516108
36	9655	9554.22704448629	-1.49285885787086	99.171736424332	0.721136120008604
37	9429	9426.43967754841	-2.04248225574352	4.6568154645284	-0.943982807976881
38	8739	9354.03443009993	-2.44846524725121	-613.874673372187	-0.522620841809225
39	9552	9400.48338530928	-2.02148594044035	150.721305987909	0.359358549534025
40	9687	9364.45881927823	-2.42573641654265	323.08748370094	-0.247868888331268
41	9019	9439.23316278641	-1.34211676916011	-421.468677163817	0.562511911194633
42	9672	9526.30387261511	-0.0438604609147463	144.274210703106	0.648123285400349
43	9206	9354.35504140844	-2.4465944170306	-145.565818218281	-1.27009465068198
44	9069	9291.77971091598	-3.19071119967936	-221.796133069612	-0.446964736972526
45	9788	9527.2849198331	-0.71668869142766	256.788915559173	1.7803555324126
46	10312	9624.44042200431	0.0993269211548291	685.944750629991	0.731004447656152
47	10105	9836.1453846405	1.50094825665009	265.358033277189	1.58103251411231
48	9863	9824.45633018931	1.42770128298662	38.7616634808706	-0.0985099258053247
49	9656	9747.28623095349	1.00155298250141	-89.9896545216511	-0.585877635757095
50	9295	9801.81087570147	1.33980741539451	-507.689491013506	0.397278009267572
51	9946	9816.19609858694	1.44365870110054	129.591292219789	0.0962860833989687
52	9701	9676.98596332113	0.0702665582549311	26.2914908472161	-1.03368270761176
53	9049	9569.02176377413	-1.13320562813747	-518.277126906325	-0.793405203278772
54	10190	9686.25045124673	0.25460996684276	501.834441164578	0.871728956117933
55	9706	9795.0789773556	1.49863032220728	-90.8441273525262	0.803221347283888
56	9765	9964.84872657975	3.26699000070155	-202.598691584486	1.2499298240844
57	9893	9928.37892705858	2.90252604503863	-34.7268604832437	-0.295966261330206
58	9994	9736.87158805364	1.39225477947911	260.326960789066	-1.44999649381141
59	10433	9841.18774283132	2.07126977318297	590.116688495433	0.76798106755937
60	10073	9924.94122240685	2.55338459304143	146.713100588801	0.609219810787897
61	10112	10052.8132706441	3.28399085571903	57.1252793317945	0.93323450938399
62	9266	9964.62182780775	2.70104439329983	-697.121896116203	-0.679342920495002
63	9820	9805.67089725743	1.51386933441251	16.9685497523312	-1.19660501909699
64	10097	9863.90276177727	1.99201048491282	232.174591084731	0.418818861641066
65	9115	9841.3251277941	1.76344637881469	-725.926126884434	-0.181327852971248
66	10411	9901.65124060739	2.33314214817596	508.396942604828	0.432822110943608
67	9678	9895.08909514198	2.24753785445854	-216.944135860392	-0.0659119108685137
68	10408	10131.5307794712	4.36822757991437	272.640305354015	1.73986640983884
69	10153	10180.0122695507	4.72970004680046	-27.7355548402914	0.328371402792495
70	10368	10200.9411957027	4.84730992876548	166.792668177107	0.120723392715742
71	10581	10156.2710577479	4.52693610955514	425.543313786251	-0.369175546528211
72	10597	10266.9940206333	5.16344572117128	328.259379373369	0.791496624619376
73	10680	10388.5949601272	5.85285140561279	289.491977748363	0.866895756082703
74	9738	10404.4051843852	5.91494617666305	-666.568450539532	0.0740051431809526
75	9556	10104.9725355273	3.83205984289739	-543.978681308488	-2.26496731138744

\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 & 9420.72572088135 & -4.57650590562583 & -334.77068502008 & -1.94832687028407 \tabularnewline
3 & 9084 & 9148.22896222675 & -22.2243875445831 & -61.4635790451628 & -1.35926283014435 \tabularnewline
4 & 9743 & 9343.35355583652 & -8.81461752562042 & 396.784788453786 & 1.35805752508255 \tabularnewline
5 & 8587 & 9095.71396620184 & -19.3902960412747 & -504.920651031314 & -1.70074936554354 \tabularnewline
6 & 9731 & 9271.82128915795 & -13.6798179021033 & 455.857775217391 & 1.45002004532437 \tabularnewline
7 & 9563 & 9434.35676669054 & -10.0348186806924 & 125.592546987779 & 1.31901459662823 \tabularnewline
8 & 9998 & 9698.07258538314 & -5.33029079398532 & 295.167550090146 & 2.05145162030975 \tabularnewline
9 & 9437 & 9674.89508662169 & -5.62166049542184 & -237.584831043575 & -0.133629936115216 \tabularnewline
10 & 10038 & 9807.96467915003 & -3.34401391015703 & 227.627651635858 & 1.03724069661718 \tabularnewline
11 & 9918 & 9889.11518580483 & -1.93839485651972 & 27.4196919882493 & 0.631405014655373 \tabularnewline
12 & 9252 & 9667.90745025653 & -5.59764314597327 & -412.107445483491 & -1.63795975603681 \tabularnewline
13 & 9737 & 9552.08375903964 & -3.60454864393269 & 186.883929022552 & -0.867939210236263 \tabularnewline
14 & 9035 & 9409.58737849509 & -2.67974580145488 & -372.124540115769 & -1.07955414058433 \tabularnewline
15 & 9133 & 9311.85260831709 & -4.16578471700865 & -177.346353697658 & -0.67260262783964 \tabularnewline
16 & 9487 & 9154.69504412586 & -8.33829473764172 & 334.598059687382 & -1.05056490127207 \tabularnewline
17 & 8700 & 9193.57731081212 & -6.97830915198858 & -494.30224905625 & 0.333409728930745 \tabularnewline
18 & 9627 & 9253.45730004762 & -5.3077628287418 & 372.474755364865 & 0.48735258280257 \tabularnewline
19 & 8947 & 9171.22093233486 & -6.85029544798299 & -222.960500206711 & -0.570797213653731 \tabularnewline
20 & 9283 & 9097.5457827484 & -7.92883151314275 & 186.562423078578 & -0.499482497733582 \tabularnewline
21 & 8829 & 9105.0035157116 & -7.72121733031172 & -276.259972475282 & 0.11528118429673 \tabularnewline
22 & 9947 & 9330.4210576024 & -5.0818419303781 & 612.685407331218 & 1.74695555872627 \tabularnewline
23 & 9628 & 9424.02459976685 & -4.23497529720333 & 202.325354263228 & 0.738987074020824 \tabularnewline
24 & 9318 & 9518.24229039398 & -3.76506232719794 & -201.892865568379 & 0.738153151287752 \tabularnewline
25 & 9605 & 9459.67413326003 & -3.82937372764132 & 146.249788945676 & -0.413062021293639 \tabularnewline
26 & 8640 & 9244.03549954723 & -4.56264527965705 & -600.495828111361 & -1.58338539719983 \tabularnewline
27 & 9214 & 9214.61328985033 & -4.8113126915217 & -0.210167812057477 & -0.181312783575778 \tabularnewline
28 & 9567 & 9224.50668800261 & -4.57503226375296 & 342.261022635839 & 0.105442009715022 \tabularnewline
29 & 8547 & 9155.48462432579 & -5.80637815883035 & -607.469429877878 & -0.463515977768877 \tabularnewline
30 & 9185 & 8982.93319758843 & -8.99054792563163 & 204.729986011092 & -1.21607829142995 \tabularnewline
31 & 9470 & 9195.95738085327 & -5.1769613828464 & 270.438745464098 & 1.64065882867935 \tabularnewline
32 & 9123 & 9183.67709105827 & -5.28013567594385 & -60.5604467156372 & -0.0529175082976271 \tabularnewline
33 & 9278 & 9382.20732402294 & -2.87427936202179 & -107.575648890438 & 1.52370115173463 \tabularnewline
34 & 10170 & 9524.11187032098 & -1.54142129368911 & 643.48809553436 & 1.08336129684396 \tabularnewline
35 & 9434 & 9459.8408060871 & -1.96807599454922 & -24.7993398517645 & -0.469425120516108 \tabularnewline
36 & 9655 & 9554.22704448629 & -1.49285885787086 & 99.171736424332 & 0.721136120008604 \tabularnewline
37 & 9429 & 9426.43967754841 & -2.04248225574352 & 4.6568154645284 & -0.943982807976881 \tabularnewline
38 & 8739 & 9354.03443009993 & -2.44846524725121 & -613.874673372187 & -0.522620841809225 \tabularnewline
39 & 9552 & 9400.48338530928 & -2.02148594044035 & 150.721305987909 & 0.359358549534025 \tabularnewline
40 & 9687 & 9364.45881927823 & -2.42573641654265 & 323.08748370094 & -0.247868888331268 \tabularnewline
41 & 9019 & 9439.23316278641 & -1.34211676916011 & -421.468677163817 & 0.562511911194633 \tabularnewline
42 & 9672 & 9526.30387261511 & -0.0438604609147463 & 144.274210703106 & 0.648123285400349 \tabularnewline
43 & 9206 & 9354.35504140844 & -2.4465944170306 & -145.565818218281 & -1.27009465068198 \tabularnewline
44 & 9069 & 9291.77971091598 & -3.19071119967936 & -221.796133069612 & -0.446964736972526 \tabularnewline
45 & 9788 & 9527.2849198331 & -0.71668869142766 & 256.788915559173 & 1.7803555324126 \tabularnewline
46 & 10312 & 9624.44042200431 & 0.0993269211548291 & 685.944750629991 & 0.731004447656152 \tabularnewline
47 & 10105 & 9836.1453846405 & 1.50094825665009 & 265.358033277189 & 1.58103251411231 \tabularnewline
48 & 9863 & 9824.45633018931 & 1.42770128298662 & 38.7616634808706 & -0.0985099258053247 \tabularnewline
49 & 9656 & 9747.28623095349 & 1.00155298250141 & -89.9896545216511 & -0.585877635757095 \tabularnewline
50 & 9295 & 9801.81087570147 & 1.33980741539451 & -507.689491013506 & 0.397278009267572 \tabularnewline
51 & 9946 & 9816.19609858694 & 1.44365870110054 & 129.591292219789 & 0.0962860833989687 \tabularnewline
52 & 9701 & 9676.98596332113 & 0.0702665582549311 & 26.2914908472161 & -1.03368270761176 \tabularnewline
53 & 9049 & 9569.02176377413 & -1.13320562813747 & -518.277126906325 & -0.793405203278772 \tabularnewline
54 & 10190 & 9686.25045124673 & 0.25460996684276 & 501.834441164578 & 0.871728956117933 \tabularnewline
55 & 9706 & 9795.0789773556 & 1.49863032220728 & -90.8441273525262 & 0.803221347283888 \tabularnewline
56 & 9765 & 9964.84872657975 & 3.26699000070155 & -202.598691584486 & 1.2499298240844 \tabularnewline
57 & 9893 & 9928.37892705858 & 2.90252604503863 & -34.7268604832437 & -0.295966261330206 \tabularnewline
58 & 9994 & 9736.87158805364 & 1.39225477947911 & 260.326960789066 & -1.44999649381141 \tabularnewline
59 & 10433 & 9841.18774283132 & 2.07126977318297 & 590.116688495433 & 0.76798106755937 \tabularnewline
60 & 10073 & 9924.94122240685 & 2.55338459304143 & 146.713100588801 & 0.609219810787897 \tabularnewline
61 & 10112 & 10052.8132706441 & 3.28399085571903 & 57.1252793317945 & 0.93323450938399 \tabularnewline
62 & 9266 & 9964.62182780775 & 2.70104439329983 & -697.121896116203 & -0.679342920495002 \tabularnewline
63 & 9820 & 9805.67089725743 & 1.51386933441251 & 16.9685497523312 & -1.19660501909699 \tabularnewline
64 & 10097 & 9863.90276177727 & 1.99201048491282 & 232.174591084731 & 0.418818861641066 \tabularnewline
65 & 9115 & 9841.3251277941 & 1.76344637881469 & -725.926126884434 & -0.181327852971248 \tabularnewline
66 & 10411 & 9901.65124060739 & 2.33314214817596 & 508.396942604828 & 0.432822110943608 \tabularnewline
67 & 9678 & 9895.08909514198 & 2.24753785445854 & -216.944135860392 & -0.0659119108685137 \tabularnewline
68 & 10408 & 10131.5307794712 & 4.36822757991437 & 272.640305354015 & 1.73986640983884 \tabularnewline
69 & 10153 & 10180.0122695507 & 4.72970004680046 & -27.7355548402914 & 0.328371402792495 \tabularnewline
70 & 10368 & 10200.9411957027 & 4.84730992876548 & 166.792668177107 & 0.120723392715742 \tabularnewline
71 & 10581 & 10156.2710577479 & 4.52693610955514 & 425.543313786251 & -0.369175546528211 \tabularnewline
72 & 10597 & 10266.9940206333 & 5.16344572117128 & 328.259379373369 & 0.791496624619376 \tabularnewline
73 & 10680 & 10388.5949601272 & 5.85285140561279 & 289.491977748363 & 0.866895756082703 \tabularnewline
74 & 9738 & 10404.4051843852 & 5.91494617666305 & -666.568450539532 & 0.0740051431809526 \tabularnewline
75 & 9556 & 10104.9725355273 & 3.83205984289739 & -543.978681308488 & -2.26496731138744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=188524&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]9420.72572088135[/C][C]-4.57650590562583[/C][C]-334.77068502008[/C][C]-1.94832687028407[/C][/ROW]
[ROW][C]3[/C][C]9084[/C][C]9148.22896222675[/C][C]-22.2243875445831[/C][C]-61.4635790451628[/C][C]-1.35926283014435[/C][/ROW]
[ROW][C]4[/C][C]9743[/C][C]9343.35355583652[/C][C]-8.81461752562042[/C][C]396.784788453786[/C][C]1.35805752508255[/C][/ROW]
[ROW][C]5[/C][C]8587[/C][C]9095.71396620184[/C][C]-19.3902960412747[/C][C]-504.920651031314[/C][C]-1.70074936554354[/C][/ROW]
[ROW][C]6[/C][C]9731[/C][C]9271.82128915795[/C][C]-13.6798179021033[/C][C]455.857775217391[/C][C]1.45002004532437[/C][/ROW]
[ROW][C]7[/C][C]9563[/C][C]9434.35676669054[/C][C]-10.0348186806924[/C][C]125.592546987779[/C][C]1.31901459662823[/C][/ROW]
[ROW][C]8[/C][C]9998[/C][C]9698.07258538314[/C][C]-5.33029079398532[/C][C]295.167550090146[/C][C]2.05145162030975[/C][/ROW]
[ROW][C]9[/C][C]9437[/C][C]9674.89508662169[/C][C]-5.62166049542184[/C][C]-237.584831043575[/C][C]-0.133629936115216[/C][/ROW]
[ROW][C]10[/C][C]10038[/C][C]9807.96467915003[/C][C]-3.34401391015703[/C][C]227.627651635858[/C][C]1.03724069661718[/C][/ROW]
[ROW][C]11[/C][C]9918[/C][C]9889.11518580483[/C][C]-1.93839485651972[/C][C]27.4196919882493[/C][C]0.631405014655373[/C][/ROW]
[ROW][C]12[/C][C]9252[/C][C]9667.90745025653[/C][C]-5.59764314597327[/C][C]-412.107445483491[/C][C]-1.63795975603681[/C][/ROW]
[ROW][C]13[/C][C]9737[/C][C]9552.08375903964[/C][C]-3.60454864393269[/C][C]186.883929022552[/C][C]-0.867939210236263[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9409.58737849509[/C][C]-2.67974580145488[/C][C]-372.124540115769[/C][C]-1.07955414058433[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9311.85260831709[/C][C]-4.16578471700865[/C][C]-177.346353697658[/C][C]-0.67260262783964[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9154.69504412586[/C][C]-8.33829473764172[/C][C]334.598059687382[/C][C]-1.05056490127207[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]9193.57731081212[/C][C]-6.97830915198858[/C][C]-494.30224905625[/C][C]0.333409728930745[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9253.45730004762[/C][C]-5.3077628287418[/C][C]372.474755364865[/C][C]0.48735258280257[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9171.22093233486[/C][C]-6.85029544798299[/C][C]-222.960500206711[/C][C]-0.570797213653731[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9097.5457827484[/C][C]-7.92883151314275[/C][C]186.562423078578[/C][C]-0.499482497733582[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9105.0035157116[/C][C]-7.72121733031172[/C][C]-276.259972475282[/C][C]0.11528118429673[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9330.4210576024[/C][C]-5.0818419303781[/C][C]612.685407331218[/C][C]1.74695555872627[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9424.02459976685[/C][C]-4.23497529720333[/C][C]202.325354263228[/C][C]0.738987074020824[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]9518.24229039398[/C][C]-3.76506232719794[/C][C]-201.892865568379[/C][C]0.738153151287752[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9459.67413326003[/C][C]-3.82937372764132[/C][C]146.249788945676[/C][C]-0.413062021293639[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]9244.03549954723[/C][C]-4.56264527965705[/C][C]-600.495828111361[/C][C]-1.58338539719983[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]9214.61328985033[/C][C]-4.8113126915217[/C][C]-0.210167812057477[/C][C]-0.181312783575778[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9224.50668800261[/C][C]-4.57503226375296[/C][C]342.261022635839[/C][C]0.105442009715022[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]9155.48462432579[/C][C]-5.80637815883035[/C][C]-607.469429877878[/C][C]-0.463515977768877[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]8982.93319758843[/C][C]-8.99054792563163[/C][C]204.729986011092[/C][C]-1.21607829142995[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]9195.95738085327[/C][C]-5.1769613828464[/C][C]270.438745464098[/C][C]1.64065882867935[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9183.67709105827[/C][C]-5.28013567594385[/C][C]-60.5604467156372[/C][C]-0.0529175082976271[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]9382.20732402294[/C][C]-2.87427936202179[/C][C]-107.575648890438[/C][C]1.52370115173463[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9524.11187032098[/C][C]-1.54142129368911[/C][C]643.48809553436[/C][C]1.08336129684396[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9459.8408060871[/C][C]-1.96807599454922[/C][C]-24.7993398517645[/C][C]-0.469425120516108[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9554.22704448629[/C][C]-1.49285885787086[/C][C]99.171736424332[/C][C]0.721136120008604[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9426.43967754841[/C][C]-2.04248225574352[/C][C]4.6568154645284[/C][C]-0.943982807976881[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]9354.03443009993[/C][C]-2.44846524725121[/C][C]-613.874673372187[/C][C]-0.522620841809225[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9400.48338530928[/C][C]-2.02148594044035[/C][C]150.721305987909[/C][C]0.359358549534025[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9364.45881927823[/C][C]-2.42573641654265[/C][C]323.08748370094[/C][C]-0.247868888331268[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]9439.23316278641[/C][C]-1.34211676916011[/C][C]-421.468677163817[/C][C]0.562511911194633[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9526.30387261511[/C][C]-0.0438604609147463[/C][C]144.274210703106[/C][C]0.648123285400349[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9354.35504140844[/C][C]-2.4465944170306[/C][C]-145.565818218281[/C][C]-1.27009465068198[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9291.77971091598[/C][C]-3.19071119967936[/C][C]-221.796133069612[/C][C]-0.446964736972526[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9527.2849198331[/C][C]-0.71668869142766[/C][C]256.788915559173[/C][C]1.7803555324126[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]9624.44042200431[/C][C]0.0993269211548291[/C][C]685.944750629991[/C][C]0.731004447656152[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9836.1453846405[/C][C]1.50094825665009[/C][C]265.358033277189[/C][C]1.58103251411231[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9824.45633018931[/C][C]1.42770128298662[/C][C]38.7616634808706[/C][C]-0.0985099258053247[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9747.28623095349[/C][C]1.00155298250141[/C][C]-89.9896545216511[/C][C]-0.585877635757095[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9801.81087570147[/C][C]1.33980741539451[/C][C]-507.689491013506[/C][C]0.397278009267572[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9816.19609858694[/C][C]1.44365870110054[/C][C]129.591292219789[/C][C]0.0962860833989687[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]9676.98596332113[/C][C]0.0702665582549311[/C][C]26.2914908472161[/C][C]-1.03368270761176[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9569.02176377413[/C][C]-1.13320562813747[/C][C]-518.277126906325[/C][C]-0.793405203278772[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9686.25045124673[/C][C]0.25460996684276[/C][C]501.834441164578[/C][C]0.871728956117933[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9795.0789773556[/C][C]1.49863032220728[/C][C]-90.8441273525262[/C][C]0.803221347283888[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9964.84872657975[/C][C]3.26699000070155[/C][C]-202.598691584486[/C][C]1.2499298240844[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]9928.37892705858[/C][C]2.90252604503863[/C][C]-34.7268604832437[/C][C]-0.295966261330206[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]9736.87158805364[/C][C]1.39225477947911[/C][C]260.326960789066[/C][C]-1.44999649381141[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]9841.18774283132[/C][C]2.07126977318297[/C][C]590.116688495433[/C][C]0.76798106755937[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]9924.94122240685[/C][C]2.55338459304143[/C][C]146.713100588801[/C][C]0.609219810787897[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]10052.8132706441[/C][C]3.28399085571903[/C][C]57.1252793317945[/C][C]0.93323450938399[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9964.62182780775[/C][C]2.70104439329983[/C][C]-697.121896116203[/C][C]-0.679342920495002[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]9805.67089725743[/C][C]1.51386933441251[/C][C]16.9685497523312[/C][C]-1.19660501909699[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9863.90276177727[/C][C]1.99201048491282[/C][C]232.174591084731[/C][C]0.418818861641066[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9841.3251277941[/C][C]1.76344637881469[/C][C]-725.926126884434[/C][C]-0.181327852971248[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]9901.65124060739[/C][C]2.33314214817596[/C][C]508.396942604828[/C][C]0.432822110943608[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9895.08909514198[/C][C]2.24753785445854[/C][C]-216.944135860392[/C][C]-0.0659119108685137[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]10131.5307794712[/C][C]4.36822757991437[/C][C]272.640305354015[/C][C]1.73986640983884[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10180.0122695507[/C][C]4.72970004680046[/C][C]-27.7355548402914[/C][C]0.328371402792495[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10200.9411957027[/C][C]4.84730992876548[/C][C]166.792668177107[/C][C]0.120723392715742[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10156.2710577479[/C][C]4.52693610955514[/C][C]425.543313786251[/C][C]-0.369175546528211[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10266.9940206333[/C][C]5.16344572117128[/C][C]328.259379373369[/C][C]0.791496624619376[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10388.5949601272[/C][C]5.85285140561279[/C][C]289.491977748363[/C][C]0.866895756082703[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]10404.4051843852[/C][C]5.91494617666305[/C][C]-666.568450539532[/C][C]0.0740051431809526[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10104.9725355273[/C][C]3.83205984289739[/C][C]-543.978681308488[/C][C]-2.26496731138744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=188524&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=188524&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	9420.72572088135	-4.57650590562583	-334.77068502008	-1.94832687028407
3	9084	9148.22896222675	-22.2243875445831	-61.4635790451628	-1.35926283014435
4	9743	9343.35355583652	-8.81461752562042	396.784788453786	1.35805752508255
5	8587	9095.71396620184	-19.3902960412747	-504.920651031314	-1.70074936554354
6	9731	9271.82128915795	-13.6798179021033	455.857775217391	1.45002004532437
7	9563	9434.35676669054	-10.0348186806924	125.592546987779	1.31901459662823
8	9998	9698.07258538314	-5.33029079398532	295.167550090146	2.05145162030975
9	9437	9674.89508662169	-5.62166049542184	-237.584831043575	-0.133629936115216
10	10038	9807.96467915003	-3.34401391015703	227.627651635858	1.03724069661718
11	9918	9889.11518580483	-1.93839485651972	27.4196919882493	0.631405014655373
12	9252	9667.90745025653	-5.59764314597327	-412.107445483491	-1.63795975603681
13	9737	9552.08375903964	-3.60454864393269	186.883929022552	-0.867939210236263
14	9035	9409.58737849509	-2.67974580145488	-372.124540115769	-1.07955414058433
15	9133	9311.85260831709	-4.16578471700865	-177.346353697658	-0.67260262783964
16	9487	9154.69504412586	-8.33829473764172	334.598059687382	-1.05056490127207
17	8700	9193.57731081212	-6.97830915198858	-494.30224905625	0.333409728930745
18	9627	9253.45730004762	-5.3077628287418	372.474755364865	0.48735258280257
19	8947	9171.22093233486	-6.85029544798299	-222.960500206711	-0.570797213653731
20	9283	9097.5457827484	-7.92883151314275	186.562423078578	-0.499482497733582
21	8829	9105.0035157116	-7.72121733031172	-276.259972475282	0.11528118429673
22	9947	9330.4210576024	-5.0818419303781	612.685407331218	1.74695555872627
23	9628	9424.02459976685	-4.23497529720333	202.325354263228	0.738987074020824
24	9318	9518.24229039398	-3.76506232719794	-201.892865568379	0.738153151287752
25	9605	9459.67413326003	-3.82937372764132	146.249788945676	-0.413062021293639
26	8640	9244.03549954723	-4.56264527965705	-600.495828111361	-1.58338539719983
27	9214	9214.61328985033	-4.8113126915217	-0.210167812057477	-0.181312783575778
28	9567	9224.50668800261	-4.57503226375296	342.261022635839	0.105442009715022
29	8547	9155.48462432579	-5.80637815883035	-607.469429877878	-0.463515977768877
30	9185	8982.93319758843	-8.99054792563163	204.729986011092	-1.21607829142995
31	9470	9195.95738085327	-5.1769613828464	270.438745464098	1.64065882867935
32	9123	9183.67709105827	-5.28013567594385	-60.5604467156372	-0.0529175082976271
33	9278	9382.20732402294	-2.87427936202179	-107.575648890438	1.52370115173463
34	10170	9524.11187032098	-1.54142129368911	643.48809553436	1.08336129684396
35	9434	9459.8408060871	-1.96807599454922	-24.7993398517645	-0.469425120516108
36	9655	9554.22704448629	-1.49285885787086	99.171736424332	0.721136120008604
37	9429	9426.43967754841	-2.04248225574352	4.6568154645284	-0.943982807976881
38	8739	9354.03443009993	-2.44846524725121	-613.874673372187	-0.522620841809225
39	9552	9400.48338530928	-2.02148594044035	150.721305987909	0.359358549534025
40	9687	9364.45881927823	-2.42573641654265	323.08748370094	-0.247868888331268
41	9019	9439.23316278641	-1.34211676916011	-421.468677163817	0.562511911194633
42	9672	9526.30387261511	-0.0438604609147463	144.274210703106	0.648123285400349
43	9206	9354.35504140844	-2.4465944170306	-145.565818218281	-1.27009465068198
44	9069	9291.77971091598	-3.19071119967936	-221.796133069612	-0.446964736972526
45	9788	9527.2849198331	-0.71668869142766	256.788915559173	1.7803555324126
46	10312	9624.44042200431	0.0993269211548291	685.944750629991	0.731004447656152
47	10105	9836.1453846405	1.50094825665009	265.358033277189	1.58103251411231
48	9863	9824.45633018931	1.42770128298662	38.7616634808706	-0.0985099258053247
49	9656	9747.28623095349	1.00155298250141	-89.9896545216511	-0.585877635757095
50	9295	9801.81087570147	1.33980741539451	-507.689491013506	0.397278009267572
51	9946	9816.19609858694	1.44365870110054	129.591292219789	0.0962860833989687
52	9701	9676.98596332113	0.0702665582549311	26.2914908472161	-1.03368270761176
53	9049	9569.02176377413	-1.13320562813747	-518.277126906325	-0.793405203278772
54	10190	9686.25045124673	0.25460996684276	501.834441164578	0.871728956117933
55	9706	9795.0789773556	1.49863032220728	-90.8441273525262	0.803221347283888
56	9765	9964.84872657975	3.26699000070155	-202.598691584486	1.2499298240844
57	9893	9928.37892705858	2.90252604503863	-34.7268604832437	-0.295966261330206
58	9994	9736.87158805364	1.39225477947911	260.326960789066	-1.44999649381141
59	10433	9841.18774283132	2.07126977318297	590.116688495433	0.76798106755937
60	10073	9924.94122240685	2.55338459304143	146.713100588801	0.609219810787897
61	10112	10052.8132706441	3.28399085571903	57.1252793317945	0.93323450938399
62	9266	9964.62182780775	2.70104439329983	-697.121896116203	-0.679342920495002
63	9820	9805.67089725743	1.51386933441251	16.9685497523312	-1.19660501909699
64	10097	9863.90276177727	1.99201048491282	232.174591084731	0.418818861641066
65	9115	9841.3251277941	1.76344637881469	-725.926126884434	-0.181327852971248
66	10411	9901.65124060739	2.33314214817596	508.396942604828	0.432822110943608
67	9678	9895.08909514198	2.24753785445854	-216.944135860392	-0.0659119108685137
68	10408	10131.5307794712	4.36822757991437	272.640305354015	1.73986640983884
69	10153	10180.0122695507	4.72970004680046	-27.7355548402914	0.328371402792495
70	10368	10200.9411957027	4.84730992876548	166.792668177107	0.120723392715742
71	10581	10156.2710577479	4.52693610955514	425.543313786251	-0.369175546528211
72	10597	10266.9940206333	5.16344572117128	328.259379373369	0.791496624619376
73	10680	10388.5949601272	5.85285140561279	289.491977748363	0.866895756082703
74	9738	10404.4051843852	5.91494617666305	-666.568450539532	0.0740051431809526
75	9556	10104.9725355273	3.83205984289739	-543.978681308488	-2.26496731138744

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