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rwasp_structuraltimeseries.wasp

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Structural Time Series Models

Date of computation

Tue, 29 Nov 2011 16:37:50 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322602678v2nr7zz85q20740.htm/, Retrieved Fri, 01 May 2026 14:36:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148740, Retrieved Fri, 01 May 2026 14:36:57 +0000

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Estimated Impact

328

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]
- RM D        [Structural Time Series Models] [] [2011-11-29 21:37:50] [4be1b05f688f7fa8db5b9e9e4d3a7e33] [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' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148740&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148740&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	101.76	101.76	0	0	0
2	102.37	102.317472718342	0.0347185971257907	0.0525272816583401	1.21653408394074
3	102.38	102.363096703179	0.0353709973017193	0.0169032968206491	0.0374807288619288
4	102.86	102.766012138015	0.0618267673712509	0.0939878619853349	1.26006628544049
5	102.87	102.856525994415	0.064393816668013	0.0134740055853279	0.097061455144699
6	102.92	102.895144192622	0.0617022027945909	0.0248558073780442	-0.0863355542102652
7	102.95	102.923266405444	0.0578077936647417	0.0267335945557931	-0.111558917576504
8	103.02	102.98636077963	0.0584674245134631	0.0336392203704683	0.0174495533730799
9	104.08	103.906384008719	0.1716865644344	0.173615991281025	2.82958576260238
10	104.16	104.162351654141	0.183178957965304	-0.00235165414137558	0.275755218149284
11	104.24	104.231111063131	0.167159739225348	0.0088889368694055	-0.373300151569999
12	104.33	104.306402225415	0.15405268460867	0.023597774584827	-0.299090948638062
13	104.73	104.860469594301	0.207117411886048	-0.130469594300989	1.47412309783394
14	104.86	104.856636596468	0.176237437180991	0.00336340353196357	-0.613919386963493
15	105.03	105.069025950853	0.181514555096409	-0.0390259508525292	0.114470266112151
16	105.62	105.494732795341	0.217288646304424	0.125267204658624	0.786668310564277
17	105.63	105.65756313702	0.209287094645434	-0.0275631370200721	-0.174805076258156
18	105.63	105.652031424569	0.177639829412378	-0.0220314245686483	-0.689462488526478
19	105.94	105.881191492708	0.18524587201111	0.0588085072916549	0.165392890231027
20	106.61	106.59807540262	0.263849096224094	0.0119245973797548	1.70670020286748
21	107.69	107.450004125229	0.350889138934492	0.239995874771297	1.88783100842432
22	107.78	107.820014813183	0.35372169968546	-0.0400148131827366	0.0613901764316693
23	107.93	107.97153810996	0.3237564018888	-0.0415381099598713	-0.649034296086546
24	108.48	108.474179945053	0.350196044235179	0.0058200549466619	0.573277064940319
25	108.14	108.369835684751	0.283469851835891	-0.229835684750735	-1.52703398146749
26	108.48	108.502559420457	0.261203837856898	-0.0225594204567996	-0.466573400301903
27	108.48	108.595840947403	0.236518959765353	-0.115840947402508	-0.52880654107407
28	108.89	108.754077483945	0.224963005931934	0.135922516055127	-0.250963502600213
29	108.93	108.906008556163	0.21416192660923	0.0239914438367088	-0.233533413384635
30	109.21	109.195067450371	0.225238948215853	0.0149325496287015	0.239287207579441
31	109.47	109.491641959238	0.235788138049913	-0.0216419592382327	0.22800989922013
32	109.8	109.87249692127	0.257240968771829	-0.072496921269895	0.463856853137475
33	111.73	111.227936559645	0.419656202248046	0.502063440355448	3.51250250748463
34	111.85	111.86707462599	0.452117757979214	-0.0170746259902029	0.702089726956255
35	112.12	112.249011290206	0.441743034532062	-0.129011290206267	-0.224285673286272
36	112.15	112.188971200622	0.367730337744733	-0.0389712006215618	-1.60540473444874
37	112.17	112.390198530513	0.343180227978324	-0.220198530512827	-0.544259583426675
38	112.67	112.663055464535	0.332801799953485	0.00694453546530825	-0.221512032443055
39	112.8	112.908784344848	0.320004833534149	-0.108784344847706	-0.274447825359877
40	113.44	113.263023114045	0.325047947686851	0.176976885954497	0.109440013054063
41	113.53	113.519325206873	0.314899108821231	0.0106747931268652	-0.219640800812342
42	114.53	114.362028613652	0.39283913660033	0.16797138634817	1.68370953207125
43	114.51	114.617911585248	0.372618191761931	-0.107911585248455	-0.436936613025504
44	115.05	115.284914564748	0.416080409314063	-0.234914564747819	0.939601821056264
45	116.67	116.131466885194	0.47963653068525	0.538533114805903	1.37440659451406
46	117.07	117.000315957136	0.537097267289448	0.0696840428640189	1.24250556481711
47	116.92	117.08559372415	0.470440601663566	-0.165593724149674	-1.44086873150839
48	117	117.108378747358	0.404494399091169	-0.108378747357779	-1.43164644904034
49	117.02	117.27066165781	0.368784058770885	-0.250661657810029	-0.782605866689142
50	117.35	117.372915778328	0.329478226039381	-0.0229157783284112	-0.844391729496933
51	117.36	117.497660005017	0.299379264509039	-0.137660005017083	-0.646510140053552
52	117.82	117.649255399569	0.277631536150262	0.170744600430895	-0.471422125092227
53	117.88	117.950340427492	0.281089309003789	-0.0703404274919172	0.0748875130891184
54	118.24	118.070387404352	0.257335350072416	0.169612595648408	-0.513390879696889
55	118.5	118.596688309705	0.297004046874783	-0.096688309704913	0.857194639879335
56	118.8	119.102877514441	0.327853732568367	-0.302877514440688	0.666895154371982
57	119.76	119.348102585206	0.315668020619397	0.411897414794188	-0.263489131279688
58	120.09	119.873375327826	0.346574409909749	0.216624672173993	0.668167654187716

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 101.76 & 101.76 & 0 & 0 & 0 \tabularnewline
2 & 102.37 & 102.317472718342 & 0.0347185971257907 & 0.0525272816583401 & 1.21653408394074 \tabularnewline
3 & 102.38 & 102.363096703179 & 0.0353709973017193 & 0.0169032968206491 & 0.0374807288619288 \tabularnewline
4 & 102.86 & 102.766012138015 & 0.0618267673712509 & 0.0939878619853349 & 1.26006628544049 \tabularnewline
5 & 102.87 & 102.856525994415 & 0.064393816668013 & 0.0134740055853279 & 0.097061455144699 \tabularnewline
6 & 102.92 & 102.895144192622 & 0.0617022027945909 & 0.0248558073780442 & -0.0863355542102652 \tabularnewline
7 & 102.95 & 102.923266405444 & 0.0578077936647417 & 0.0267335945557931 & -0.111558917576504 \tabularnewline
8 & 103.02 & 102.98636077963 & 0.0584674245134631 & 0.0336392203704683 & 0.0174495533730799 \tabularnewline
9 & 104.08 & 103.906384008719 & 0.1716865644344 & 0.173615991281025 & 2.82958576260238 \tabularnewline
10 & 104.16 & 104.162351654141 & 0.183178957965304 & -0.00235165414137558 & 0.275755218149284 \tabularnewline
11 & 104.24 & 104.231111063131 & 0.167159739225348 & 0.0088889368694055 & -0.373300151569999 \tabularnewline
12 & 104.33 & 104.306402225415 & 0.15405268460867 & 0.023597774584827 & -0.299090948638062 \tabularnewline
13 & 104.73 & 104.860469594301 & 0.207117411886048 & -0.130469594300989 & 1.47412309783394 \tabularnewline
14 & 104.86 & 104.856636596468 & 0.176237437180991 & 0.00336340353196357 & -0.613919386963493 \tabularnewline
15 & 105.03 & 105.069025950853 & 0.181514555096409 & -0.0390259508525292 & 0.114470266112151 \tabularnewline
16 & 105.62 & 105.494732795341 & 0.217288646304424 & 0.125267204658624 & 0.786668310564277 \tabularnewline
17 & 105.63 & 105.65756313702 & 0.209287094645434 & -0.0275631370200721 & -0.174805076258156 \tabularnewline
18 & 105.63 & 105.652031424569 & 0.177639829412378 & -0.0220314245686483 & -0.689462488526478 \tabularnewline
19 & 105.94 & 105.881191492708 & 0.18524587201111 & 0.0588085072916549 & 0.165392890231027 \tabularnewline
20 & 106.61 & 106.59807540262 & 0.263849096224094 & 0.0119245973797548 & 1.70670020286748 \tabularnewline
21 & 107.69 & 107.450004125229 & 0.350889138934492 & 0.239995874771297 & 1.88783100842432 \tabularnewline
22 & 107.78 & 107.820014813183 & 0.35372169968546 & -0.0400148131827366 & 0.0613901764316693 \tabularnewline
23 & 107.93 & 107.97153810996 & 0.3237564018888 & -0.0415381099598713 & -0.649034296086546 \tabularnewline
24 & 108.48 & 108.474179945053 & 0.350196044235179 & 0.0058200549466619 & 0.573277064940319 \tabularnewline
25 & 108.14 & 108.369835684751 & 0.283469851835891 & -0.229835684750735 & -1.52703398146749 \tabularnewline
26 & 108.48 & 108.502559420457 & 0.261203837856898 & -0.0225594204567996 & -0.466573400301903 \tabularnewline
27 & 108.48 & 108.595840947403 & 0.236518959765353 & -0.115840947402508 & -0.52880654107407 \tabularnewline
28 & 108.89 & 108.754077483945 & 0.224963005931934 & 0.135922516055127 & -0.250963502600213 \tabularnewline
29 & 108.93 & 108.906008556163 & 0.21416192660923 & 0.0239914438367088 & -0.233533413384635 \tabularnewline
30 & 109.21 & 109.195067450371 & 0.225238948215853 & 0.0149325496287015 & 0.239287207579441 \tabularnewline
31 & 109.47 & 109.491641959238 & 0.235788138049913 & -0.0216419592382327 & 0.22800989922013 \tabularnewline
32 & 109.8 & 109.87249692127 & 0.257240968771829 & -0.072496921269895 & 0.463856853137475 \tabularnewline
33 & 111.73 & 111.227936559645 & 0.419656202248046 & 0.502063440355448 & 3.51250250748463 \tabularnewline
34 & 111.85 & 111.86707462599 & 0.452117757979214 & -0.0170746259902029 & 0.702089726956255 \tabularnewline
35 & 112.12 & 112.249011290206 & 0.441743034532062 & -0.129011290206267 & -0.224285673286272 \tabularnewline
36 & 112.15 & 112.188971200622 & 0.367730337744733 & -0.0389712006215618 & -1.60540473444874 \tabularnewline
37 & 112.17 & 112.390198530513 & 0.343180227978324 & -0.220198530512827 & -0.544259583426675 \tabularnewline
38 & 112.67 & 112.663055464535 & 0.332801799953485 & 0.00694453546530825 & -0.221512032443055 \tabularnewline
39 & 112.8 & 112.908784344848 & 0.320004833534149 & -0.108784344847706 & -0.274447825359877 \tabularnewline
40 & 113.44 & 113.263023114045 & 0.325047947686851 & 0.176976885954497 & 0.109440013054063 \tabularnewline
41 & 113.53 & 113.519325206873 & 0.314899108821231 & 0.0106747931268652 & -0.219640800812342 \tabularnewline
42 & 114.53 & 114.362028613652 & 0.39283913660033 & 0.16797138634817 & 1.68370953207125 \tabularnewline
43 & 114.51 & 114.617911585248 & 0.372618191761931 & -0.107911585248455 & -0.436936613025504 \tabularnewline
44 & 115.05 & 115.284914564748 & 0.416080409314063 & -0.234914564747819 & 0.939601821056264 \tabularnewline
45 & 116.67 & 116.131466885194 & 0.47963653068525 & 0.538533114805903 & 1.37440659451406 \tabularnewline
46 & 117.07 & 117.000315957136 & 0.537097267289448 & 0.0696840428640189 & 1.24250556481711 \tabularnewline
47 & 116.92 & 117.08559372415 & 0.470440601663566 & -0.165593724149674 & -1.44086873150839 \tabularnewline
48 & 117 & 117.108378747358 & 0.404494399091169 & -0.108378747357779 & -1.43164644904034 \tabularnewline
49 & 117.02 & 117.27066165781 & 0.368784058770885 & -0.250661657810029 & -0.782605866689142 \tabularnewline
50 & 117.35 & 117.372915778328 & 0.329478226039381 & -0.0229157783284112 & -0.844391729496933 \tabularnewline
51 & 117.36 & 117.497660005017 & 0.299379264509039 & -0.137660005017083 & -0.646510140053552 \tabularnewline
52 & 117.82 & 117.649255399569 & 0.277631536150262 & 0.170744600430895 & -0.471422125092227 \tabularnewline
53 & 117.88 & 117.950340427492 & 0.281089309003789 & -0.0703404274919172 & 0.0748875130891184 \tabularnewline
54 & 118.24 & 118.070387404352 & 0.257335350072416 & 0.169612595648408 & -0.513390879696889 \tabularnewline
55 & 118.5 & 118.596688309705 & 0.297004046874783 & -0.096688309704913 & 0.857194639879335 \tabularnewline
56 & 118.8 & 119.102877514441 & 0.327853732568367 & -0.302877514440688 & 0.666895154371982 \tabularnewline
57 & 119.76 & 119.348102585206 & 0.315668020619397 & 0.411897414794188 & -0.263489131279688 \tabularnewline
58 & 120.09 & 119.873375327826 & 0.346574409909749 & 0.216624672173993 & 0.668167654187716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148740&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]101.76[/C][C]101.76[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]102.37[/C][C]102.317472718342[/C][C]0.0347185971257907[/C][C]0.0525272816583401[/C][C]1.21653408394074[/C][/ROW]
[ROW][C]3[/C][C]102.38[/C][C]102.363096703179[/C][C]0.0353709973017193[/C][C]0.0169032968206491[/C][C]0.0374807288619288[/C][/ROW]
[ROW][C]4[/C][C]102.86[/C][C]102.766012138015[/C][C]0.0618267673712509[/C][C]0.0939878619853349[/C][C]1.26006628544049[/C][/ROW]
[ROW][C]5[/C][C]102.87[/C][C]102.856525994415[/C][C]0.064393816668013[/C][C]0.0134740055853279[/C][C]0.097061455144699[/C][/ROW]
[ROW][C]6[/C][C]102.92[/C][C]102.895144192622[/C][C]0.0617022027945909[/C][C]0.0248558073780442[/C][C]-0.0863355542102652[/C][/ROW]
[ROW][C]7[/C][C]102.95[/C][C]102.923266405444[/C][C]0.0578077936647417[/C][C]0.0267335945557931[/C][C]-0.111558917576504[/C][/ROW]
[ROW][C]8[/C][C]103.02[/C][C]102.98636077963[/C][C]0.0584674245134631[/C][C]0.0336392203704683[/C][C]0.0174495533730799[/C][/ROW]
[ROW][C]9[/C][C]104.08[/C][C]103.906384008719[/C][C]0.1716865644344[/C][C]0.173615991281025[/C][C]2.82958576260238[/C][/ROW]
[ROW][C]10[/C][C]104.16[/C][C]104.162351654141[/C][C]0.183178957965304[/C][C]-0.00235165414137558[/C][C]0.275755218149284[/C][/ROW]
[ROW][C]11[/C][C]104.24[/C][C]104.231111063131[/C][C]0.167159739225348[/C][C]0.0088889368694055[/C][C]-0.373300151569999[/C][/ROW]
[ROW][C]12[/C][C]104.33[/C][C]104.306402225415[/C][C]0.15405268460867[/C][C]0.023597774584827[/C][C]-0.299090948638062[/C][/ROW]
[ROW][C]13[/C][C]104.73[/C][C]104.860469594301[/C][C]0.207117411886048[/C][C]-0.130469594300989[/C][C]1.47412309783394[/C][/ROW]
[ROW][C]14[/C][C]104.86[/C][C]104.856636596468[/C][C]0.176237437180991[/C][C]0.00336340353196357[/C][C]-0.613919386963493[/C][/ROW]
[ROW][C]15[/C][C]105.03[/C][C]105.069025950853[/C][C]0.181514555096409[/C][C]-0.0390259508525292[/C][C]0.114470266112151[/C][/ROW]
[ROW][C]16[/C][C]105.62[/C][C]105.494732795341[/C][C]0.217288646304424[/C][C]0.125267204658624[/C][C]0.786668310564277[/C][/ROW]
[ROW][C]17[/C][C]105.63[/C][C]105.65756313702[/C][C]0.209287094645434[/C][C]-0.0275631370200721[/C][C]-0.174805076258156[/C][/ROW]
[ROW][C]18[/C][C]105.63[/C][C]105.652031424569[/C][C]0.177639829412378[/C][C]-0.0220314245686483[/C][C]-0.689462488526478[/C][/ROW]
[ROW][C]19[/C][C]105.94[/C][C]105.881191492708[/C][C]0.18524587201111[/C][C]0.0588085072916549[/C][C]0.165392890231027[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.59807540262[/C][C]0.263849096224094[/C][C]0.0119245973797548[/C][C]1.70670020286748[/C][/ROW]
[ROW][C]21[/C][C]107.69[/C][C]107.450004125229[/C][C]0.350889138934492[/C][C]0.239995874771297[/C][C]1.88783100842432[/C][/ROW]
[ROW][C]22[/C][C]107.78[/C][C]107.820014813183[/C][C]0.35372169968546[/C][C]-0.0400148131827366[/C][C]0.0613901764316693[/C][/ROW]
[ROW][C]23[/C][C]107.93[/C][C]107.97153810996[/C][C]0.3237564018888[/C][C]-0.0415381099598713[/C][C]-0.649034296086546[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.474179945053[/C][C]0.350196044235179[/C][C]0.0058200549466619[/C][C]0.573277064940319[/C][/ROW]
[ROW][C]25[/C][C]108.14[/C][C]108.369835684751[/C][C]0.283469851835891[/C][C]-0.229835684750735[/C][C]-1.52703398146749[/C][/ROW]
[ROW][C]26[/C][C]108.48[/C][C]108.502559420457[/C][C]0.261203837856898[/C][C]-0.0225594204567996[/C][C]-0.466573400301903[/C][/ROW]
[ROW][C]27[/C][C]108.48[/C][C]108.595840947403[/C][C]0.236518959765353[/C][C]-0.115840947402508[/C][C]-0.52880654107407[/C][/ROW]
[ROW][C]28[/C][C]108.89[/C][C]108.754077483945[/C][C]0.224963005931934[/C][C]0.135922516055127[/C][C]-0.250963502600213[/C][/ROW]
[ROW][C]29[/C][C]108.93[/C][C]108.906008556163[/C][C]0.21416192660923[/C][C]0.0239914438367088[/C][C]-0.233533413384635[/C][/ROW]
[ROW][C]30[/C][C]109.21[/C][C]109.195067450371[/C][C]0.225238948215853[/C][C]0.0149325496287015[/C][C]0.239287207579441[/C][/ROW]
[ROW][C]31[/C][C]109.47[/C][C]109.491641959238[/C][C]0.235788138049913[/C][C]-0.0216419592382327[/C][C]0.22800989922013[/C][/ROW]
[ROW][C]32[/C][C]109.8[/C][C]109.87249692127[/C][C]0.257240968771829[/C][C]-0.072496921269895[/C][C]0.463856853137475[/C][/ROW]
[ROW][C]33[/C][C]111.73[/C][C]111.227936559645[/C][C]0.419656202248046[/C][C]0.502063440355448[/C][C]3.51250250748463[/C][/ROW]
[ROW][C]34[/C][C]111.85[/C][C]111.86707462599[/C][C]0.452117757979214[/C][C]-0.0170746259902029[/C][C]0.702089726956255[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]112.249011290206[/C][C]0.441743034532062[/C][C]-0.129011290206267[/C][C]-0.224285673286272[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]112.188971200622[/C][C]0.367730337744733[/C][C]-0.0389712006215618[/C][C]-1.60540473444874[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]112.390198530513[/C][C]0.343180227978324[/C][C]-0.220198530512827[/C][C]-0.544259583426675[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]112.663055464535[/C][C]0.332801799953485[/C][C]0.00694453546530825[/C][C]-0.221512032443055[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]112.908784344848[/C][C]0.320004833534149[/C][C]-0.108784344847706[/C][C]-0.274447825359877[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]113.263023114045[/C][C]0.325047947686851[/C][C]0.176976885954497[/C][C]0.109440013054063[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]113.519325206873[/C][C]0.314899108821231[/C][C]0.0106747931268652[/C][C]-0.219640800812342[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]114.362028613652[/C][C]0.39283913660033[/C][C]0.16797138634817[/C][C]1.68370953207125[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]114.617911585248[/C][C]0.372618191761931[/C][C]-0.107911585248455[/C][C]-0.436936613025504[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]115.284914564748[/C][C]0.416080409314063[/C][C]-0.234914564747819[/C][C]0.939601821056264[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]116.131466885194[/C][C]0.47963653068525[/C][C]0.538533114805903[/C][C]1.37440659451406[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]117.000315957136[/C][C]0.537097267289448[/C][C]0.0696840428640189[/C][C]1.24250556481711[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]117.08559372415[/C][C]0.470440601663566[/C][C]-0.165593724149674[/C][C]-1.44086873150839[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]117.108378747358[/C][C]0.404494399091169[/C][C]-0.108378747357779[/C][C]-1.43164644904034[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]117.27066165781[/C][C]0.368784058770885[/C][C]-0.250661657810029[/C][C]-0.782605866689142[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]117.372915778328[/C][C]0.329478226039381[/C][C]-0.0229157783284112[/C][C]-0.844391729496933[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]117.497660005017[/C][C]0.299379264509039[/C][C]-0.137660005017083[/C][C]-0.646510140053552[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]117.649255399569[/C][C]0.277631536150262[/C][C]0.170744600430895[/C][C]-0.471422125092227[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]117.950340427492[/C][C]0.281089309003789[/C][C]-0.0703404274919172[/C][C]0.0748875130891184[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]118.070387404352[/C][C]0.257335350072416[/C][C]0.169612595648408[/C][C]-0.513390879696889[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]118.596688309705[/C][C]0.297004046874783[/C][C]-0.096688309704913[/C][C]0.857194639879335[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]119.102877514441[/C][C]0.327853732568367[/C][C]-0.302877514440688[/C][C]0.666895154371982[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]119.348102585206[/C][C]0.315668020619397[/C][C]0.411897414794188[/C][C]-0.263489131279688[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]119.873375327826[/C][C]0.346574409909749[/C][C]0.216624672173993[/C][C]0.668167654187716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148740&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	101.76	101.76	0	0	0
2	102.37	102.317472718342	0.0347185971257907	0.0525272816583401	1.21653408394074
3	102.38	102.363096703179	0.0353709973017193	0.0169032968206491	0.0374807288619288
4	102.86	102.766012138015	0.0618267673712509	0.0939878619853349	1.26006628544049
5	102.87	102.856525994415	0.064393816668013	0.0134740055853279	0.097061455144699
6	102.92	102.895144192622	0.0617022027945909	0.0248558073780442	-0.0863355542102652
7	102.95	102.923266405444	0.0578077936647417	0.0267335945557931	-0.111558917576504
8	103.02	102.98636077963	0.0584674245134631	0.0336392203704683	0.0174495533730799
9	104.08	103.906384008719	0.1716865644344	0.173615991281025	2.82958576260238
10	104.16	104.162351654141	0.183178957965304	-0.00235165414137558	0.275755218149284
11	104.24	104.231111063131	0.167159739225348	0.0088889368694055	-0.373300151569999
12	104.33	104.306402225415	0.15405268460867	0.023597774584827	-0.299090948638062
13	104.73	104.860469594301	0.207117411886048	-0.130469594300989	1.47412309783394
14	104.86	104.856636596468	0.176237437180991	0.00336340353196357	-0.613919386963493
15	105.03	105.069025950853	0.181514555096409	-0.0390259508525292	0.114470266112151
16	105.62	105.494732795341	0.217288646304424	0.125267204658624	0.786668310564277
17	105.63	105.65756313702	0.209287094645434	-0.0275631370200721	-0.174805076258156
18	105.63	105.652031424569	0.177639829412378	-0.0220314245686483	-0.689462488526478
19	105.94	105.881191492708	0.18524587201111	0.0588085072916549	0.165392890231027
20	106.61	106.59807540262	0.263849096224094	0.0119245973797548	1.70670020286748
21	107.69	107.450004125229	0.350889138934492	0.239995874771297	1.88783100842432
22	107.78	107.820014813183	0.35372169968546	-0.0400148131827366	0.0613901764316693
23	107.93	107.97153810996	0.3237564018888	-0.0415381099598713	-0.649034296086546
24	108.48	108.474179945053	0.350196044235179	0.0058200549466619	0.573277064940319
25	108.14	108.369835684751	0.283469851835891	-0.229835684750735	-1.52703398146749
26	108.48	108.502559420457	0.261203837856898	-0.0225594204567996	-0.466573400301903
27	108.48	108.595840947403	0.236518959765353	-0.115840947402508	-0.52880654107407
28	108.89	108.754077483945	0.224963005931934	0.135922516055127	-0.250963502600213
29	108.93	108.906008556163	0.21416192660923	0.0239914438367088	-0.233533413384635
30	109.21	109.195067450371	0.225238948215853	0.0149325496287015	0.239287207579441
31	109.47	109.491641959238	0.235788138049913	-0.0216419592382327	0.22800989922013
32	109.8	109.87249692127	0.257240968771829	-0.072496921269895	0.463856853137475
33	111.73	111.227936559645	0.419656202248046	0.502063440355448	3.51250250748463
34	111.85	111.86707462599	0.452117757979214	-0.0170746259902029	0.702089726956255
35	112.12	112.249011290206	0.441743034532062	-0.129011290206267	-0.224285673286272
36	112.15	112.188971200622	0.367730337744733	-0.0389712006215618	-1.60540473444874
37	112.17	112.390198530513	0.343180227978324	-0.220198530512827	-0.544259583426675
38	112.67	112.663055464535	0.332801799953485	0.00694453546530825	-0.221512032443055
39	112.8	112.908784344848	0.320004833534149	-0.108784344847706	-0.274447825359877
40	113.44	113.263023114045	0.325047947686851	0.176976885954497	0.109440013054063
41	113.53	113.519325206873	0.314899108821231	0.0106747931268652	-0.219640800812342
42	114.53	114.362028613652	0.39283913660033	0.16797138634817	1.68370953207125
43	114.51	114.617911585248	0.372618191761931	-0.107911585248455	-0.436936613025504
44	115.05	115.284914564748	0.416080409314063	-0.234914564747819	0.939601821056264
45	116.67	116.131466885194	0.47963653068525	0.538533114805903	1.37440659451406
46	117.07	117.000315957136	0.537097267289448	0.0696840428640189	1.24250556481711
47	116.92	117.08559372415	0.470440601663566	-0.165593724149674	-1.44086873150839
48	117	117.108378747358	0.404494399091169	-0.108378747357779	-1.43164644904034
49	117.02	117.27066165781	0.368784058770885	-0.250661657810029	-0.782605866689142
50	117.35	117.372915778328	0.329478226039381	-0.0229157783284112	-0.844391729496933
51	117.36	117.497660005017	0.299379264509039	-0.137660005017083	-0.646510140053552
52	117.82	117.649255399569	0.277631536150262	0.170744600430895	-0.471422125092227
53	117.88	117.950340427492	0.281089309003789	-0.0703404274919172	0.0748875130891184
54	118.24	118.070387404352	0.257335350072416	0.169612595648408	-0.513390879696889
55	118.5	118.596688309705	0.297004046874783	-0.096688309704913	0.857194639879335
56	118.8	119.102877514441	0.327853732568367	-0.302877514440688	0.666895154371982
57	119.76	119.348102585206	0.315668020619397	0.411897414794188	-0.263489131279688
58	120.09	119.873375327826	0.346574409909749	0.216624672173993	0.668167654187716

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