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rwasp_structuraltimeseries.wasp

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Structural Time Series Models

Date of computation

Fri, 04 Dec 2009 08:05:58 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t125993924898g41sltvia5jis.htm/, Retrieved Sat, 27 Apr 2024 15:34:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63716, Retrieved Sat, 27 Apr 2024 15:34:45 +0000

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WS 9 Estimation of Box-Jenkins ARIMA models

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Structural Time Series Models] [] [2009-11-27 15:02:30] [b98453cac15ba1066b407e146608df68]
-    D      [Structural Time Series Models] [WS 9 Estimation o...] [2009-12-04 15:05:58] [9b6f46453e60f88d91cef176fe926003] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63716&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]2 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=63716&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63716&T=0

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	14.5	14.5	0	0	0
2	14.3	14.3532218182990	-0.00650225312906405	-0.0532218182989612	-0.151829303867976
3	15.3	14.9042468127159	0.0221512184686178	0.395753187284099	0.680304199751437
4	14.4	14.6934835096618	0.0150706721362367	-0.293483509661792	-0.337630616060789
5	13.7	14.0989306329845	0.00584767975717651	-0.398930632984534	-0.90856652746136
6	14.2	14.0448094080469	0.00526892341835372	0.155190591953142	-0.0894615253839601
7	13.5	13.7278684502808	0.00238740292848135	-0.227868450280822	-0.480207980211774
8	11.9	12.6440390367895	-0.0078565033500251	-0.74403903678947	-1.61756646487085
9	14.6	13.5443622179084	0.00104458290109341	1.0556377820916	1.35193602981695
10	15.6	14.8616318798438	0.0140556822103159	0.738368120156154	1.95920789642376
11	14.1	14.6717808787331	0.01205412414273	-0.571780878733093	-0.303522151587398
12	14.9	14.7612690248497	0.0128056502406377	0.138730975150275	0.115265945672613
13	14.2	14.5505149719730	0.0193929732869372	-0.350514971973031	-0.360797676478492
14	14.6	14.7394672222748	0.0195642190422452	-0.139467222274828	0.251732325083284
15	17.2	15.8595821180274	0.042461483965316	1.34041788197258	1.51102678726127
16	15.4	15.8020613150722	0.0402579077027993	-0.402061315072151	-0.142486226205362
17	14.3	15.1757455510875	0.0296765015125833	-0.875745551087479	-0.982445746081785
18	17.5	16.0677923826787	0.0385983579899382	1.4322076173213	1.28323239136818
19	14.5	15.2616428316980	0.0321521798218614	-0.761642831698038	-1.25856164838959
20	14.4	15.3386659103121	0.0324655419080657	-0.938665910312065	0.0668356042082085
21	16.6	15.7416778414265	0.0351287782094691	0.858322158573519	0.551782821700158
22	16.7	15.8647353203460	0.0357516574602543	0.835264679654023	0.13090789383413
23	16.6	16.5749556669574	0.0393142507167759	0.0250443330426124	1.00331810435859
24	16.9	16.76615084066	0.0393901374549768	0.133849159340004	0.226268981842783
25	15.7	16.5898405928147	0.0405413055923513	-0.889840592814692	-0.326194337796170
26	16.4	16.8379800330433	0.0408874335213664	-0.437980033043308	0.307617912360923
27	18.4	16.9475124945745	0.0416588342943506	1.4524875054255	0.0983964622634089
28	16.9	17.0523186369762	0.0426108584669144	-0.152318636976206	0.0908400463021881
29	16.5	17.3896860995715	0.0466630120987782	-0.889686099571456	0.432104020782224
30	18.3	16.9607051215087	0.0415969334380195	1.33929487849132	-0.705324316528581
31	15.1	16.3608499895819	0.0363632815578634	-1.26084998958185	-0.954898009220748
32	15.7	16.5261959018995	0.0372418509196335	-0.82619590189947	0.192173761268289
33	18.1	16.9973193674175	0.0398732773335018	1.10268063258254	0.646351461294702
34	16.8	16.6983749639089	0.0381654497863639	0.101625036091081	-0.504334933047932
35	18.9	17.8347830546934	0.0415688789169400	1.06521694530657	1.63337616668555
36	19	18.5204423605592	0.0419639633318892	0.479557639440806	0.959233167815239
37	18.1	18.9519756382336	0.0418571561531171	-0.851975638233591	0.581186433947571
38	17.8	18.7006636190141	0.0409743418313897	-0.900663619014137	-0.432837243733768
39	21.5	19.4512550753658	0.0466396815812547	2.04874492463417	1.03175368849035
40	17.1	18.4323237136876	0.0348119442346677	-1.33232371368758	-1.54675674779101
41	18.7	18.7468442202362	0.0380031856588257	-0.0468442202362262	0.409968934751498
42	19	18.0757165571750	0.0309373212186635	0.924283442824951	-1.04921918481289
43	16.4	17.8185541078603	0.0285942280798430	-1.41855410786029	-0.428367511942265
44	16.9	17.8260446084405	0.0284548936807973	-0.926044608440547	-0.0314293942089173
45	18.6	17.6662617069595	0.0274504521770733	0.933738293040485	-0.280321827806223
46	19.3	18.7806352783862	0.0318024844573274	0.519364721613836	1.61730217470358
47	19.4	18.8986393765442	0.0320175585937234	0.50136062345577	0.128186919162402
48	17.6	18.0816056319130	0.0309064284464227	-0.481605631912962	-1.26286987421494
49	18.6	18.6754807804339	0.0317361484265937	-0.0754807804339405	0.836215106867895
50	18.1	19.0382459477397	0.0329165860636176	-0.938245947739723	0.488374871941854
51	20.4	18.4722753592372	0.0289860915915749	1.92772464076283	-0.876166727396246
52	18.1	18.9202244690803	0.0326861257621256	-0.820224469080279	0.611785974620364
53	19.6	19.1689471734590	0.0347497108593148	0.431052826540968	0.317135766264417
54	19.9	19.0294631028693	0.0331919999304526	0.870536897130678	-0.257552919549820
55	19.2	19.8471734825025	0.0392044550188137	-0.647173482502464	1.16511728205475
56	17.8	19.4208104028436	0.0362949361160086	-1.62081040284357	-0.692773534588495
57	19.2	19.0312195574406	0.0342141799336740	0.168780442559367	-0.633818145267439
58	22	20.2376482368600	0.0384144868396215	1.76235176313997	1.74347338170622
59	21.1	20.4401322403705	0.0388167140884143	0.659867759629505	0.243898459514867
60	19.5	20.394964725237	0.0386609491135392	-0.894964725237015	-0.124787568852385
61	22.2	21.4369025094406	0.0409214615431257	0.763097490559361	1.48771109188717
62	20.9	21.6985276655376	0.0417476902809566	-0.798527665537587	0.325708355771775
63	22.2	21.1204839693465	0.0381808792588933	1.07951603065353	-0.90993732336224
64	23.5	22.8049983601181	0.0503878153577447	0.695001639881928	2.41351501765741
65	21.5	22.1385222746870	0.0445442367829420	-0.638522274687041	-1.05422109455686
66	24.3	22.8813269991486	0.0500757768112967	1.41867300085143	1.03198623927225
67	22.8	23.1546643815529	0.0516455052942918	-0.354664381552921	0.331273151295866
68	20.3	22.5418608010356	0.0477669899088914	-2.24186080103563	-0.987815705053212
69	23.7	23.2900740674559	0.0509801363543038	0.409925932544065	1.04170245144483
70	23.3	22.5377815915662	0.0482167783924409	0.762218408433842	-1.19418333655362
71	19.6	20.6285373143518	0.0431727674353351	-1.02853731435178	-2.90863295597613
72	18	19.7426512718360	0.0410861558289649	-1.74265127183596	-1.37943338834347
73	17.3	17.9895305123466	0.036322510472855	-0.68953051234658	-2.65871347167898
74	16.8	17.5240270957728	0.0344329381781700	-0.72402709577282	-0.741025416888488
75	18.2	17.6215394311672	0.0347612324495996	0.578460568832749	0.0928257205832044
76	16.5	16.5622898879485	0.0277117694342975	-0.0622898879484602	-1.60820758490952
77	16	16.6613997601635	0.0282177641002253	-0.661399760163488	0.105166035732995
78	18.4	16.8868131282224	0.0296029686147793	1.51318687177761	0.291496508415680

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 14.5 & 14.5 & 0 & 0 & 0 \tabularnewline
2 & 14.3 & 14.3532218182990 & -0.00650225312906405 & -0.0532218182989612 & -0.151829303867976 \tabularnewline
3 & 15.3 & 14.9042468127159 & 0.0221512184686178 & 0.395753187284099 & 0.680304199751437 \tabularnewline
4 & 14.4 & 14.6934835096618 & 0.0150706721362367 & -0.293483509661792 & -0.337630616060789 \tabularnewline
5 & 13.7 & 14.0989306329845 & 0.00584767975717651 & -0.398930632984534 & -0.90856652746136 \tabularnewline
6 & 14.2 & 14.0448094080469 & 0.00526892341835372 & 0.155190591953142 & -0.0894615253839601 \tabularnewline
7 & 13.5 & 13.7278684502808 & 0.00238740292848135 & -0.227868450280822 & -0.480207980211774 \tabularnewline
8 & 11.9 & 12.6440390367895 & -0.0078565033500251 & -0.74403903678947 & -1.61756646487085 \tabularnewline
9 & 14.6 & 13.5443622179084 & 0.00104458290109341 & 1.0556377820916 & 1.35193602981695 \tabularnewline
10 & 15.6 & 14.8616318798438 & 0.0140556822103159 & 0.738368120156154 & 1.95920789642376 \tabularnewline
11 & 14.1 & 14.6717808787331 & 0.01205412414273 & -0.571780878733093 & -0.303522151587398 \tabularnewline
12 & 14.9 & 14.7612690248497 & 0.0128056502406377 & 0.138730975150275 & 0.115265945672613 \tabularnewline
13 & 14.2 & 14.5505149719730 & 0.0193929732869372 & -0.350514971973031 & -0.360797676478492 \tabularnewline
14 & 14.6 & 14.7394672222748 & 0.0195642190422452 & -0.139467222274828 & 0.251732325083284 \tabularnewline
15 & 17.2 & 15.8595821180274 & 0.042461483965316 & 1.34041788197258 & 1.51102678726127 \tabularnewline
16 & 15.4 & 15.8020613150722 & 0.0402579077027993 & -0.402061315072151 & -0.142486226205362 \tabularnewline
17 & 14.3 & 15.1757455510875 & 0.0296765015125833 & -0.875745551087479 & -0.982445746081785 \tabularnewline
18 & 17.5 & 16.0677923826787 & 0.0385983579899382 & 1.4322076173213 & 1.28323239136818 \tabularnewline
19 & 14.5 & 15.2616428316980 & 0.0321521798218614 & -0.761642831698038 & -1.25856164838959 \tabularnewline
20 & 14.4 & 15.3386659103121 & 0.0324655419080657 & -0.938665910312065 & 0.0668356042082085 \tabularnewline
21 & 16.6 & 15.7416778414265 & 0.0351287782094691 & 0.858322158573519 & 0.551782821700158 \tabularnewline
22 & 16.7 & 15.8647353203460 & 0.0357516574602543 & 0.835264679654023 & 0.13090789383413 \tabularnewline
23 & 16.6 & 16.5749556669574 & 0.0393142507167759 & 0.0250443330426124 & 1.00331810435859 \tabularnewline
24 & 16.9 & 16.76615084066 & 0.0393901374549768 & 0.133849159340004 & 0.226268981842783 \tabularnewline
25 & 15.7 & 16.5898405928147 & 0.0405413055923513 & -0.889840592814692 & -0.326194337796170 \tabularnewline
26 & 16.4 & 16.8379800330433 & 0.0408874335213664 & -0.437980033043308 & 0.307617912360923 \tabularnewline
27 & 18.4 & 16.9475124945745 & 0.0416588342943506 & 1.4524875054255 & 0.0983964622634089 \tabularnewline
28 & 16.9 & 17.0523186369762 & 0.0426108584669144 & -0.152318636976206 & 0.0908400463021881 \tabularnewline
29 & 16.5 & 17.3896860995715 & 0.0466630120987782 & -0.889686099571456 & 0.432104020782224 \tabularnewline
30 & 18.3 & 16.9607051215087 & 0.0415969334380195 & 1.33929487849132 & -0.705324316528581 \tabularnewline
31 & 15.1 & 16.3608499895819 & 0.0363632815578634 & -1.26084998958185 & -0.954898009220748 \tabularnewline
32 & 15.7 & 16.5261959018995 & 0.0372418509196335 & -0.82619590189947 & 0.192173761268289 \tabularnewline
33 & 18.1 & 16.9973193674175 & 0.0398732773335018 & 1.10268063258254 & 0.646351461294702 \tabularnewline
34 & 16.8 & 16.6983749639089 & 0.0381654497863639 & 0.101625036091081 & -0.504334933047932 \tabularnewline
35 & 18.9 & 17.8347830546934 & 0.0415688789169400 & 1.06521694530657 & 1.63337616668555 \tabularnewline
36 & 19 & 18.5204423605592 & 0.0419639633318892 & 0.479557639440806 & 0.959233167815239 \tabularnewline
37 & 18.1 & 18.9519756382336 & 0.0418571561531171 & -0.851975638233591 & 0.581186433947571 \tabularnewline
38 & 17.8 & 18.7006636190141 & 0.0409743418313897 & -0.900663619014137 & -0.432837243733768 \tabularnewline
39 & 21.5 & 19.4512550753658 & 0.0466396815812547 & 2.04874492463417 & 1.03175368849035 \tabularnewline
40 & 17.1 & 18.4323237136876 & 0.0348119442346677 & -1.33232371368758 & -1.54675674779101 \tabularnewline
41 & 18.7 & 18.7468442202362 & 0.0380031856588257 & -0.0468442202362262 & 0.409968934751498 \tabularnewline
42 & 19 & 18.0757165571750 & 0.0309373212186635 & 0.924283442824951 & -1.04921918481289 \tabularnewline
43 & 16.4 & 17.8185541078603 & 0.0285942280798430 & -1.41855410786029 & -0.428367511942265 \tabularnewline
44 & 16.9 & 17.8260446084405 & 0.0284548936807973 & -0.926044608440547 & -0.0314293942089173 \tabularnewline
45 & 18.6 & 17.6662617069595 & 0.0274504521770733 & 0.933738293040485 & -0.280321827806223 \tabularnewline
46 & 19.3 & 18.7806352783862 & 0.0318024844573274 & 0.519364721613836 & 1.61730217470358 \tabularnewline
47 & 19.4 & 18.8986393765442 & 0.0320175585937234 & 0.50136062345577 & 0.128186919162402 \tabularnewline
48 & 17.6 & 18.0816056319130 & 0.0309064284464227 & -0.481605631912962 & -1.26286987421494 \tabularnewline
49 & 18.6 & 18.6754807804339 & 0.0317361484265937 & -0.0754807804339405 & 0.836215106867895 \tabularnewline
50 & 18.1 & 19.0382459477397 & 0.0329165860636176 & -0.938245947739723 & 0.488374871941854 \tabularnewline
51 & 20.4 & 18.4722753592372 & 0.0289860915915749 & 1.92772464076283 & -0.876166727396246 \tabularnewline
52 & 18.1 & 18.9202244690803 & 0.0326861257621256 & -0.820224469080279 & 0.611785974620364 \tabularnewline
53 & 19.6 & 19.1689471734590 & 0.0347497108593148 & 0.431052826540968 & 0.317135766264417 \tabularnewline
54 & 19.9 & 19.0294631028693 & 0.0331919999304526 & 0.870536897130678 & -0.257552919549820 \tabularnewline
55 & 19.2 & 19.8471734825025 & 0.0392044550188137 & -0.647173482502464 & 1.16511728205475 \tabularnewline
56 & 17.8 & 19.4208104028436 & 0.0362949361160086 & -1.62081040284357 & -0.692773534588495 \tabularnewline
57 & 19.2 & 19.0312195574406 & 0.0342141799336740 & 0.168780442559367 & -0.633818145267439 \tabularnewline
58 & 22 & 20.2376482368600 & 0.0384144868396215 & 1.76235176313997 & 1.74347338170622 \tabularnewline
59 & 21.1 & 20.4401322403705 & 0.0388167140884143 & 0.659867759629505 & 0.243898459514867 \tabularnewline
60 & 19.5 & 20.394964725237 & 0.0386609491135392 & -0.894964725237015 & -0.124787568852385 \tabularnewline
61 & 22.2 & 21.4369025094406 & 0.0409214615431257 & 0.763097490559361 & 1.48771109188717 \tabularnewline
62 & 20.9 & 21.6985276655376 & 0.0417476902809566 & -0.798527665537587 & 0.325708355771775 \tabularnewline
63 & 22.2 & 21.1204839693465 & 0.0381808792588933 & 1.07951603065353 & -0.90993732336224 \tabularnewline
64 & 23.5 & 22.8049983601181 & 0.0503878153577447 & 0.695001639881928 & 2.41351501765741 \tabularnewline
65 & 21.5 & 22.1385222746870 & 0.0445442367829420 & -0.638522274687041 & -1.05422109455686 \tabularnewline
66 & 24.3 & 22.8813269991486 & 0.0500757768112967 & 1.41867300085143 & 1.03198623927225 \tabularnewline
67 & 22.8 & 23.1546643815529 & 0.0516455052942918 & -0.354664381552921 & 0.331273151295866 \tabularnewline
68 & 20.3 & 22.5418608010356 & 0.0477669899088914 & -2.24186080103563 & -0.987815705053212 \tabularnewline
69 & 23.7 & 23.2900740674559 & 0.0509801363543038 & 0.409925932544065 & 1.04170245144483 \tabularnewline
70 & 23.3 & 22.5377815915662 & 0.0482167783924409 & 0.762218408433842 & -1.19418333655362 \tabularnewline
71 & 19.6 & 20.6285373143518 & 0.0431727674353351 & -1.02853731435178 & -2.90863295597613 \tabularnewline
72 & 18 & 19.7426512718360 & 0.0410861558289649 & -1.74265127183596 & -1.37943338834347 \tabularnewline
73 & 17.3 & 17.9895305123466 & 0.036322510472855 & -0.68953051234658 & -2.65871347167898 \tabularnewline
74 & 16.8 & 17.5240270957728 & 0.0344329381781700 & -0.72402709577282 & -0.741025416888488 \tabularnewline
75 & 18.2 & 17.6215394311672 & 0.0347612324495996 & 0.578460568832749 & 0.0928257205832044 \tabularnewline
76 & 16.5 & 16.5622898879485 & 0.0277117694342975 & -0.0622898879484602 & -1.60820758490952 \tabularnewline
77 & 16 & 16.6613997601635 & 0.0282177641002253 & -0.661399760163488 & 0.105166035732995 \tabularnewline
78 & 18.4 & 16.8868131282224 & 0.0296029686147793 & 1.51318687177761 & 0.291496508415680 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63716&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]14.5[/C][C]14.5[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]14.3[/C][C]14.3532218182990[/C][C]-0.00650225312906405[/C][C]-0.0532218182989612[/C][C]-0.151829303867976[/C][/ROW]
[ROW][C]3[/C][C]15.3[/C][C]14.9042468127159[/C][C]0.0221512184686178[/C][C]0.395753187284099[/C][C]0.680304199751437[/C][/ROW]
[ROW][C]4[/C][C]14.4[/C][C]14.6934835096618[/C][C]0.0150706721362367[/C][C]-0.293483509661792[/C][C]-0.337630616060789[/C][/ROW]
[ROW][C]5[/C][C]13.7[/C][C]14.0989306329845[/C][C]0.00584767975717651[/C][C]-0.398930632984534[/C][C]-0.90856652746136[/C][/ROW]
[ROW][C]6[/C][C]14.2[/C][C]14.0448094080469[/C][C]0.00526892341835372[/C][C]0.155190591953142[/C][C]-0.0894615253839601[/C][/ROW]
[ROW][C]7[/C][C]13.5[/C][C]13.7278684502808[/C][C]0.00238740292848135[/C][C]-0.227868450280822[/C][C]-0.480207980211774[/C][/ROW]
[ROW][C]8[/C][C]11.9[/C][C]12.6440390367895[/C][C]-0.0078565033500251[/C][C]-0.74403903678947[/C][C]-1.61756646487085[/C][/ROW]
[ROW][C]9[/C][C]14.6[/C][C]13.5443622179084[/C][C]0.00104458290109341[/C][C]1.0556377820916[/C][C]1.35193602981695[/C][/ROW]
[ROW][C]10[/C][C]15.6[/C][C]14.8616318798438[/C][C]0.0140556822103159[/C][C]0.738368120156154[/C][C]1.95920789642376[/C][/ROW]
[ROW][C]11[/C][C]14.1[/C][C]14.6717808787331[/C][C]0.01205412414273[/C][C]-0.571780878733093[/C][C]-0.303522151587398[/C][/ROW]
[ROW][C]12[/C][C]14.9[/C][C]14.7612690248497[/C][C]0.0128056502406377[/C][C]0.138730975150275[/C][C]0.115265945672613[/C][/ROW]
[ROW][C]13[/C][C]14.2[/C][C]14.5505149719730[/C][C]0.0193929732869372[/C][C]-0.350514971973031[/C][C]-0.360797676478492[/C][/ROW]
[ROW][C]14[/C][C]14.6[/C][C]14.7394672222748[/C][C]0.0195642190422452[/C][C]-0.139467222274828[/C][C]0.251732325083284[/C][/ROW]
[ROW][C]15[/C][C]17.2[/C][C]15.8595821180274[/C][C]0.042461483965316[/C][C]1.34041788197258[/C][C]1.51102678726127[/C][/ROW]
[ROW][C]16[/C][C]15.4[/C][C]15.8020613150722[/C][C]0.0402579077027993[/C][C]-0.402061315072151[/C][C]-0.142486226205362[/C][/ROW]
[ROW][C]17[/C][C]14.3[/C][C]15.1757455510875[/C][C]0.0296765015125833[/C][C]-0.875745551087479[/C][C]-0.982445746081785[/C][/ROW]
[ROW][C]18[/C][C]17.5[/C][C]16.0677923826787[/C][C]0.0385983579899382[/C][C]1.4322076173213[/C][C]1.28323239136818[/C][/ROW]
[ROW][C]19[/C][C]14.5[/C][C]15.2616428316980[/C][C]0.0321521798218614[/C][C]-0.761642831698038[/C][C]-1.25856164838959[/C][/ROW]
[ROW][C]20[/C][C]14.4[/C][C]15.3386659103121[/C][C]0.0324655419080657[/C][C]-0.938665910312065[/C][C]0.0668356042082085[/C][/ROW]
[ROW][C]21[/C][C]16.6[/C][C]15.7416778414265[/C][C]0.0351287782094691[/C][C]0.858322158573519[/C][C]0.551782821700158[/C][/ROW]
[ROW][C]22[/C][C]16.7[/C][C]15.8647353203460[/C][C]0.0357516574602543[/C][C]0.835264679654023[/C][C]0.13090789383413[/C][/ROW]
[ROW][C]23[/C][C]16.6[/C][C]16.5749556669574[/C][C]0.0393142507167759[/C][C]0.0250443330426124[/C][C]1.00331810435859[/C][/ROW]
[ROW][C]24[/C][C]16.9[/C][C]16.76615084066[/C][C]0.0393901374549768[/C][C]0.133849159340004[/C][C]0.226268981842783[/C][/ROW]
[ROW][C]25[/C][C]15.7[/C][C]16.5898405928147[/C][C]0.0405413055923513[/C][C]-0.889840592814692[/C][C]-0.326194337796170[/C][/ROW]
[ROW][C]26[/C][C]16.4[/C][C]16.8379800330433[/C][C]0.0408874335213664[/C][C]-0.437980033043308[/C][C]0.307617912360923[/C][/ROW]
[ROW][C]27[/C][C]18.4[/C][C]16.9475124945745[/C][C]0.0416588342943506[/C][C]1.4524875054255[/C][C]0.0983964622634089[/C][/ROW]
[ROW][C]28[/C][C]16.9[/C][C]17.0523186369762[/C][C]0.0426108584669144[/C][C]-0.152318636976206[/C][C]0.0908400463021881[/C][/ROW]
[ROW][C]29[/C][C]16.5[/C][C]17.3896860995715[/C][C]0.0466630120987782[/C][C]-0.889686099571456[/C][C]0.432104020782224[/C][/ROW]
[ROW][C]30[/C][C]18.3[/C][C]16.9607051215087[/C][C]0.0415969334380195[/C][C]1.33929487849132[/C][C]-0.705324316528581[/C][/ROW]
[ROW][C]31[/C][C]15.1[/C][C]16.3608499895819[/C][C]0.0363632815578634[/C][C]-1.26084998958185[/C][C]-0.954898009220748[/C][/ROW]
[ROW][C]32[/C][C]15.7[/C][C]16.5261959018995[/C][C]0.0372418509196335[/C][C]-0.82619590189947[/C][C]0.192173761268289[/C][/ROW]
[ROW][C]33[/C][C]18.1[/C][C]16.9973193674175[/C][C]0.0398732773335018[/C][C]1.10268063258254[/C][C]0.646351461294702[/C][/ROW]
[ROW][C]34[/C][C]16.8[/C][C]16.6983749639089[/C][C]0.0381654497863639[/C][C]0.101625036091081[/C][C]-0.504334933047932[/C][/ROW]
[ROW][C]35[/C][C]18.9[/C][C]17.8347830546934[/C][C]0.0415688789169400[/C][C]1.06521694530657[/C][C]1.63337616668555[/C][/ROW]
[ROW][C]36[/C][C]19[/C][C]18.5204423605592[/C][C]0.0419639633318892[/C][C]0.479557639440806[/C][C]0.959233167815239[/C][/ROW]
[ROW][C]37[/C][C]18.1[/C][C]18.9519756382336[/C][C]0.0418571561531171[/C][C]-0.851975638233591[/C][C]0.581186433947571[/C][/ROW]
[ROW][C]38[/C][C]17.8[/C][C]18.7006636190141[/C][C]0.0409743418313897[/C][C]-0.900663619014137[/C][C]-0.432837243733768[/C][/ROW]
[ROW][C]39[/C][C]21.5[/C][C]19.4512550753658[/C][C]0.0466396815812547[/C][C]2.04874492463417[/C][C]1.03175368849035[/C][/ROW]
[ROW][C]40[/C][C]17.1[/C][C]18.4323237136876[/C][C]0.0348119442346677[/C][C]-1.33232371368758[/C][C]-1.54675674779101[/C][/ROW]
[ROW][C]41[/C][C]18.7[/C][C]18.7468442202362[/C][C]0.0380031856588257[/C][C]-0.0468442202362262[/C][C]0.409968934751498[/C][/ROW]
[ROW][C]42[/C][C]19[/C][C]18.0757165571750[/C][C]0.0309373212186635[/C][C]0.924283442824951[/C][C]-1.04921918481289[/C][/ROW]
[ROW][C]43[/C][C]16.4[/C][C]17.8185541078603[/C][C]0.0285942280798430[/C][C]-1.41855410786029[/C][C]-0.428367511942265[/C][/ROW]
[ROW][C]44[/C][C]16.9[/C][C]17.8260446084405[/C][C]0.0284548936807973[/C][C]-0.926044608440547[/C][C]-0.0314293942089173[/C][/ROW]
[ROW][C]45[/C][C]18.6[/C][C]17.6662617069595[/C][C]0.0274504521770733[/C][C]0.933738293040485[/C][C]-0.280321827806223[/C][/ROW]
[ROW][C]46[/C][C]19.3[/C][C]18.7806352783862[/C][C]0.0318024844573274[/C][C]0.519364721613836[/C][C]1.61730217470358[/C][/ROW]
[ROW][C]47[/C][C]19.4[/C][C]18.8986393765442[/C][C]0.0320175585937234[/C][C]0.50136062345577[/C][C]0.128186919162402[/C][/ROW]
[ROW][C]48[/C][C]17.6[/C][C]18.0816056319130[/C][C]0.0309064284464227[/C][C]-0.481605631912962[/C][C]-1.26286987421494[/C][/ROW]
[ROW][C]49[/C][C]18.6[/C][C]18.6754807804339[/C][C]0.0317361484265937[/C][C]-0.0754807804339405[/C][C]0.836215106867895[/C][/ROW]
[ROW][C]50[/C][C]18.1[/C][C]19.0382459477397[/C][C]0.0329165860636176[/C][C]-0.938245947739723[/C][C]0.488374871941854[/C][/ROW]
[ROW][C]51[/C][C]20.4[/C][C]18.4722753592372[/C][C]0.0289860915915749[/C][C]1.92772464076283[/C][C]-0.876166727396246[/C][/ROW]
[ROW][C]52[/C][C]18.1[/C][C]18.9202244690803[/C][C]0.0326861257621256[/C][C]-0.820224469080279[/C][C]0.611785974620364[/C][/ROW]
[ROW][C]53[/C][C]19.6[/C][C]19.1689471734590[/C][C]0.0347497108593148[/C][C]0.431052826540968[/C][C]0.317135766264417[/C][/ROW]
[ROW][C]54[/C][C]19.9[/C][C]19.0294631028693[/C][C]0.0331919999304526[/C][C]0.870536897130678[/C][C]-0.257552919549820[/C][/ROW]
[ROW][C]55[/C][C]19.2[/C][C]19.8471734825025[/C][C]0.0392044550188137[/C][C]-0.647173482502464[/C][C]1.16511728205475[/C][/ROW]
[ROW][C]56[/C][C]17.8[/C][C]19.4208104028436[/C][C]0.0362949361160086[/C][C]-1.62081040284357[/C][C]-0.692773534588495[/C][/ROW]
[ROW][C]57[/C][C]19.2[/C][C]19.0312195574406[/C][C]0.0342141799336740[/C][C]0.168780442559367[/C][C]-0.633818145267439[/C][/ROW]
[ROW][C]58[/C][C]22[/C][C]20.2376482368600[/C][C]0.0384144868396215[/C][C]1.76235176313997[/C][C]1.74347338170622[/C][/ROW]
[ROW][C]59[/C][C]21.1[/C][C]20.4401322403705[/C][C]0.0388167140884143[/C][C]0.659867759629505[/C][C]0.243898459514867[/C][/ROW]
[ROW][C]60[/C][C]19.5[/C][C]20.394964725237[/C][C]0.0386609491135392[/C][C]-0.894964725237015[/C][C]-0.124787568852385[/C][/ROW]
[ROW][C]61[/C][C]22.2[/C][C]21.4369025094406[/C][C]0.0409214615431257[/C][C]0.763097490559361[/C][C]1.48771109188717[/C][/ROW]
[ROW][C]62[/C][C]20.9[/C][C]21.6985276655376[/C][C]0.0417476902809566[/C][C]-0.798527665537587[/C][C]0.325708355771775[/C][/ROW]
[ROW][C]63[/C][C]22.2[/C][C]21.1204839693465[/C][C]0.0381808792588933[/C][C]1.07951603065353[/C][C]-0.90993732336224[/C][/ROW]
[ROW][C]64[/C][C]23.5[/C][C]22.8049983601181[/C][C]0.0503878153577447[/C][C]0.695001639881928[/C][C]2.41351501765741[/C][/ROW]
[ROW][C]65[/C][C]21.5[/C][C]22.1385222746870[/C][C]0.0445442367829420[/C][C]-0.638522274687041[/C][C]-1.05422109455686[/C][/ROW]
[ROW][C]66[/C][C]24.3[/C][C]22.8813269991486[/C][C]0.0500757768112967[/C][C]1.41867300085143[/C][C]1.03198623927225[/C][/ROW]
[ROW][C]67[/C][C]22.8[/C][C]23.1546643815529[/C][C]0.0516455052942918[/C][C]-0.354664381552921[/C][C]0.331273151295866[/C][/ROW]
[ROW][C]68[/C][C]20.3[/C][C]22.5418608010356[/C][C]0.0477669899088914[/C][C]-2.24186080103563[/C][C]-0.987815705053212[/C][/ROW]
[ROW][C]69[/C][C]23.7[/C][C]23.2900740674559[/C][C]0.0509801363543038[/C][C]0.409925932544065[/C][C]1.04170245144483[/C][/ROW]
[ROW][C]70[/C][C]23.3[/C][C]22.5377815915662[/C][C]0.0482167783924409[/C][C]0.762218408433842[/C][C]-1.19418333655362[/C][/ROW]
[ROW][C]71[/C][C]19.6[/C][C]20.6285373143518[/C][C]0.0431727674353351[/C][C]-1.02853731435178[/C][C]-2.90863295597613[/C][/ROW]
[ROW][C]72[/C][C]18[/C][C]19.7426512718360[/C][C]0.0410861558289649[/C][C]-1.74265127183596[/C][C]-1.37943338834347[/C][/ROW]
[ROW][C]73[/C][C]17.3[/C][C]17.9895305123466[/C][C]0.036322510472855[/C][C]-0.68953051234658[/C][C]-2.65871347167898[/C][/ROW]
[ROW][C]74[/C][C]16.8[/C][C]17.5240270957728[/C][C]0.0344329381781700[/C][C]-0.72402709577282[/C][C]-0.741025416888488[/C][/ROW]
[ROW][C]75[/C][C]18.2[/C][C]17.6215394311672[/C][C]0.0347612324495996[/C][C]0.578460568832749[/C][C]0.0928257205832044[/C][/ROW]
[ROW][C]76[/C][C]16.5[/C][C]16.5622898879485[/C][C]0.0277117694342975[/C][C]-0.0622898879484602[/C][C]-1.60820758490952[/C][/ROW]
[ROW][C]77[/C][C]16[/C][C]16.6613997601635[/C][C]0.0282177641002253[/C][C]-0.661399760163488[/C][C]0.105166035732995[/C][/ROW]
[ROW][C]78[/C][C]18.4[/C][C]16.8868131282224[/C][C]0.0296029686147793[/C][C]1.51318687177761[/C][C]0.291496508415680[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63716&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63716&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	14.5	14.5	0	0	0
2	14.3	14.3532218182990	-0.00650225312906405	-0.0532218182989612	-0.151829303867976
3	15.3	14.9042468127159	0.0221512184686178	0.395753187284099	0.680304199751437
4	14.4	14.6934835096618	0.0150706721362367	-0.293483509661792	-0.337630616060789
5	13.7	14.0989306329845	0.00584767975717651	-0.398930632984534	-0.90856652746136
6	14.2	14.0448094080469	0.00526892341835372	0.155190591953142	-0.0894615253839601
7	13.5	13.7278684502808	0.00238740292848135	-0.227868450280822	-0.480207980211774
8	11.9	12.6440390367895	-0.0078565033500251	-0.74403903678947	-1.61756646487085
9	14.6	13.5443622179084	0.00104458290109341	1.0556377820916	1.35193602981695
10	15.6	14.8616318798438	0.0140556822103159	0.738368120156154	1.95920789642376
11	14.1	14.6717808787331	0.01205412414273	-0.571780878733093	-0.303522151587398
12	14.9	14.7612690248497	0.0128056502406377	0.138730975150275	0.115265945672613
13	14.2	14.5505149719730	0.0193929732869372	-0.350514971973031	-0.360797676478492
14	14.6	14.7394672222748	0.0195642190422452	-0.139467222274828	0.251732325083284
15	17.2	15.8595821180274	0.042461483965316	1.34041788197258	1.51102678726127
16	15.4	15.8020613150722	0.0402579077027993	-0.402061315072151	-0.142486226205362
17	14.3	15.1757455510875	0.0296765015125833	-0.875745551087479	-0.982445746081785
18	17.5	16.0677923826787	0.0385983579899382	1.4322076173213	1.28323239136818
19	14.5	15.2616428316980	0.0321521798218614	-0.761642831698038	-1.25856164838959
20	14.4	15.3386659103121	0.0324655419080657	-0.938665910312065	0.0668356042082085
21	16.6	15.7416778414265	0.0351287782094691	0.858322158573519	0.551782821700158
22	16.7	15.8647353203460	0.0357516574602543	0.835264679654023	0.13090789383413
23	16.6	16.5749556669574	0.0393142507167759	0.0250443330426124	1.00331810435859
24	16.9	16.76615084066	0.0393901374549768	0.133849159340004	0.226268981842783
25	15.7	16.5898405928147	0.0405413055923513	-0.889840592814692	-0.326194337796170
26	16.4	16.8379800330433	0.0408874335213664	-0.437980033043308	0.307617912360923
27	18.4	16.9475124945745	0.0416588342943506	1.4524875054255	0.0983964622634089
28	16.9	17.0523186369762	0.0426108584669144	-0.152318636976206	0.0908400463021881
29	16.5	17.3896860995715	0.0466630120987782	-0.889686099571456	0.432104020782224
30	18.3	16.9607051215087	0.0415969334380195	1.33929487849132	-0.705324316528581
31	15.1	16.3608499895819	0.0363632815578634	-1.26084998958185	-0.954898009220748
32	15.7	16.5261959018995	0.0372418509196335	-0.82619590189947	0.192173761268289
33	18.1	16.9973193674175	0.0398732773335018	1.10268063258254	0.646351461294702
34	16.8	16.6983749639089	0.0381654497863639	0.101625036091081	-0.504334933047932
35	18.9	17.8347830546934	0.0415688789169400	1.06521694530657	1.63337616668555
36	19	18.5204423605592	0.0419639633318892	0.479557639440806	0.959233167815239
37	18.1	18.9519756382336	0.0418571561531171	-0.851975638233591	0.581186433947571
38	17.8	18.7006636190141	0.0409743418313897	-0.900663619014137	-0.432837243733768
39	21.5	19.4512550753658	0.0466396815812547	2.04874492463417	1.03175368849035
40	17.1	18.4323237136876	0.0348119442346677	-1.33232371368758	-1.54675674779101
41	18.7	18.7468442202362	0.0380031856588257	-0.0468442202362262	0.409968934751498
42	19	18.0757165571750	0.0309373212186635	0.924283442824951	-1.04921918481289
43	16.4	17.8185541078603	0.0285942280798430	-1.41855410786029	-0.428367511942265
44	16.9	17.8260446084405	0.0284548936807973	-0.926044608440547	-0.0314293942089173
45	18.6	17.6662617069595	0.0274504521770733	0.933738293040485	-0.280321827806223
46	19.3	18.7806352783862	0.0318024844573274	0.519364721613836	1.61730217470358
47	19.4	18.8986393765442	0.0320175585937234	0.50136062345577	0.128186919162402
48	17.6	18.0816056319130	0.0309064284464227	-0.481605631912962	-1.26286987421494
49	18.6	18.6754807804339	0.0317361484265937	-0.0754807804339405	0.836215106867895
50	18.1	19.0382459477397	0.0329165860636176	-0.938245947739723	0.488374871941854
51	20.4	18.4722753592372	0.0289860915915749	1.92772464076283	-0.876166727396246
52	18.1	18.9202244690803	0.0326861257621256	-0.820224469080279	0.611785974620364
53	19.6	19.1689471734590	0.0347497108593148	0.431052826540968	0.317135766264417
54	19.9	19.0294631028693	0.0331919999304526	0.870536897130678	-0.257552919549820
55	19.2	19.8471734825025	0.0392044550188137	-0.647173482502464	1.16511728205475
56	17.8	19.4208104028436	0.0362949361160086	-1.62081040284357	-0.692773534588495
57	19.2	19.0312195574406	0.0342141799336740	0.168780442559367	-0.633818145267439
58	22	20.2376482368600	0.0384144868396215	1.76235176313997	1.74347338170622
59	21.1	20.4401322403705	0.0388167140884143	0.659867759629505	0.243898459514867
60	19.5	20.394964725237	0.0386609491135392	-0.894964725237015	-0.124787568852385
61	22.2	21.4369025094406	0.0409214615431257	0.763097490559361	1.48771109188717
62	20.9	21.6985276655376	0.0417476902809566	-0.798527665537587	0.325708355771775
63	22.2	21.1204839693465	0.0381808792588933	1.07951603065353	-0.90993732336224
64	23.5	22.8049983601181	0.0503878153577447	0.695001639881928	2.41351501765741
65	21.5	22.1385222746870	0.0445442367829420	-0.638522274687041	-1.05422109455686
66	24.3	22.8813269991486	0.0500757768112967	1.41867300085143	1.03198623927225
67	22.8	23.1546643815529	0.0516455052942918	-0.354664381552921	0.331273151295866
68	20.3	22.5418608010356	0.0477669899088914	-2.24186080103563	-0.987815705053212
69	23.7	23.2900740674559	0.0509801363543038	0.409925932544065	1.04170245144483
70	23.3	22.5377815915662	0.0482167783924409	0.762218408433842	-1.19418333655362
71	19.6	20.6285373143518	0.0431727674353351	-1.02853731435178	-2.90863295597613
72	18	19.7426512718360	0.0410861558289649	-1.74265127183596	-1.37943338834347
73	17.3	17.9895305123466	0.036322510472855	-0.68953051234658	-2.65871347167898
74	16.8	17.5240270957728	0.0344329381781700	-0.72402709577282	-0.741025416888488
75	18.2	17.6215394311672	0.0347612324495996	0.578460568832749	0.0928257205832044
76	16.5	16.5622898879485	0.0277117694342975	-0.0622898879484602	-1.60820758490952
77	16	16.6613997601635	0.0282177641002253	-0.661399760163488	0.105166035732995
78	18.4	16.8868131282224	0.0296029686147793	1.51318687177761	0.291496508415680

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