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Author

*The author of this computation has been verified*

R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Tue, 07 Dec 2010 12:42:20 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/07/t1291725686an71zfrgjvifte3.htm/, Retrieved Fri, 15 Aug 2025 04:51:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106239, Retrieved Fri, 15 Aug 2025 04:51:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

403

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Structural Time Series Models] [HPC Retail Sales] [2008-03-06 16:52:55] [74be16979710d4c4e7c6647856088456]
- R  D    [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456]
-  M D        [Structural Time Series Models] [] [2010-12-07 12:42:20] [ae555db68faeb138426117ca316fbf2a] [Current]
- RMP           [Exponential Smoothing] [] [2010-12-07 12:46:53] [b2f924a86c4fbfa8afa1027f3839f526] 
- RMPD            [Multiple Regression] [] [2010-12-07 12:51:30] [b2f924a86c4fbfa8afa1027f3839f526] 
-    D              [Multiple Regression] [] [2010-12-09 16:17:21] [b2f924a86c4fbfa8afa1027f3839f526] 
-    D            [Exponential Smoothing] [] [2010-12-09 16:12:25] [b2f924a86c4fbfa8afa1027f3839f526] 
-    D          [Structural Time Series Models] [] [2010-12-09 16:08:50] [b2f924a86c4fbfa8afa1027f3839f526] 
- R               [Structural Time Series Models] [] [2010-12-10 12:32:01] [b2f924a86c4fbfa8afa1027f3839f526] 

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Dataseries X:

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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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106239&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106239&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106239&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	9700	9700	0	0	0
2	9081	9420.62455281495	-4.5890426297954	-334.626271902039	-1.94825201291792
3	9084	9148.2077517124	-22.2303618909331	-61.4190688909295	-1.35872117365695
4	9743	9343.40355518114	-8.8193715342712	396.708384935167	1.35850437495548
5	8587	9095.70202034107	-19.3928504723650	-504.874476723729	-1.70098600051497
6	9731	9271.86407345205	-13.6836322275629	455.785036080261	1.45024067345611
7	9563	9434.40844999122	-10.0399239606939	125.514093292607	1.31890702427521
8	9998	9698.13795425041	-5.33632031363061	295.060465637396	2.05127007984087
9	9437	9674.89595659924	-5.62859801659247	-237.581978828241	-0.134046595619623
10	10038	9807.97758753645	-3.35094274695094	227.593480956693	1.03721999324648
11	9918	9889.12380139853	-1.94548511099250	27.3982918679218	0.631326425854686
12	9252	9667.85545584089	-5.6050188046502	-412.021472076373	-1.63810580704716
13	9737	9552.0412545418	-3.61040227495166	186.943252254166	-0.867707542115775
14	9035	9409.52966529666	-2.68610765998603	-372.045359372442	-1.07943661012622
15	9133	9311.8021903386	-4.17279616924874	-177.283195680046	-0.672370905652503
16	9487	9154.66553084616	-8.34497094258953	334.647008087387	-1.05021514512539
17	8700	9193.55821813077	-6.9846990075786	-494.289731604054	0.333489306211107
18	9627	9253.4586044127	-5.31403601802089	372.463723032358	0.487484467042734
19	8947	9171.21697982802	-6.8558937647209	-222.945610987148	-0.570707897539624
20	9283	9097.55670913712	-7.93365258961034	186.560772068260	-0.499253744665062
21	8829	9105.02135657368	-7.72594706235133	-276.280234763893	0.115351198940874
22	9947	9330.49146897202	-5.08649185514184	612.580274984794	1.74711149030179
23	9628	9424.08534386672	-4.23982836968727	202.250390752836	0.738833540386894
24	9318	9518.27043512378	-3.77030289426937	-201.934851549524	0.737829998929544
25	9605	9459.6525333162	-3.83436376185997	146.280162888563	-0.413336377929872
26	8640	9243.96375879017	-4.5673021732229	-600.392639825714	-1.58347703966637
27	9214	9214.56358112121	-4.81574726388101	-0.157408460500335	-0.181087518937939
28	9567	9224.46897353754	-4.57916825516746	342.296465463807	0.105542558958506
29	8547	9155.45177696454	-5.81034756066413	-607.427922744883	-0.463382439639212
30	9185	8982.89970567253	-8.99400504744033	204.786549860404	-1.21588207581558
31	9470	9195.98429437877	-5.18028867497022	270.379490905194	1.64089527434201
32	9123	9183.67228549114	-5.28384289359201	-60.5541585213881	-0.0531211458806797
33	9278	9382.238653821	-2.87829799995906	-107.636861116059	1.52376779855306
34	10170	9524.17096509914	-1.54558636518991	643.407657381585	1.08343245497791
35	9434	9459.87903816316	-1.97218082081931	-24.8282625863602	-0.469477382632173
36	9655	9554.28603843822	-1.49714181641705	99.0984420902315	0.721210944559087
37	9429	9426.43881059238	-2.04658905859906	4.67679322160564	-0.944253596916056
38	8739	9353.99551485272	-2.45262076854173	-613.825140780271	-0.522791335292416
39	9552	9400.4538714729	-2.0255327633396	150.743709316006	0.359400179017050
40	9687	9364.41978943982	-2.42987756385864	323.131332353283	-0.247868711532408
41	9019	9439.20439028914	-1.34601321892296	-421.450841987691	0.562529215139126
42	9672	9526.26882372462	-0.047847268485069	144.296967051820	0.648008784330493
43	9206	9354.29953962991	-2.45049008702385	-145.485846509328	-1.27002892558780
44	9069	9291.74798991872	-3.19410451169397	-221.756334733109	-0.446692690210052
45	9788	9527.3417025869	-0.719835326329942	256.696550113955	1.78077301638989
46	10312	9624.51109713784	0.096027957588888	685.859787070915	0.731020408457668
47	10105	9836.2318452694	1.49713127116114	265.240934276026	1.58093275393686
48	9863	9824.50498151234	1.42373578282638	38.7154690254109	-0.0987486279718978
49	9656	9747.28483630863	0.997551636934981	-89.9762517528914	-0.586130706721582
50	9295	9801.80000511374	1.33567199133678	-507.6861449915	0.397175228268162
51	9946	9816.17047588593	1.43942942766346	129.615247558962	0.096192398012906
52	9701	9676.92268320296	0.0656899687826051	26.3750423304587	-1.03376292817842
53	9049	9568.96478398853	-1.13769998998178	-518.205210398125	-0.793200338741033
54	10190	9686.23967611857	0.250703430598917	501.827789847443	0.871968273634657
55	9706	9795.05731572663	1.49455614989545	-90.8376573032048	0.803048404502364
56	9765	9964.83782038248	3.26280650936327	-202.611880267706	1.24985211411604
57	9893	9928.37450467282	2.89852693427271	-34.7169593287432	-0.295842154417687
58	9994	9736.86782675455	1.38879256112751	260.358382812888	-1.44974137909044
59	10433	9841.25817106834	2.06803443808084	590.030267379287	0.768443002439589
60	10073	9925.0086381795	2.54992803660270	146.634013698928	0.609127917613946
61	10112	10052.8594328691	3.28013450841469	57.0615418148054	0.932957672188076
62	9266	9964.6145447027	2.69702650226427	-697.100793514692	-0.679604846605334
63	9820	9805.62721745523	1.50975423348385	17.0356306578212	-1.19665516212745
64	10097	9863.86565054821	1.98797486111284	232.203534808297	0.418831124021567
65	9115	9841.26216105916	1.75920451005729	-725.859346237903	-0.181460233955533
66	10411	9901.6122055634	2.3291757362672	508.427267971591	0.432962988604558
67	9678	9895.06325750294	2.24374033344239	-216.917323822984	-0.0657746447297351
68	10408	10131.5737565930	4.36484884925401	272.562933780309	1.74014104808724
69	10153	10180.0375683428	4.72613312181003	-27.7668886134338	0.328215053005083
70	10368	10200.9474765953	4.84359730176286	166.784335743943	0.120589854460093
71	10581	10156.2839481808	4.52340528299437	425.537312848946	-0.369042073997497
72	10597	10267.0495364991	5.15994571093786	328.187955970625	0.79171878968827
73	10680	10388.6627388489	5.84920868267741	289.407355389986	0.86687876213114
74	9738	10404.4257558570	5.91101679723834	-666.58971639717	0.0736698387168638
75	9556	10104.8935041481	3.82775190582163	-543.854804388791	-2.26531949085490

\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 & 9420.62455281495 & -4.5890426297954 & -334.626271902039 & -1.94825201291792 \tabularnewline
3 & 9084 & 9148.2077517124 & -22.2303618909331 & -61.4190688909295 & -1.35872117365695 \tabularnewline
4 & 9743 & 9343.40355518114 & -8.8193715342712 & 396.708384935167 & 1.35850437495548 \tabularnewline
5 & 8587 & 9095.70202034107 & -19.3928504723650 & -504.874476723729 & -1.70098600051497 \tabularnewline
6 & 9731 & 9271.86407345205 & -13.6836322275629 & 455.785036080261 & 1.45024067345611 \tabularnewline
7 & 9563 & 9434.40844999122 & -10.0399239606939 & 125.514093292607 & 1.31890702427521 \tabularnewline
8 & 9998 & 9698.13795425041 & -5.33632031363061 & 295.060465637396 & 2.05127007984087 \tabularnewline
9 & 9437 & 9674.89595659924 & -5.62859801659247 & -237.581978828241 & -0.134046595619623 \tabularnewline
10 & 10038 & 9807.97758753645 & -3.35094274695094 & 227.593480956693 & 1.03721999324648 \tabularnewline
11 & 9918 & 9889.12380139853 & -1.94548511099250 & 27.3982918679218 & 0.631326425854686 \tabularnewline
12 & 9252 & 9667.85545584089 & -5.6050188046502 & -412.021472076373 & -1.63810580704716 \tabularnewline
13 & 9737 & 9552.0412545418 & -3.61040227495166 & 186.943252254166 & -0.867707542115775 \tabularnewline
14 & 9035 & 9409.52966529666 & -2.68610765998603 & -372.045359372442 & -1.07943661012622 \tabularnewline
15 & 9133 & 9311.8021903386 & -4.17279616924874 & -177.283195680046 & -0.672370905652503 \tabularnewline
16 & 9487 & 9154.66553084616 & -8.34497094258953 & 334.647008087387 & -1.05021514512539 \tabularnewline
17 & 8700 & 9193.55821813077 & -6.9846990075786 & -494.289731604054 & 0.333489306211107 \tabularnewline
18 & 9627 & 9253.4586044127 & -5.31403601802089 & 372.463723032358 & 0.487484467042734 \tabularnewline
19 & 8947 & 9171.21697982802 & -6.8558937647209 & -222.945610987148 & -0.570707897539624 \tabularnewline
20 & 9283 & 9097.55670913712 & -7.93365258961034 & 186.560772068260 & -0.499253744665062 \tabularnewline
21 & 8829 & 9105.02135657368 & -7.72594706235133 & -276.280234763893 & 0.115351198940874 \tabularnewline
22 & 9947 & 9330.49146897202 & -5.08649185514184 & 612.580274984794 & 1.74711149030179 \tabularnewline
23 & 9628 & 9424.08534386672 & -4.23982836968727 & 202.250390752836 & 0.738833540386894 \tabularnewline
24 & 9318 & 9518.27043512378 & -3.77030289426937 & -201.934851549524 & 0.737829998929544 \tabularnewline
25 & 9605 & 9459.6525333162 & -3.83436376185997 & 146.280162888563 & -0.413336377929872 \tabularnewline
26 & 8640 & 9243.96375879017 & -4.5673021732229 & -600.392639825714 & -1.58347703966637 \tabularnewline
27 & 9214 & 9214.56358112121 & -4.81574726388101 & -0.157408460500335 & -0.181087518937939 \tabularnewline
28 & 9567 & 9224.46897353754 & -4.57916825516746 & 342.296465463807 & 0.105542558958506 \tabularnewline
29 & 8547 & 9155.45177696454 & -5.81034756066413 & -607.427922744883 & -0.463382439639212 \tabularnewline
30 & 9185 & 8982.89970567253 & -8.99400504744033 & 204.786549860404 & -1.21588207581558 \tabularnewline
31 & 9470 & 9195.98429437877 & -5.18028867497022 & 270.379490905194 & 1.64089527434201 \tabularnewline
32 & 9123 & 9183.67228549114 & -5.28384289359201 & -60.5541585213881 & -0.0531211458806797 \tabularnewline
33 & 9278 & 9382.238653821 & -2.87829799995906 & -107.636861116059 & 1.52376779855306 \tabularnewline
34 & 10170 & 9524.17096509914 & -1.54558636518991 & 643.407657381585 & 1.08343245497791 \tabularnewline
35 & 9434 & 9459.87903816316 & -1.97218082081931 & -24.8282625863602 & -0.469477382632173 \tabularnewline
36 & 9655 & 9554.28603843822 & -1.49714181641705 & 99.0984420902315 & 0.721210944559087 \tabularnewline
37 & 9429 & 9426.43881059238 & -2.04658905859906 & 4.67679322160564 & -0.944253596916056 \tabularnewline
38 & 8739 & 9353.99551485272 & -2.45262076854173 & -613.825140780271 & -0.522791335292416 \tabularnewline
39 & 9552 & 9400.4538714729 & -2.0255327633396 & 150.743709316006 & 0.359400179017050 \tabularnewline
40 & 9687 & 9364.41978943982 & -2.42987756385864 & 323.131332353283 & -0.247868711532408 \tabularnewline
41 & 9019 & 9439.20439028914 & -1.34601321892296 & -421.450841987691 & 0.562529215139126 \tabularnewline
42 & 9672 & 9526.26882372462 & -0.047847268485069 & 144.296967051820 & 0.648008784330493 \tabularnewline
43 & 9206 & 9354.29953962991 & -2.45049008702385 & -145.485846509328 & -1.27002892558780 \tabularnewline
44 & 9069 & 9291.74798991872 & -3.19410451169397 & -221.756334733109 & -0.446692690210052 \tabularnewline
45 & 9788 & 9527.3417025869 & -0.719835326329942 & 256.696550113955 & 1.78077301638989 \tabularnewline
46 & 10312 & 9624.51109713784 & 0.096027957588888 & 685.859787070915 & 0.731020408457668 \tabularnewline
47 & 10105 & 9836.2318452694 & 1.49713127116114 & 265.240934276026 & 1.58093275393686 \tabularnewline
48 & 9863 & 9824.50498151234 & 1.42373578282638 & 38.7154690254109 & -0.0987486279718978 \tabularnewline
49 & 9656 & 9747.28483630863 & 0.997551636934981 & -89.9762517528914 & -0.586130706721582 \tabularnewline
50 & 9295 & 9801.80000511374 & 1.33567199133678 & -507.6861449915 & 0.397175228268162 \tabularnewline
51 & 9946 & 9816.17047588593 & 1.43942942766346 & 129.615247558962 & 0.096192398012906 \tabularnewline
52 & 9701 & 9676.92268320296 & 0.0656899687826051 & 26.3750423304587 & -1.03376292817842 \tabularnewline
53 & 9049 & 9568.96478398853 & -1.13769998998178 & -518.205210398125 & -0.793200338741033 \tabularnewline
54 & 10190 & 9686.23967611857 & 0.250703430598917 & 501.827789847443 & 0.871968273634657 \tabularnewline
55 & 9706 & 9795.05731572663 & 1.49455614989545 & -90.8376573032048 & 0.803048404502364 \tabularnewline
56 & 9765 & 9964.83782038248 & 3.26280650936327 & -202.611880267706 & 1.24985211411604 \tabularnewline
57 & 9893 & 9928.37450467282 & 2.89852693427271 & -34.7169593287432 & -0.295842154417687 \tabularnewline
58 & 9994 & 9736.86782675455 & 1.38879256112751 & 260.358382812888 & -1.44974137909044 \tabularnewline
59 & 10433 & 9841.25817106834 & 2.06803443808084 & 590.030267379287 & 0.768443002439589 \tabularnewline
60 & 10073 & 9925.0086381795 & 2.54992803660270 & 146.634013698928 & 0.609127917613946 \tabularnewline
61 & 10112 & 10052.8594328691 & 3.28013450841469 & 57.0615418148054 & 0.932957672188076 \tabularnewline
62 & 9266 & 9964.6145447027 & 2.69702650226427 & -697.100793514692 & -0.679604846605334 \tabularnewline
63 & 9820 & 9805.62721745523 & 1.50975423348385 & 17.0356306578212 & -1.19665516212745 \tabularnewline
64 & 10097 & 9863.86565054821 & 1.98797486111284 & 232.203534808297 & 0.418831124021567 \tabularnewline
65 & 9115 & 9841.26216105916 & 1.75920451005729 & -725.859346237903 & -0.181460233955533 \tabularnewline
66 & 10411 & 9901.6122055634 & 2.3291757362672 & 508.427267971591 & 0.432962988604558 \tabularnewline
67 & 9678 & 9895.06325750294 & 2.24374033344239 & -216.917323822984 & -0.0657746447297351 \tabularnewline
68 & 10408 & 10131.5737565930 & 4.36484884925401 & 272.562933780309 & 1.74014104808724 \tabularnewline
69 & 10153 & 10180.0375683428 & 4.72613312181003 & -27.7668886134338 & 0.328215053005083 \tabularnewline
70 & 10368 & 10200.9474765953 & 4.84359730176286 & 166.784335743943 & 0.120589854460093 \tabularnewline
71 & 10581 & 10156.2839481808 & 4.52340528299437 & 425.537312848946 & -0.369042073997497 \tabularnewline
72 & 10597 & 10267.0495364991 & 5.15994571093786 & 328.187955970625 & 0.79171878968827 \tabularnewline
73 & 10680 & 10388.6627388489 & 5.84920868267741 & 289.407355389986 & 0.86687876213114 \tabularnewline
74 & 9738 & 10404.4257558570 & 5.91101679723834 & -666.58971639717 & 0.0736698387168638 \tabularnewline
75 & 9556 & 10104.8935041481 & 3.82775190582163 & -543.854804388791 & -2.26531949085490 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106239&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]9420.62455281495[/C][C]-4.5890426297954[/C][C]-334.626271902039[/C][C]-1.94825201291792[/C][/ROW]
[ROW][C]3[/C][C]9084[/C][C]9148.2077517124[/C][C]-22.2303618909331[/C][C]-61.4190688909295[/C][C]-1.35872117365695[/C][/ROW]
[ROW][C]4[/C][C]9743[/C][C]9343.40355518114[/C][C]-8.8193715342712[/C][C]396.708384935167[/C][C]1.35850437495548[/C][/ROW]
[ROW][C]5[/C][C]8587[/C][C]9095.70202034107[/C][C]-19.3928504723650[/C][C]-504.874476723729[/C][C]-1.70098600051497[/C][/ROW]
[ROW][C]6[/C][C]9731[/C][C]9271.86407345205[/C][C]-13.6836322275629[/C][C]455.785036080261[/C][C]1.45024067345611[/C][/ROW]
[ROW][C]7[/C][C]9563[/C][C]9434.40844999122[/C][C]-10.0399239606939[/C][C]125.514093292607[/C][C]1.31890702427521[/C][/ROW]
[ROW][C]8[/C][C]9998[/C][C]9698.13795425041[/C][C]-5.33632031363061[/C][C]295.060465637396[/C][C]2.05127007984087[/C][/ROW]
[ROW][C]9[/C][C]9437[/C][C]9674.89595659924[/C][C]-5.62859801659247[/C][C]-237.581978828241[/C][C]-0.134046595619623[/C][/ROW]
[ROW][C]10[/C][C]10038[/C][C]9807.97758753645[/C][C]-3.35094274695094[/C][C]227.593480956693[/C][C]1.03721999324648[/C][/ROW]
[ROW][C]11[/C][C]9918[/C][C]9889.12380139853[/C][C]-1.94548511099250[/C][C]27.3982918679218[/C][C]0.631326425854686[/C][/ROW]
[ROW][C]12[/C][C]9252[/C][C]9667.85545584089[/C][C]-5.6050188046502[/C][C]-412.021472076373[/C][C]-1.63810580704716[/C][/ROW]
[ROW][C]13[/C][C]9737[/C][C]9552.0412545418[/C][C]-3.61040227495166[/C][C]186.943252254166[/C][C]-0.867707542115775[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9409.52966529666[/C][C]-2.68610765998603[/C][C]-372.045359372442[/C][C]-1.07943661012622[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9311.8021903386[/C][C]-4.17279616924874[/C][C]-177.283195680046[/C][C]-0.672370905652503[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9154.66553084616[/C][C]-8.34497094258953[/C][C]334.647008087387[/C][C]-1.05021514512539[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]9193.55821813077[/C][C]-6.9846990075786[/C][C]-494.289731604054[/C][C]0.333489306211107[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9253.4586044127[/C][C]-5.31403601802089[/C][C]372.463723032358[/C][C]0.487484467042734[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9171.21697982802[/C][C]-6.8558937647209[/C][C]-222.945610987148[/C][C]-0.570707897539624[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9097.55670913712[/C][C]-7.93365258961034[/C][C]186.560772068260[/C][C]-0.499253744665062[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9105.02135657368[/C][C]-7.72594706235133[/C][C]-276.280234763893[/C][C]0.115351198940874[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9330.49146897202[/C][C]-5.08649185514184[/C][C]612.580274984794[/C][C]1.74711149030179[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9424.08534386672[/C][C]-4.23982836968727[/C][C]202.250390752836[/C][C]0.738833540386894[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]9518.27043512378[/C][C]-3.77030289426937[/C][C]-201.934851549524[/C][C]0.737829998929544[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9459.6525333162[/C][C]-3.83436376185997[/C][C]146.280162888563[/C][C]-0.413336377929872[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]9243.96375879017[/C][C]-4.5673021732229[/C][C]-600.392639825714[/C][C]-1.58347703966637[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]9214.56358112121[/C][C]-4.81574726388101[/C][C]-0.157408460500335[/C][C]-0.181087518937939[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9224.46897353754[/C][C]-4.57916825516746[/C][C]342.296465463807[/C][C]0.105542558958506[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]9155.45177696454[/C][C]-5.81034756066413[/C][C]-607.427922744883[/C][C]-0.463382439639212[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]8982.89970567253[/C][C]-8.99400504744033[/C][C]204.786549860404[/C][C]-1.21588207581558[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]9195.98429437877[/C][C]-5.18028867497022[/C][C]270.379490905194[/C][C]1.64089527434201[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9183.67228549114[/C][C]-5.28384289359201[/C][C]-60.5541585213881[/C][C]-0.0531211458806797[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]9382.238653821[/C][C]-2.87829799995906[/C][C]-107.636861116059[/C][C]1.52376779855306[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9524.17096509914[/C][C]-1.54558636518991[/C][C]643.407657381585[/C][C]1.08343245497791[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9459.87903816316[/C][C]-1.97218082081931[/C][C]-24.8282625863602[/C][C]-0.469477382632173[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9554.28603843822[/C][C]-1.49714181641705[/C][C]99.0984420902315[/C][C]0.721210944559087[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9426.43881059238[/C][C]-2.04658905859906[/C][C]4.67679322160564[/C][C]-0.944253596916056[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]9353.99551485272[/C][C]-2.45262076854173[/C][C]-613.825140780271[/C][C]-0.522791335292416[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9400.4538714729[/C][C]-2.0255327633396[/C][C]150.743709316006[/C][C]0.359400179017050[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9364.41978943982[/C][C]-2.42987756385864[/C][C]323.131332353283[/C][C]-0.247868711532408[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]9439.20439028914[/C][C]-1.34601321892296[/C][C]-421.450841987691[/C][C]0.562529215139126[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9526.26882372462[/C][C]-0.047847268485069[/C][C]144.296967051820[/C][C]0.648008784330493[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9354.29953962991[/C][C]-2.45049008702385[/C][C]-145.485846509328[/C][C]-1.27002892558780[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9291.74798991872[/C][C]-3.19410451169397[/C][C]-221.756334733109[/C][C]-0.446692690210052[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9527.3417025869[/C][C]-0.719835326329942[/C][C]256.696550113955[/C][C]1.78077301638989[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]9624.51109713784[/C][C]0.096027957588888[/C][C]685.859787070915[/C][C]0.731020408457668[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9836.2318452694[/C][C]1.49713127116114[/C][C]265.240934276026[/C][C]1.58093275393686[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9824.50498151234[/C][C]1.42373578282638[/C][C]38.7154690254109[/C][C]-0.0987486279718978[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9747.28483630863[/C][C]0.997551636934981[/C][C]-89.9762517528914[/C][C]-0.586130706721582[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9801.80000511374[/C][C]1.33567199133678[/C][C]-507.6861449915[/C][C]0.397175228268162[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9816.17047588593[/C][C]1.43942942766346[/C][C]129.615247558962[/C][C]0.096192398012906[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]9676.92268320296[/C][C]0.0656899687826051[/C][C]26.3750423304587[/C][C]-1.03376292817842[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9568.96478398853[/C][C]-1.13769998998178[/C][C]-518.205210398125[/C][C]-0.793200338741033[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9686.23967611857[/C][C]0.250703430598917[/C][C]501.827789847443[/C][C]0.871968273634657[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9795.05731572663[/C][C]1.49455614989545[/C][C]-90.8376573032048[/C][C]0.803048404502364[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9964.83782038248[/C][C]3.26280650936327[/C][C]-202.611880267706[/C][C]1.24985211411604[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]9928.37450467282[/C][C]2.89852693427271[/C][C]-34.7169593287432[/C][C]-0.295842154417687[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]9736.86782675455[/C][C]1.38879256112751[/C][C]260.358382812888[/C][C]-1.44974137909044[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]9841.25817106834[/C][C]2.06803443808084[/C][C]590.030267379287[/C][C]0.768443002439589[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]9925.0086381795[/C][C]2.54992803660270[/C][C]146.634013698928[/C][C]0.609127917613946[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]10052.8594328691[/C][C]3.28013450841469[/C][C]57.0615418148054[/C][C]0.932957672188076[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9964.6145447027[/C][C]2.69702650226427[/C][C]-697.100793514692[/C][C]-0.679604846605334[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]9805.62721745523[/C][C]1.50975423348385[/C][C]17.0356306578212[/C][C]-1.19665516212745[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9863.86565054821[/C][C]1.98797486111284[/C][C]232.203534808297[/C][C]0.418831124021567[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9841.26216105916[/C][C]1.75920451005729[/C][C]-725.859346237903[/C][C]-0.181460233955533[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]9901.6122055634[/C][C]2.3291757362672[/C][C]508.427267971591[/C][C]0.432962988604558[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9895.06325750294[/C][C]2.24374033344239[/C][C]-216.917323822984[/C][C]-0.0657746447297351[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]10131.5737565930[/C][C]4.36484884925401[/C][C]272.562933780309[/C][C]1.74014104808724[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10180.0375683428[/C][C]4.72613312181003[/C][C]-27.7668886134338[/C][C]0.328215053005083[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10200.9474765953[/C][C]4.84359730176286[/C][C]166.784335743943[/C][C]0.120589854460093[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10156.2839481808[/C][C]4.52340528299437[/C][C]425.537312848946[/C][C]-0.369042073997497[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10267.0495364991[/C][C]5.15994571093786[/C][C]328.187955970625[/C][C]0.79171878968827[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10388.6627388489[/C][C]5.84920868267741[/C][C]289.407355389986[/C][C]0.86687876213114[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]10404.4257558570[/C][C]5.91101679723834[/C][C]-666.58971639717[/C][C]0.0736698387168638[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10104.8935041481[/C][C]3.82775190582163[/C][C]-543.854804388791[/C][C]-2.26531949085490[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106239&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106239&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	9420.62455281495	-4.5890426297954	-334.626271902039	-1.94825201291792
3	9084	9148.2077517124	-22.2303618909331	-61.4190688909295	-1.35872117365695
4	9743	9343.40355518114	-8.8193715342712	396.708384935167	1.35850437495548
5	8587	9095.70202034107	-19.3928504723650	-504.874476723729	-1.70098600051497
6	9731	9271.86407345205	-13.6836322275629	455.785036080261	1.45024067345611
7	9563	9434.40844999122	-10.0399239606939	125.514093292607	1.31890702427521
8	9998	9698.13795425041	-5.33632031363061	295.060465637396	2.05127007984087
9	9437	9674.89595659924	-5.62859801659247	-237.581978828241	-0.134046595619623
10	10038	9807.97758753645	-3.35094274695094	227.593480956693	1.03721999324648
11	9918	9889.12380139853	-1.94548511099250	27.3982918679218	0.631326425854686
12	9252	9667.85545584089	-5.6050188046502	-412.021472076373	-1.63810580704716
13	9737	9552.0412545418	-3.61040227495166	186.943252254166	-0.867707542115775
14	9035	9409.52966529666	-2.68610765998603	-372.045359372442	-1.07943661012622
15	9133	9311.8021903386	-4.17279616924874	-177.283195680046	-0.672370905652503
16	9487	9154.66553084616	-8.34497094258953	334.647008087387	-1.05021514512539
17	8700	9193.55821813077	-6.9846990075786	-494.289731604054	0.333489306211107
18	9627	9253.4586044127	-5.31403601802089	372.463723032358	0.487484467042734
19	8947	9171.21697982802	-6.8558937647209	-222.945610987148	-0.570707897539624
20	9283	9097.55670913712	-7.93365258961034	186.560772068260	-0.499253744665062
21	8829	9105.02135657368	-7.72594706235133	-276.280234763893	0.115351198940874
22	9947	9330.49146897202	-5.08649185514184	612.580274984794	1.74711149030179
23	9628	9424.08534386672	-4.23982836968727	202.250390752836	0.738833540386894
24	9318	9518.27043512378	-3.77030289426937	-201.934851549524	0.737829998929544
25	9605	9459.6525333162	-3.83436376185997	146.280162888563	-0.413336377929872
26	8640	9243.96375879017	-4.5673021732229	-600.392639825714	-1.58347703966637
27	9214	9214.56358112121	-4.81574726388101	-0.157408460500335	-0.181087518937939
28	9567	9224.46897353754	-4.57916825516746	342.296465463807	0.105542558958506
29	8547	9155.45177696454	-5.81034756066413	-607.427922744883	-0.463382439639212
30	9185	8982.89970567253	-8.99400504744033	204.786549860404	-1.21588207581558
31	9470	9195.98429437877	-5.18028867497022	270.379490905194	1.64089527434201
32	9123	9183.67228549114	-5.28384289359201	-60.5541585213881	-0.0531211458806797
33	9278	9382.238653821	-2.87829799995906	-107.636861116059	1.52376779855306
34	10170	9524.17096509914	-1.54558636518991	643.407657381585	1.08343245497791
35	9434	9459.87903816316	-1.97218082081931	-24.8282625863602	-0.469477382632173
36	9655	9554.28603843822	-1.49714181641705	99.0984420902315	0.721210944559087
37	9429	9426.43881059238	-2.04658905859906	4.67679322160564	-0.944253596916056
38	8739	9353.99551485272	-2.45262076854173	-613.825140780271	-0.522791335292416
39	9552	9400.4538714729	-2.0255327633396	150.743709316006	0.359400179017050
40	9687	9364.41978943982	-2.42987756385864	323.131332353283	-0.247868711532408
41	9019	9439.20439028914	-1.34601321892296	-421.450841987691	0.562529215139126
42	9672	9526.26882372462	-0.047847268485069	144.296967051820	0.648008784330493
43	9206	9354.29953962991	-2.45049008702385	-145.485846509328	-1.27002892558780
44	9069	9291.74798991872	-3.19410451169397	-221.756334733109	-0.446692690210052
45	9788	9527.3417025869	-0.719835326329942	256.696550113955	1.78077301638989
46	10312	9624.51109713784	0.096027957588888	685.859787070915	0.731020408457668
47	10105	9836.2318452694	1.49713127116114	265.240934276026	1.58093275393686
48	9863	9824.50498151234	1.42373578282638	38.7154690254109	-0.0987486279718978
49	9656	9747.28483630863	0.997551636934981	-89.9762517528914	-0.586130706721582
50	9295	9801.80000511374	1.33567199133678	-507.6861449915	0.397175228268162
51	9946	9816.17047588593	1.43942942766346	129.615247558962	0.096192398012906
52	9701	9676.92268320296	0.0656899687826051	26.3750423304587	-1.03376292817842
53	9049	9568.96478398853	-1.13769998998178	-518.205210398125	-0.793200338741033
54	10190	9686.23967611857	0.250703430598917	501.827789847443	0.871968273634657
55	9706	9795.05731572663	1.49455614989545	-90.8376573032048	0.803048404502364
56	9765	9964.83782038248	3.26280650936327	-202.611880267706	1.24985211411604
57	9893	9928.37450467282	2.89852693427271	-34.7169593287432	-0.295842154417687
58	9994	9736.86782675455	1.38879256112751	260.358382812888	-1.44974137909044
59	10433	9841.25817106834	2.06803443808084	590.030267379287	0.768443002439589
60	10073	9925.0086381795	2.54992803660270	146.634013698928	0.609127917613946
61	10112	10052.8594328691	3.28013450841469	57.0615418148054	0.932957672188076
62	9266	9964.6145447027	2.69702650226427	-697.100793514692	-0.679604846605334
63	9820	9805.62721745523	1.50975423348385	17.0356306578212	-1.19665516212745
64	10097	9863.86565054821	1.98797486111284	232.203534808297	0.418831124021567
65	9115	9841.26216105916	1.75920451005729	-725.859346237903	-0.181460233955533
66	10411	9901.6122055634	2.3291757362672	508.427267971591	0.432962988604558
67	9678	9895.06325750294	2.24374033344239	-216.917323822984	-0.0657746447297351
68	10408	10131.5737565930	4.36484884925401	272.562933780309	1.74014104808724
69	10153	10180.0375683428	4.72613312181003	-27.7668886134338	0.328215053005083
70	10368	10200.9474765953	4.84359730176286	166.784335743943	0.120589854460093
71	10581	10156.2839481808	4.52340528299437	425.537312848946	-0.369042073997497
72	10597	10267.0495364991	5.15994571093786	328.187955970625	0.79171878968827
73	10680	10388.6627388489	5.84920868267741	289.407355389986	0.86687876213114
74	9738	10404.4257558570	5.91101679723834	-666.58971639717	0.0736698387168638
75	9556	10104.8935041481	3.82775190582163	-543.854804388791	-2.26531949085490

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$resid)
myfit <- mylevel+myseas
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')
grid()
dev.off()
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='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