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R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Tue, 30 Nov 2010 15:46:51 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/30/t129113193671gmvpyyqo9tu0s.htm/, Retrieved Fri, 09 May 2025 13:02:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103645, Retrieved Fri, 09 May 2025 13:02:26 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

345

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] [Structural decomp...] [2010-11-30 15:46:51] [27f38de572a508a633f0ad2411de6a3e] [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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103645&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103645&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	'George Udny Yule' @ 72.249.76.132

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	37	37	0	0	0
2	30	34.0671216941213	-0.315647564790337	-0.31564756420223	-0.291558207717331
3	47	39.2754159647873	0.113018493807602	0.113018493807602	0.578107943214642
4	35	37.5988237864005	0.00609133324206647	0.00609133324206532	-0.194826675503084
5	30	34.6320001040144	-0.138701975676196	-0.138701975676196	-0.332720022217105
6	43	37.8293262532751	0.000285907581016487	0.000285907581015099	0.380390337897555
7	82	54.7345055002265	0.62635014152385	0.626350141523854	1.95163954894543
8	40	49.2755246002829	0.420161822917526	0.420161822917527	-0.708354793270166
9	47	48.5140071337029	0.382767179877118	0.382767179877118	-0.138315627892971
10	19	37.4418734766951	0.0393381287320684	0.0393381287320691	-1.34590727617731
11	52	42.9493225713565	0.196172304749665	0.196172304749665	0.644218893332828
12	136	78.0933079792282	1.16141281737792	1.16141281737792	4.12555501966769
13	80	82.405037674586	0.803640669539752	-8.84004735984471	0.530702819484212
14	42	65.0516229548378	0.0542762836813006	0.0542762800922897	-1.77265834157425
15	54	60.6291616810058	-0.0882405583830091	-0.088240558383007	-0.486105172608378
16	66	62.6908790939866	-0.0332794524032328	-0.0332794524032380	0.244988724128414
17	81	69.6599622576009	0.117309882915424	0.117309882915424	0.817045414994713
18	63	67.1730843092634	0.0681303204142184	0.0681303204142267	-0.307662362506208
19	137	93.4363647150941	0.517998469675756	0.517998469675762	3.11621286205938
20	72	85.5313411834837	0.382951410803086	0.382951410803083	-1.00607462956371
21	107	93.6607944645395	0.501082284767511	0.501082284767512	0.927555972162997
22	58	80.4581507083647	0.299773952706316	0.299773952706319	-1.64344569595362
23	36	63.9282717919332	0.0595876339530189	0.0595876339530240	-2.02043376961061
24	52	59.4901342371581	-0.00312292677736641	-0.00312292677736388	-0.540352334075333
25	79	65.1690426899526	-0.296953819164317	3.26649201321126	0.816165646442566
26	77	69.9327223130034	-0.163312320080150	-0.163312322518920	0.539272135660072
27	54	63.696644480193	-0.286949059374766	-0.286949059374757	-0.689461813374959
28	84	71.36192367388	-0.156425160934276	-0.156425160934279	0.929873009781318
29	48	62.5185716246564	-0.277014316578656	-0.277014316578658	-1.03081504793801
30	96	74.9978916868859	-0.120642791282769	-0.120642791282758	1.52551438746289
31	83	77.957327068086	-0.0861183040178078	-0.0861183040177992	0.369943849126872
32	66	73.475654327657	-0.132359631914891	-0.132359631914895	-0.529282107445417
33	61	68.7937954814648	-0.178114250777881	-0.178114250777882	-0.548661028790547
34	53	62.8678560875564	-0.234074404504519	-0.234074404504517	-0.693846020030631
35	30	50.5756706788763	-0.348672470763643	-0.348672470763633	-1.45650350855119
36	74	59.201726585533	-0.264956524801259	-0.264956524801255	1.08452121249381
37	69	61.1893369280218	-0.340368376575945	3.74405214385024	0.306764690482265
38	59	60.2507129540982	-0.351984696680386	-0.351984698212666	-0.066248576140395
39	42	53.1654926142638	-0.452751478680410	-0.452751478680399	-0.780052519204419
40	65	57.5263519187164	-0.394566544141757	-0.394566544141754	0.569637095178366
41	70	62.1043985930574	-0.343602933535737	-0.343602933535741	0.594751043722194
42	100	76.1679614815683	-0.212865165055240	-0.212865165055235	1.73294071933137
43	63	71.2077381412589	-0.252361260117054	-0.252361260117045	-0.572833479964084
44	105	83.7167245568239	-0.152461310528321	-0.152461310528320	1.54266792276289
45	82	83.0393651242567	-0.156399367687836	-0.156399367687836	-0.0635234520492033
46	81	82.2413505760636	-0.161070698414878	-0.161070698414877	-0.0777025118569286
47	75	79.5098004563027	-0.179382579357404	-0.179382579357389	-0.311435709355405
48	102	87.8170695670264	-0.119905104111077	-0.119905104111073	1.02853626661158
49	121	98.1776365906012	-0.379305767555715	4.17236344605525	1.38956946142677
50	98	98.0252471038806	-0.375822002172828	-0.3758220051039	0.0256770062449916
51	76	89.551338558132	-0.471632224648908	-0.471632224648893	-0.949062463098624
52	77	84.7142848944818	-0.513393193667197	-0.513393193667215	-0.520173830686708
53	63	76.4680432022279	-0.576207605766888	-0.576207605766901	-0.929151736810298
54	37	61.6154720271693	-0.679047834469404	-0.67904783446939	-1.72303017901997
55	35	51.5422352461928	-0.741186105626393	-0.741186105626385	-1.13661230541679
56	23	40.7467671380797	-0.803858613012813	-0.803858613012816	-1.21823775261747
57	40	40.262604186947	-0.801945924159431	-0.80194592415943	0.0387700424106709
58	29	35.8754559445217	-0.822791267543264	-0.822791267543263	-0.435018971173871
59	37	36.0806574502545	-0.816934544693994	-0.816934544693976	0.124777017289439
60	51	41.4056556852203	-0.782462054720102	-0.782462054720095	0.745672735826488
61	20	30.8154211638528	-0.589907706695399	6.4889847728376	-1.27958777101575
62	28	29.5929232536214	-0.597938619671958	-0.597938618900505	-0.0725809712450768
63	13	23.1643585852979	-0.654976183051592	-0.654976183051577	-0.688446400776884
64	22	22.5639684032535	-0.654544118317453	-0.654544118317453	0.00653360043588675
65	25	23.3065448214487	-0.645144805925538	-0.645144805925545	0.168378293764226
66	13	19.3067416834582	-0.665179475688209	-0.665179475688207	-0.40577759389535
67	16	17.9072892961621	-0.669210268870825	-0.669210268870812	-0.0889989704429047
68	13	15.9132811790094	-0.676070590934731	-0.676070590934732	-0.160765922038189
69	16	15.7710589955398	-0.673414637318863	-0.673414637318866	0.0648296106054625
70	17	16.0530142911655	-0.668791046538752	-0.668791046538751	0.116069874743964
71	9	13.2647473091235	-0.678851458114668	-0.678851458114651	-0.257571998873056
72	17	14.4742974934467	-0.670012753262825	-0.670012753262816	0.229532537273078
73	25	15.108446727048	-0.691229840461706	7.60352824346882	0.168327091104721
74	14	14.5224697436582	-0.690090782816285	-0.690090781198667	0.0121934073330585
75	8	11.8921815668287	-0.706269006103503	-0.706269006103486	-0.230287521451263
76	7	9.88412868911363	-0.715056437033845	-0.715056437033845	-0.156307444342482
77	10	9.74499471328324	-0.711749866376998	-0.711749866377005	0.0695562316457681
78	7	8.54205488396047	-0.714255113106516	-0.714255113106513	-0.0595073600282687
79	10	8.89933859595211	-0.709227947786835	-0.709227947786822	0.130042020223480
80	3	6.52786932164335	-0.716589688967188	-0.71658968896719	-0.201933830992266

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 37 & 37 & 0 & 0 & 0 \tabularnewline
2 & 30 & 34.0671216941213 & -0.315647564790337 & -0.31564756420223 & -0.291558207717331 \tabularnewline
3 & 47 & 39.2754159647873 & 0.113018493807602 & 0.113018493807602 & 0.578107943214642 \tabularnewline
4 & 35 & 37.5988237864005 & 0.00609133324206647 & 0.00609133324206532 & -0.194826675503084 \tabularnewline
5 & 30 & 34.6320001040144 & -0.138701975676196 & -0.138701975676196 & -0.332720022217105 \tabularnewline
6 & 43 & 37.8293262532751 & 0.000285907581016487 & 0.000285907581015099 & 0.380390337897555 \tabularnewline
7 & 82 & 54.7345055002265 & 0.62635014152385 & 0.626350141523854 & 1.95163954894543 \tabularnewline
8 & 40 & 49.2755246002829 & 0.420161822917526 & 0.420161822917527 & -0.708354793270166 \tabularnewline
9 & 47 & 48.5140071337029 & 0.382767179877118 & 0.382767179877118 & -0.138315627892971 \tabularnewline
10 & 19 & 37.4418734766951 & 0.0393381287320684 & 0.0393381287320691 & -1.34590727617731 \tabularnewline
11 & 52 & 42.9493225713565 & 0.196172304749665 & 0.196172304749665 & 0.644218893332828 \tabularnewline
12 & 136 & 78.0933079792282 & 1.16141281737792 & 1.16141281737792 & 4.12555501966769 \tabularnewline
13 & 80 & 82.405037674586 & 0.803640669539752 & -8.84004735984471 & 0.530702819484212 \tabularnewline
14 & 42 & 65.0516229548378 & 0.0542762836813006 & 0.0542762800922897 & -1.77265834157425 \tabularnewline
15 & 54 & 60.6291616810058 & -0.0882405583830091 & -0.088240558383007 & -0.486105172608378 \tabularnewline
16 & 66 & 62.6908790939866 & -0.0332794524032328 & -0.0332794524032380 & 0.244988724128414 \tabularnewline
17 & 81 & 69.6599622576009 & 0.117309882915424 & 0.117309882915424 & 0.817045414994713 \tabularnewline
18 & 63 & 67.1730843092634 & 0.0681303204142184 & 0.0681303204142267 & -0.307662362506208 \tabularnewline
19 & 137 & 93.4363647150941 & 0.517998469675756 & 0.517998469675762 & 3.11621286205938 \tabularnewline
20 & 72 & 85.5313411834837 & 0.382951410803086 & 0.382951410803083 & -1.00607462956371 \tabularnewline
21 & 107 & 93.6607944645395 & 0.501082284767511 & 0.501082284767512 & 0.927555972162997 \tabularnewline
22 & 58 & 80.4581507083647 & 0.299773952706316 & 0.299773952706319 & -1.64344569595362 \tabularnewline
23 & 36 & 63.9282717919332 & 0.0595876339530189 & 0.0595876339530240 & -2.02043376961061 \tabularnewline
24 & 52 & 59.4901342371581 & -0.00312292677736641 & -0.00312292677736388 & -0.540352334075333 \tabularnewline
25 & 79 & 65.1690426899526 & -0.296953819164317 & 3.26649201321126 & 0.816165646442566 \tabularnewline
26 & 77 & 69.9327223130034 & -0.163312320080150 & -0.163312322518920 & 0.539272135660072 \tabularnewline
27 & 54 & 63.696644480193 & -0.286949059374766 & -0.286949059374757 & -0.689461813374959 \tabularnewline
28 & 84 & 71.36192367388 & -0.156425160934276 & -0.156425160934279 & 0.929873009781318 \tabularnewline
29 & 48 & 62.5185716246564 & -0.277014316578656 & -0.277014316578658 & -1.03081504793801 \tabularnewline
30 & 96 & 74.9978916868859 & -0.120642791282769 & -0.120642791282758 & 1.52551438746289 \tabularnewline
31 & 83 & 77.957327068086 & -0.0861183040178078 & -0.0861183040177992 & 0.369943849126872 \tabularnewline
32 & 66 & 73.475654327657 & -0.132359631914891 & -0.132359631914895 & -0.529282107445417 \tabularnewline
33 & 61 & 68.7937954814648 & -0.178114250777881 & -0.178114250777882 & -0.548661028790547 \tabularnewline
34 & 53 & 62.8678560875564 & -0.234074404504519 & -0.234074404504517 & -0.693846020030631 \tabularnewline
35 & 30 & 50.5756706788763 & -0.348672470763643 & -0.348672470763633 & -1.45650350855119 \tabularnewline
36 & 74 & 59.201726585533 & -0.264956524801259 & -0.264956524801255 & 1.08452121249381 \tabularnewline
37 & 69 & 61.1893369280218 & -0.340368376575945 & 3.74405214385024 & 0.306764690482265 \tabularnewline
38 & 59 & 60.2507129540982 & -0.351984696680386 & -0.351984698212666 & -0.066248576140395 \tabularnewline
39 & 42 & 53.1654926142638 & -0.452751478680410 & -0.452751478680399 & -0.780052519204419 \tabularnewline
40 & 65 & 57.5263519187164 & -0.394566544141757 & -0.394566544141754 & 0.569637095178366 \tabularnewline
41 & 70 & 62.1043985930574 & -0.343602933535737 & -0.343602933535741 & 0.594751043722194 \tabularnewline
42 & 100 & 76.1679614815683 & -0.212865165055240 & -0.212865165055235 & 1.73294071933137 \tabularnewline
43 & 63 & 71.2077381412589 & -0.252361260117054 & -0.252361260117045 & -0.572833479964084 \tabularnewline
44 & 105 & 83.7167245568239 & -0.152461310528321 & -0.152461310528320 & 1.54266792276289 \tabularnewline
45 & 82 & 83.0393651242567 & -0.156399367687836 & -0.156399367687836 & -0.0635234520492033 \tabularnewline
46 & 81 & 82.2413505760636 & -0.161070698414878 & -0.161070698414877 & -0.0777025118569286 \tabularnewline
47 & 75 & 79.5098004563027 & -0.179382579357404 & -0.179382579357389 & -0.311435709355405 \tabularnewline
48 & 102 & 87.8170695670264 & -0.119905104111077 & -0.119905104111073 & 1.02853626661158 \tabularnewline
49 & 121 & 98.1776365906012 & -0.379305767555715 & 4.17236344605525 & 1.38956946142677 \tabularnewline
50 & 98 & 98.0252471038806 & -0.375822002172828 & -0.3758220051039 & 0.0256770062449916 \tabularnewline
51 & 76 & 89.551338558132 & -0.471632224648908 & -0.471632224648893 & -0.949062463098624 \tabularnewline
52 & 77 & 84.7142848944818 & -0.513393193667197 & -0.513393193667215 & -0.520173830686708 \tabularnewline
53 & 63 & 76.4680432022279 & -0.576207605766888 & -0.576207605766901 & -0.929151736810298 \tabularnewline
54 & 37 & 61.6154720271693 & -0.679047834469404 & -0.67904783446939 & -1.72303017901997 \tabularnewline
55 & 35 & 51.5422352461928 & -0.741186105626393 & -0.741186105626385 & -1.13661230541679 \tabularnewline
56 & 23 & 40.7467671380797 & -0.803858613012813 & -0.803858613012816 & -1.21823775261747 \tabularnewline
57 & 40 & 40.262604186947 & -0.801945924159431 & -0.80194592415943 & 0.0387700424106709 \tabularnewline
58 & 29 & 35.8754559445217 & -0.822791267543264 & -0.822791267543263 & -0.435018971173871 \tabularnewline
59 & 37 & 36.0806574502545 & -0.816934544693994 & -0.816934544693976 & 0.124777017289439 \tabularnewline
60 & 51 & 41.4056556852203 & -0.782462054720102 & -0.782462054720095 & 0.745672735826488 \tabularnewline
61 & 20 & 30.8154211638528 & -0.589907706695399 & 6.4889847728376 & -1.27958777101575 \tabularnewline
62 & 28 & 29.5929232536214 & -0.597938619671958 & -0.597938618900505 & -0.0725809712450768 \tabularnewline
63 & 13 & 23.1643585852979 & -0.654976183051592 & -0.654976183051577 & -0.688446400776884 \tabularnewline
64 & 22 & 22.5639684032535 & -0.654544118317453 & -0.654544118317453 & 0.00653360043588675 \tabularnewline
65 & 25 & 23.3065448214487 & -0.645144805925538 & -0.645144805925545 & 0.168378293764226 \tabularnewline
66 & 13 & 19.3067416834582 & -0.665179475688209 & -0.665179475688207 & -0.40577759389535 \tabularnewline
67 & 16 & 17.9072892961621 & -0.669210268870825 & -0.669210268870812 & -0.0889989704429047 \tabularnewline
68 & 13 & 15.9132811790094 & -0.676070590934731 & -0.676070590934732 & -0.160765922038189 \tabularnewline
69 & 16 & 15.7710589955398 & -0.673414637318863 & -0.673414637318866 & 0.0648296106054625 \tabularnewline
70 & 17 & 16.0530142911655 & -0.668791046538752 & -0.668791046538751 & 0.116069874743964 \tabularnewline
71 & 9 & 13.2647473091235 & -0.678851458114668 & -0.678851458114651 & -0.257571998873056 \tabularnewline
72 & 17 & 14.4742974934467 & -0.670012753262825 & -0.670012753262816 & 0.229532537273078 \tabularnewline
73 & 25 & 15.108446727048 & -0.691229840461706 & 7.60352824346882 & 0.168327091104721 \tabularnewline
74 & 14 & 14.5224697436582 & -0.690090782816285 & -0.690090781198667 & 0.0121934073330585 \tabularnewline
75 & 8 & 11.8921815668287 & -0.706269006103503 & -0.706269006103486 & -0.230287521451263 \tabularnewline
76 & 7 & 9.88412868911363 & -0.715056437033845 & -0.715056437033845 & -0.156307444342482 \tabularnewline
77 & 10 & 9.74499471328324 & -0.711749866376998 & -0.711749866377005 & 0.0695562316457681 \tabularnewline
78 & 7 & 8.54205488396047 & -0.714255113106516 & -0.714255113106513 & -0.0595073600282687 \tabularnewline
79 & 10 & 8.89933859595211 & -0.709227947786835 & -0.709227947786822 & 0.130042020223480 \tabularnewline
80 & 3 & 6.52786932164335 & -0.716589688967188 & -0.71658968896719 & -0.201933830992266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103645&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]37[/C][C]37[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]30[/C][C]34.0671216941213[/C][C]-0.315647564790337[/C][C]-0.31564756420223[/C][C]-0.291558207717331[/C][/ROW]
[ROW][C]3[/C][C]47[/C][C]39.2754159647873[/C][C]0.113018493807602[/C][C]0.113018493807602[/C][C]0.578107943214642[/C][/ROW]
[ROW][C]4[/C][C]35[/C][C]37.5988237864005[/C][C]0.00609133324206647[/C][C]0.00609133324206532[/C][C]-0.194826675503084[/C][/ROW]
[ROW][C]5[/C][C]30[/C][C]34.6320001040144[/C][C]-0.138701975676196[/C][C]-0.138701975676196[/C][C]-0.332720022217105[/C][/ROW]
[ROW][C]6[/C][C]43[/C][C]37.8293262532751[/C][C]0.000285907581016487[/C][C]0.000285907581015099[/C][C]0.380390337897555[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]54.7345055002265[/C][C]0.62635014152385[/C][C]0.626350141523854[/C][C]1.95163954894543[/C][/ROW]
[ROW][C]8[/C][C]40[/C][C]49.2755246002829[/C][C]0.420161822917526[/C][C]0.420161822917527[/C][C]-0.708354793270166[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]48.5140071337029[/C][C]0.382767179877118[/C][C]0.382767179877118[/C][C]-0.138315627892971[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]37.4418734766951[/C][C]0.0393381287320684[/C][C]0.0393381287320691[/C][C]-1.34590727617731[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]42.9493225713565[/C][C]0.196172304749665[/C][C]0.196172304749665[/C][C]0.644218893332828[/C][/ROW]
[ROW][C]12[/C][C]136[/C][C]78.0933079792282[/C][C]1.16141281737792[/C][C]1.16141281737792[/C][C]4.12555501966769[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]82.405037674586[/C][C]0.803640669539752[/C][C]-8.84004735984471[/C][C]0.530702819484212[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]65.0516229548378[/C][C]0.0542762836813006[/C][C]0.0542762800922897[/C][C]-1.77265834157425[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]60.6291616810058[/C][C]-0.0882405583830091[/C][C]-0.088240558383007[/C][C]-0.486105172608378[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]62.6908790939866[/C][C]-0.0332794524032328[/C][C]-0.0332794524032380[/C][C]0.244988724128414[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]69.6599622576009[/C][C]0.117309882915424[/C][C]0.117309882915424[/C][C]0.817045414994713[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]67.1730843092634[/C][C]0.0681303204142184[/C][C]0.0681303204142267[/C][C]-0.307662362506208[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]93.4363647150941[/C][C]0.517998469675756[/C][C]0.517998469675762[/C][C]3.11621286205938[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]85.5313411834837[/C][C]0.382951410803086[/C][C]0.382951410803083[/C][C]-1.00607462956371[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]93.6607944645395[/C][C]0.501082284767511[/C][C]0.501082284767512[/C][C]0.927555972162997[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]80.4581507083647[/C][C]0.299773952706316[/C][C]0.299773952706319[/C][C]-1.64344569595362[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]63.9282717919332[/C][C]0.0595876339530189[/C][C]0.0595876339530240[/C][C]-2.02043376961061[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]59.4901342371581[/C][C]-0.00312292677736641[/C][C]-0.00312292677736388[/C][C]-0.540352334075333[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]65.1690426899526[/C][C]-0.296953819164317[/C][C]3.26649201321126[/C][C]0.816165646442566[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]69.9327223130034[/C][C]-0.163312320080150[/C][C]-0.163312322518920[/C][C]0.539272135660072[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]63.696644480193[/C][C]-0.286949059374766[/C][C]-0.286949059374757[/C][C]-0.689461813374959[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]71.36192367388[/C][C]-0.156425160934276[/C][C]-0.156425160934279[/C][C]0.929873009781318[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]62.5185716246564[/C][C]-0.277014316578656[/C][C]-0.277014316578658[/C][C]-1.03081504793801[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]74.9978916868859[/C][C]-0.120642791282769[/C][C]-0.120642791282758[/C][C]1.52551438746289[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]77.957327068086[/C][C]-0.0861183040178078[/C][C]-0.0861183040177992[/C][C]0.369943849126872[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]73.475654327657[/C][C]-0.132359631914891[/C][C]-0.132359631914895[/C][C]-0.529282107445417[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]68.7937954814648[/C][C]-0.178114250777881[/C][C]-0.178114250777882[/C][C]-0.548661028790547[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]62.8678560875564[/C][C]-0.234074404504519[/C][C]-0.234074404504517[/C][C]-0.693846020030631[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]50.5756706788763[/C][C]-0.348672470763643[/C][C]-0.348672470763633[/C][C]-1.45650350855119[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]59.201726585533[/C][C]-0.264956524801259[/C][C]-0.264956524801255[/C][C]1.08452121249381[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]61.1893369280218[/C][C]-0.340368376575945[/C][C]3.74405214385024[/C][C]0.306764690482265[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]60.2507129540982[/C][C]-0.351984696680386[/C][C]-0.351984698212666[/C][C]-0.066248576140395[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]53.1654926142638[/C][C]-0.452751478680410[/C][C]-0.452751478680399[/C][C]-0.780052519204419[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]57.5263519187164[/C][C]-0.394566544141757[/C][C]-0.394566544141754[/C][C]0.569637095178366[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]62.1043985930574[/C][C]-0.343602933535737[/C][C]-0.343602933535741[/C][C]0.594751043722194[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]76.1679614815683[/C][C]-0.212865165055240[/C][C]-0.212865165055235[/C][C]1.73294071933137[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]71.2077381412589[/C][C]-0.252361260117054[/C][C]-0.252361260117045[/C][C]-0.572833479964084[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]83.7167245568239[/C][C]-0.152461310528321[/C][C]-0.152461310528320[/C][C]1.54266792276289[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]83.0393651242567[/C][C]-0.156399367687836[/C][C]-0.156399367687836[/C][C]-0.0635234520492033[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]82.2413505760636[/C][C]-0.161070698414878[/C][C]-0.161070698414877[/C][C]-0.0777025118569286[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]79.5098004563027[/C][C]-0.179382579357404[/C][C]-0.179382579357389[/C][C]-0.311435709355405[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]87.8170695670264[/C][C]-0.119905104111077[/C][C]-0.119905104111073[/C][C]1.02853626661158[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]98.1776365906012[/C][C]-0.379305767555715[/C][C]4.17236344605525[/C][C]1.38956946142677[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]98.0252471038806[/C][C]-0.375822002172828[/C][C]-0.3758220051039[/C][C]0.0256770062449916[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]89.551338558132[/C][C]-0.471632224648908[/C][C]-0.471632224648893[/C][C]-0.949062463098624[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]84.7142848944818[/C][C]-0.513393193667197[/C][C]-0.513393193667215[/C][C]-0.520173830686708[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]76.4680432022279[/C][C]-0.576207605766888[/C][C]-0.576207605766901[/C][C]-0.929151736810298[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]61.6154720271693[/C][C]-0.679047834469404[/C][C]-0.67904783446939[/C][C]-1.72303017901997[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]51.5422352461928[/C][C]-0.741186105626393[/C][C]-0.741186105626385[/C][C]-1.13661230541679[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]40.7467671380797[/C][C]-0.803858613012813[/C][C]-0.803858613012816[/C][C]-1.21823775261747[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]40.262604186947[/C][C]-0.801945924159431[/C][C]-0.80194592415943[/C][C]0.0387700424106709[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]35.8754559445217[/C][C]-0.822791267543264[/C][C]-0.822791267543263[/C][C]-0.435018971173871[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]36.0806574502545[/C][C]-0.816934544693994[/C][C]-0.816934544693976[/C][C]0.124777017289439[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]41.4056556852203[/C][C]-0.782462054720102[/C][C]-0.782462054720095[/C][C]0.745672735826488[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]30.8154211638528[/C][C]-0.589907706695399[/C][C]6.4889847728376[/C][C]-1.27958777101575[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]29.5929232536214[/C][C]-0.597938619671958[/C][C]-0.597938618900505[/C][C]-0.0725809712450768[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]23.1643585852979[/C][C]-0.654976183051592[/C][C]-0.654976183051577[/C][C]-0.688446400776884[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]22.5639684032535[/C][C]-0.654544118317453[/C][C]-0.654544118317453[/C][C]0.00653360043588675[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]23.3065448214487[/C][C]-0.645144805925538[/C][C]-0.645144805925545[/C][C]0.168378293764226[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]19.3067416834582[/C][C]-0.665179475688209[/C][C]-0.665179475688207[/C][C]-0.40577759389535[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]17.9072892961621[/C][C]-0.669210268870825[/C][C]-0.669210268870812[/C][C]-0.0889989704429047[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]15.9132811790094[/C][C]-0.676070590934731[/C][C]-0.676070590934732[/C][C]-0.160765922038189[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]15.7710589955398[/C][C]-0.673414637318863[/C][C]-0.673414637318866[/C][C]0.0648296106054625[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]16.0530142911655[/C][C]-0.668791046538752[/C][C]-0.668791046538751[/C][C]0.116069874743964[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]13.2647473091235[/C][C]-0.678851458114668[/C][C]-0.678851458114651[/C][C]-0.257571998873056[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]14.4742974934467[/C][C]-0.670012753262825[/C][C]-0.670012753262816[/C][C]0.229532537273078[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]15.108446727048[/C][C]-0.691229840461706[/C][C]7.60352824346882[/C][C]0.168327091104721[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]14.5224697436582[/C][C]-0.690090782816285[/C][C]-0.690090781198667[/C][C]0.0121934073330585[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]11.8921815668287[/C][C]-0.706269006103503[/C][C]-0.706269006103486[/C][C]-0.230287521451263[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]9.88412868911363[/C][C]-0.715056437033845[/C][C]-0.715056437033845[/C][C]-0.156307444342482[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]9.74499471328324[/C][C]-0.711749866376998[/C][C]-0.711749866377005[/C][C]0.0695562316457681[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]8.54205488396047[/C][C]-0.714255113106516[/C][C]-0.714255113106513[/C][C]-0.0595073600282687[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]8.89933859595211[/C][C]-0.709227947786835[/C][C]-0.709227947786822[/C][C]0.130042020223480[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]6.52786932164335[/C][C]-0.716589688967188[/C][C]-0.71658968896719[/C][C]-0.201933830992266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103645&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	37	37	0	0	0
2	30	34.0671216941213	-0.315647564790337	-0.31564756420223	-0.291558207717331
3	47	39.2754159647873	0.113018493807602	0.113018493807602	0.578107943214642
4	35	37.5988237864005	0.00609133324206647	0.00609133324206532	-0.194826675503084
5	30	34.6320001040144	-0.138701975676196	-0.138701975676196	-0.332720022217105
6	43	37.8293262532751	0.000285907581016487	0.000285907581015099	0.380390337897555
7	82	54.7345055002265	0.62635014152385	0.626350141523854	1.95163954894543
8	40	49.2755246002829	0.420161822917526	0.420161822917527	-0.708354793270166
9	47	48.5140071337029	0.382767179877118	0.382767179877118	-0.138315627892971
10	19	37.4418734766951	0.0393381287320684	0.0393381287320691	-1.34590727617731
11	52	42.9493225713565	0.196172304749665	0.196172304749665	0.644218893332828
12	136	78.0933079792282	1.16141281737792	1.16141281737792	4.12555501966769
13	80	82.405037674586	0.803640669539752	-8.84004735984471	0.530702819484212
14	42	65.0516229548378	0.0542762836813006	0.0542762800922897	-1.77265834157425
15	54	60.6291616810058	-0.0882405583830091	-0.088240558383007	-0.486105172608378
16	66	62.6908790939866	-0.0332794524032328	-0.0332794524032380	0.244988724128414
17	81	69.6599622576009	0.117309882915424	0.117309882915424	0.817045414994713
18	63	67.1730843092634	0.0681303204142184	0.0681303204142267	-0.307662362506208
19	137	93.4363647150941	0.517998469675756	0.517998469675762	3.11621286205938
20	72	85.5313411834837	0.382951410803086	0.382951410803083	-1.00607462956371
21	107	93.6607944645395	0.501082284767511	0.501082284767512	0.927555972162997
22	58	80.4581507083647	0.299773952706316	0.299773952706319	-1.64344569595362
23	36	63.9282717919332	0.0595876339530189	0.0595876339530240	-2.02043376961061
24	52	59.4901342371581	-0.00312292677736641	-0.00312292677736388	-0.540352334075333
25	79	65.1690426899526	-0.296953819164317	3.26649201321126	0.816165646442566
26	77	69.9327223130034	-0.163312320080150	-0.163312322518920	0.539272135660072
27	54	63.696644480193	-0.286949059374766	-0.286949059374757	-0.689461813374959
28	84	71.36192367388	-0.156425160934276	-0.156425160934279	0.929873009781318
29	48	62.5185716246564	-0.277014316578656	-0.277014316578658	-1.03081504793801
30	96	74.9978916868859	-0.120642791282769	-0.120642791282758	1.52551438746289
31	83	77.957327068086	-0.0861183040178078	-0.0861183040177992	0.369943849126872
32	66	73.475654327657	-0.132359631914891	-0.132359631914895	-0.529282107445417
33	61	68.7937954814648	-0.178114250777881	-0.178114250777882	-0.548661028790547
34	53	62.8678560875564	-0.234074404504519	-0.234074404504517	-0.693846020030631
35	30	50.5756706788763	-0.348672470763643	-0.348672470763633	-1.45650350855119
36	74	59.201726585533	-0.264956524801259	-0.264956524801255	1.08452121249381
37	69	61.1893369280218	-0.340368376575945	3.74405214385024	0.306764690482265
38	59	60.2507129540982	-0.351984696680386	-0.351984698212666	-0.066248576140395
39	42	53.1654926142638	-0.452751478680410	-0.452751478680399	-0.780052519204419
40	65	57.5263519187164	-0.394566544141757	-0.394566544141754	0.569637095178366
41	70	62.1043985930574	-0.343602933535737	-0.343602933535741	0.594751043722194
42	100	76.1679614815683	-0.212865165055240	-0.212865165055235	1.73294071933137
43	63	71.2077381412589	-0.252361260117054	-0.252361260117045	-0.572833479964084
44	105	83.7167245568239	-0.152461310528321	-0.152461310528320	1.54266792276289
45	82	83.0393651242567	-0.156399367687836	-0.156399367687836	-0.0635234520492033
46	81	82.2413505760636	-0.161070698414878	-0.161070698414877	-0.0777025118569286
47	75	79.5098004563027	-0.179382579357404	-0.179382579357389	-0.311435709355405
48	102	87.8170695670264	-0.119905104111077	-0.119905104111073	1.02853626661158
49	121	98.1776365906012	-0.379305767555715	4.17236344605525	1.38956946142677
50	98	98.0252471038806	-0.375822002172828	-0.3758220051039	0.0256770062449916
51	76	89.551338558132	-0.471632224648908	-0.471632224648893	-0.949062463098624
52	77	84.7142848944818	-0.513393193667197	-0.513393193667215	-0.520173830686708
53	63	76.4680432022279	-0.576207605766888	-0.576207605766901	-0.929151736810298
54	37	61.6154720271693	-0.679047834469404	-0.67904783446939	-1.72303017901997
55	35	51.5422352461928	-0.741186105626393	-0.741186105626385	-1.13661230541679
56	23	40.7467671380797	-0.803858613012813	-0.803858613012816	-1.21823775261747
57	40	40.262604186947	-0.801945924159431	-0.80194592415943	0.0387700424106709
58	29	35.8754559445217	-0.822791267543264	-0.822791267543263	-0.435018971173871
59	37	36.0806574502545	-0.816934544693994	-0.816934544693976	0.124777017289439
60	51	41.4056556852203	-0.782462054720102	-0.782462054720095	0.745672735826488
61	20	30.8154211638528	-0.589907706695399	6.4889847728376	-1.27958777101575
62	28	29.5929232536214	-0.597938619671958	-0.597938618900505	-0.0725809712450768
63	13	23.1643585852979	-0.654976183051592	-0.654976183051577	-0.688446400776884
64	22	22.5639684032535	-0.654544118317453	-0.654544118317453	0.00653360043588675
65	25	23.3065448214487	-0.645144805925538	-0.645144805925545	0.168378293764226
66	13	19.3067416834582	-0.665179475688209	-0.665179475688207	-0.40577759389535
67	16	17.9072892961621	-0.669210268870825	-0.669210268870812	-0.0889989704429047
68	13	15.9132811790094	-0.676070590934731	-0.676070590934732	-0.160765922038189
69	16	15.7710589955398	-0.673414637318863	-0.673414637318866	0.0648296106054625
70	17	16.0530142911655	-0.668791046538752	-0.668791046538751	0.116069874743964
71	9	13.2647473091235	-0.678851458114668	-0.678851458114651	-0.257571998873056
72	17	14.4742974934467	-0.670012753262825	-0.670012753262816	0.229532537273078
73	25	15.108446727048	-0.691229840461706	7.60352824346882	0.168327091104721
74	14	14.5224697436582	-0.690090782816285	-0.690090781198667	0.0121934073330585
75	8	11.8921815668287	-0.706269006103503	-0.706269006103486	-0.230287521451263
76	7	9.88412868911363	-0.715056437033845	-0.715056437033845	-0.156307444342482
77	10	9.74499471328324	-0.711749866376998	-0.711749866377005	0.0695562316457681
78	7	8.54205488396047	-0.714255113106516	-0.714255113106513	-0.0595073600282687
79	10	8.89933859595211	-0.709227947786835	-0.709227947786822	0.130042020223480
80	3	6.52786932164335	-0.716589688967188	-0.71658968896719	-0.201933830992266

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