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R Software Module

rwasp_structuraltimeseries.wasp

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Structural Time Series Models

Date of computation

Tue, 21 Dec 2010 12:42:27 +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/Dec/21/t1292935262ry9adwh7s7vd6ve.htm/, Retrieved Sat, 18 Apr 2026 00:52:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113425, Retrieved Sat, 18 Apr 2026 00:52:21 +0000

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Estimated Impact

421

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]
- RMPD  [Structural Time Series Models] [STSM] [2010-12-07 13:17:11] [8b7e5d4d87654725a776c7f35eb4752f]
-    D    [Structural Time Series Models] [] [2010-12-09 20:46:27] [126c9e58bb659a0bfb4675d843c2c69e]
-    D      [Structural Time Series Models] [] [2010-12-19 16:16:29] [126c9e58bb659a0bfb4675d843c2c69e]
-    D          [Structural Time Series Models] [] [2010-12-21 12:42:27] [a3cd012a7211edfe9ed4466e21aef6a6] [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	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113425&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113425&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113425&T=0

As an alternative you can also use a QR Code:

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

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

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	104.31	104.31	0	0	0
2	103.88	103.902294705550	-0.0235502905421562	-0.0222947055497816	-1.68396802191647
3	103.88	103.902212705130	-0.0230627915483656	-0.0222127051305003	0.160576516216919
4	103.86	103.882202348102	-0.0229743379049404	-0.0222023481025030	0.0207960922739162
5	103.89	103.912029756396	-0.0210390066673808	-0.0220297563956681	0.358271067967188
6	103.98	104.001683756457	-0.0161992955968004	-0.0216837564565165	0.748215093703513
7	103.98	104.001635802637	-0.0153894375142909	-0.0216358026373737	0.108789580305062
8	104.29	104.310726263410	0.00274825088015736	-0.0207262634095379	2.17859634360554
9	104.29	104.310733478046	0.0025810502502226	-0.0207334780458504	-0.0183507695207754
10	104.24	104.260862496924	-0.000853205935104232	-0.0208624969238806	-0.350259632538984
11	103.98	104.001454362635	-0.0187878521408545	-0.0214543626347393	-1.72266317912536
12	103.54	103.562346559576	-0.0493539922474934	-0.0223465595762711	-2.79492399348178
13	103.44	103.293242011366	-0.0605653637776451	0.146757988633870	-1.73779670925153
14	103.32	103.331042251593	-0.0519801085368243	-0.0110422515933838	0.555141601417225
15	103.3	103.311022702522	-0.0494380504621622	-0.0110227025217995	0.211408498502653
16	103.26	103.271017400811	-0.0486704764988985	-0.0110174008112351	0.0623290479251919
17	103.14	103.151054148554	-0.0545820478318245	-0.0110541485537382	-0.470664016636422
18	103.11	103.121042550360	-0.0525127744926746	-0.0110425503598981	0.162088201379941
19	102.91	102.921106203583	-0.0650887714572062	-0.0111062035831994	-0.971916856400752
20	103.23	103.240954328097	-0.0319019609830202	-0.0109543280968609	2.53640811558381
21	103.23	103.240942840120	-0.0291284056495086	-0.0109428401203158	0.21003656624671
22	103.14	103.150962840525	-0.0344591376692731	-0.0109628405248079	-0.40062819514297
23	102.91	102.921021428520	-0.0516863719727084	-0.0110214285201618	-1.2865862156552
24	102.42	102.431141128595	-0.0904939968173886	-0.0111411285950175	-2.88324803452654
25	102.1	102.041870481085	-0.115736024969886	0.05812951891548	-2.14835894388426
26	102.07	102.073119677213	-0.102383469934942	-0.00311967721273393	0.881819353261513
27	102.06	102.063117251125	-0.094121432454439	-0.00311725112524153	0.60740502226227
28	101.98	101.983116912324	-0.0928555399991643	-0.00311691232419478	0.0928351410039142
29	101.83	101.833118160191	-0.0979881685703347	-0.00311816019072596	-0.375634958031822
30	101.75	101.753117802721	-0.096369889170432	-0.00311780272060873	0.118234496644265
31	101.56	101.563119495771	-0.104804432737705	-0.00311949577064302	-0.615381067835623
32	101.66	101.663116126409	-0.0863345323848052	-0.00311612640918814	1.34599737485727
33	101.65	101.653114983941	-0.0794441640191125	-0.00311498394129133	0.501656293120192
34	101.61	101.613114446924	-0.0758810333994267	-0.00311444692445935	0.259209976183802
35	101.52	101.523114621774	-0.0771572452658088	-0.00311462177353093	-0.0927808640347435
36	101.31	101.313116118117	-0.0891710819846183	-0.00311611811704867	-0.8729356750975
37	101.19	101.164255139333	-0.0944947635939917	0.0257448606668044	-0.416615268446897
38	101.11	101.111885695164	-0.0906823212614798	-0.00188569516434792	0.259491666821823
39	101.1	101.101891691181	-0.0833773850690747	-0.00189169118054432	0.530149371816324
40	101.07	101.071895291033	-0.0785435153969892	-0.00189529103318753	0.350729359183862
41	100.98	100.981894588374	-0.0795812144845533	-0.00189458837432693	-0.0752769647514083
42	100.93	100.931896238314	-0.0769014032168808	-0.00189623831407626	0.194367357401417
43	100.92	100.921899631758	-0.0708399077083481	-0.00189963175764587	0.439581847152546
44	101.02	101.021907512070	-0.0553595680164641	-0.00190751206959326	1.12251338795001
45	101.01	101.011909414759	-0.0512490306604136	-0.00190941475868671	0.298036319387071
46	100.97	100.971909843856	-0.0502295554935866	-0.00190984385588771	0.0739118026397467
47	100.89	100.891908811178	-0.0529277497666185	-0.00190881117785979	-0.195606237866223
48	100.62	100.621901963855	-0.0726027157772648	-0.00190196385523712	-1.42626624398634
49	100.53	100.512961758190	-0.0758756655620918	0.0170382418103744	-0.249921541121885
50	100.48	100.481172369972	-0.071893471025049	-0.00117236997202315	0.275517192751225
51	100.48	100.481178342147	-0.0653758733014334	-0.00117834214649636	0.472369066887793
52	100.47	100.471182513954	-0.0603556698666559	-0.00118251395444556	0.36384159413811
53	100.52	100.521190074026	-0.0503511181441277	-0.00119007402650279	0.725080618390734
54	100.49	100.491191341815	-0.0485061319441162	-0.00119134181538184	0.133714907349267
55	100.47	100.471192956636	-0.0459218215221221	-0.00119295663560042	0.187296545105111
56	100.44	100.441193776809	-0.0444783759456416	-0.00119377680910751	0.104612640271396

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 104.31 & 104.31 & 0 & 0 & 0 \tabularnewline
2 & 103.88 & 103.902294705550 & -0.0235502905421562 & -0.0222947055497816 & -1.68396802191647 \tabularnewline
3 & 103.88 & 103.902212705130 & -0.0230627915483656 & -0.0222127051305003 & 0.160576516216919 \tabularnewline
4 & 103.86 & 103.882202348102 & -0.0229743379049404 & -0.0222023481025030 & 0.0207960922739162 \tabularnewline
5 & 103.89 & 103.912029756396 & -0.0210390066673808 & -0.0220297563956681 & 0.358271067967188 \tabularnewline
6 & 103.98 & 104.001683756457 & -0.0161992955968004 & -0.0216837564565165 & 0.748215093703513 \tabularnewline
7 & 103.98 & 104.001635802637 & -0.0153894375142909 & -0.0216358026373737 & 0.108789580305062 \tabularnewline
8 & 104.29 & 104.310726263410 & 0.00274825088015736 & -0.0207262634095379 & 2.17859634360554 \tabularnewline
9 & 104.29 & 104.310733478046 & 0.0025810502502226 & -0.0207334780458504 & -0.0183507695207754 \tabularnewline
10 & 104.24 & 104.260862496924 & -0.000853205935104232 & -0.0208624969238806 & -0.350259632538984 \tabularnewline
11 & 103.98 & 104.001454362635 & -0.0187878521408545 & -0.0214543626347393 & -1.72266317912536 \tabularnewline
12 & 103.54 & 103.562346559576 & -0.0493539922474934 & -0.0223465595762711 & -2.79492399348178 \tabularnewline
13 & 103.44 & 103.293242011366 & -0.0605653637776451 & 0.146757988633870 & -1.73779670925153 \tabularnewline
14 & 103.32 & 103.331042251593 & -0.0519801085368243 & -0.0110422515933838 & 0.555141601417225 \tabularnewline
15 & 103.3 & 103.311022702522 & -0.0494380504621622 & -0.0110227025217995 & 0.211408498502653 \tabularnewline
16 & 103.26 & 103.271017400811 & -0.0486704764988985 & -0.0110174008112351 & 0.0623290479251919 \tabularnewline
17 & 103.14 & 103.151054148554 & -0.0545820478318245 & -0.0110541485537382 & -0.470664016636422 \tabularnewline
18 & 103.11 & 103.121042550360 & -0.0525127744926746 & -0.0110425503598981 & 0.162088201379941 \tabularnewline
19 & 102.91 & 102.921106203583 & -0.0650887714572062 & -0.0111062035831994 & -0.971916856400752 \tabularnewline
20 & 103.23 & 103.240954328097 & -0.0319019609830202 & -0.0109543280968609 & 2.53640811558381 \tabularnewline
21 & 103.23 & 103.240942840120 & -0.0291284056495086 & -0.0109428401203158 & 0.21003656624671 \tabularnewline
22 & 103.14 & 103.150962840525 & -0.0344591376692731 & -0.0109628405248079 & -0.40062819514297 \tabularnewline
23 & 102.91 & 102.921021428520 & -0.0516863719727084 & -0.0110214285201618 & -1.2865862156552 \tabularnewline
24 & 102.42 & 102.431141128595 & -0.0904939968173886 & -0.0111411285950175 & -2.88324803452654 \tabularnewline
25 & 102.1 & 102.041870481085 & -0.115736024969886 & 0.05812951891548 & -2.14835894388426 \tabularnewline
26 & 102.07 & 102.073119677213 & -0.102383469934942 & -0.00311967721273393 & 0.881819353261513 \tabularnewline
27 & 102.06 & 102.063117251125 & -0.094121432454439 & -0.00311725112524153 & 0.60740502226227 \tabularnewline
28 & 101.98 & 101.983116912324 & -0.0928555399991643 & -0.00311691232419478 & 0.0928351410039142 \tabularnewline
29 & 101.83 & 101.833118160191 & -0.0979881685703347 & -0.00311816019072596 & -0.375634958031822 \tabularnewline
30 & 101.75 & 101.753117802721 & -0.096369889170432 & -0.00311780272060873 & 0.118234496644265 \tabularnewline
31 & 101.56 & 101.563119495771 & -0.104804432737705 & -0.00311949577064302 & -0.615381067835623 \tabularnewline
32 & 101.66 & 101.663116126409 & -0.0863345323848052 & -0.00311612640918814 & 1.34599737485727 \tabularnewline
33 & 101.65 & 101.653114983941 & -0.0794441640191125 & -0.00311498394129133 & 0.501656293120192 \tabularnewline
34 & 101.61 & 101.613114446924 & -0.0758810333994267 & -0.00311444692445935 & 0.259209976183802 \tabularnewline
35 & 101.52 & 101.523114621774 & -0.0771572452658088 & -0.00311462177353093 & -0.0927808640347435 \tabularnewline
36 & 101.31 & 101.313116118117 & -0.0891710819846183 & -0.00311611811704867 & -0.8729356750975 \tabularnewline
37 & 101.19 & 101.164255139333 & -0.0944947635939917 & 0.0257448606668044 & -0.416615268446897 \tabularnewline
38 & 101.11 & 101.111885695164 & -0.0906823212614798 & -0.00188569516434792 & 0.259491666821823 \tabularnewline
39 & 101.1 & 101.101891691181 & -0.0833773850690747 & -0.00189169118054432 & 0.530149371816324 \tabularnewline
40 & 101.07 & 101.071895291033 & -0.0785435153969892 & -0.00189529103318753 & 0.350729359183862 \tabularnewline
41 & 100.98 & 100.981894588374 & -0.0795812144845533 & -0.00189458837432693 & -0.0752769647514083 \tabularnewline
42 & 100.93 & 100.931896238314 & -0.0769014032168808 & -0.00189623831407626 & 0.194367357401417 \tabularnewline
43 & 100.92 & 100.921899631758 & -0.0708399077083481 & -0.00189963175764587 & 0.439581847152546 \tabularnewline
44 & 101.02 & 101.021907512070 & -0.0553595680164641 & -0.00190751206959326 & 1.12251338795001 \tabularnewline
45 & 101.01 & 101.011909414759 & -0.0512490306604136 & -0.00190941475868671 & 0.298036319387071 \tabularnewline
46 & 100.97 & 100.971909843856 & -0.0502295554935866 & -0.00190984385588771 & 0.0739118026397467 \tabularnewline
47 & 100.89 & 100.891908811178 & -0.0529277497666185 & -0.00190881117785979 & -0.195606237866223 \tabularnewline
48 & 100.62 & 100.621901963855 & -0.0726027157772648 & -0.00190196385523712 & -1.42626624398634 \tabularnewline
49 & 100.53 & 100.512961758190 & -0.0758756655620918 & 0.0170382418103744 & -0.249921541121885 \tabularnewline
50 & 100.48 & 100.481172369972 & -0.071893471025049 & -0.00117236997202315 & 0.275517192751225 \tabularnewline
51 & 100.48 & 100.481178342147 & -0.0653758733014334 & -0.00117834214649636 & 0.472369066887793 \tabularnewline
52 & 100.47 & 100.471182513954 & -0.0603556698666559 & -0.00118251395444556 & 0.36384159413811 \tabularnewline
53 & 100.52 & 100.521190074026 & -0.0503511181441277 & -0.00119007402650279 & 0.725080618390734 \tabularnewline
54 & 100.49 & 100.491191341815 & -0.0485061319441162 & -0.00119134181538184 & 0.133714907349267 \tabularnewline
55 & 100.47 & 100.471192956636 & -0.0459218215221221 & -0.00119295663560042 & 0.187296545105111 \tabularnewline
56 & 100.44 & 100.441193776809 & -0.0444783759456416 & -0.00119377680910751 & 0.104612640271396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113425&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]104.31[/C][C]104.31[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]103.88[/C][C]103.902294705550[/C][C]-0.0235502905421562[/C][C]-0.0222947055497816[/C][C]-1.68396802191647[/C][/ROW]
[ROW][C]3[/C][C]103.88[/C][C]103.902212705130[/C][C]-0.0230627915483656[/C][C]-0.0222127051305003[/C][C]0.160576516216919[/C][/ROW]
[ROW][C]4[/C][C]103.86[/C][C]103.882202348102[/C][C]-0.0229743379049404[/C][C]-0.0222023481025030[/C][C]0.0207960922739162[/C][/ROW]
[ROW][C]5[/C][C]103.89[/C][C]103.912029756396[/C][C]-0.0210390066673808[/C][C]-0.0220297563956681[/C][C]0.358271067967188[/C][/ROW]
[ROW][C]6[/C][C]103.98[/C][C]104.001683756457[/C][C]-0.0161992955968004[/C][C]-0.0216837564565165[/C][C]0.748215093703513[/C][/ROW]
[ROW][C]7[/C][C]103.98[/C][C]104.001635802637[/C][C]-0.0153894375142909[/C][C]-0.0216358026373737[/C][C]0.108789580305062[/C][/ROW]
[ROW][C]8[/C][C]104.29[/C][C]104.310726263410[/C][C]0.00274825088015736[/C][C]-0.0207262634095379[/C][C]2.17859634360554[/C][/ROW]
[ROW][C]9[/C][C]104.29[/C][C]104.310733478046[/C][C]0.0025810502502226[/C][C]-0.0207334780458504[/C][C]-0.0183507695207754[/C][/ROW]
[ROW][C]10[/C][C]104.24[/C][C]104.260862496924[/C][C]-0.000853205935104232[/C][C]-0.0208624969238806[/C][C]-0.350259632538984[/C][/ROW]
[ROW][C]11[/C][C]103.98[/C][C]104.001454362635[/C][C]-0.0187878521408545[/C][C]-0.0214543626347393[/C][C]-1.72266317912536[/C][/ROW]
[ROW][C]12[/C][C]103.54[/C][C]103.562346559576[/C][C]-0.0493539922474934[/C][C]-0.0223465595762711[/C][C]-2.79492399348178[/C][/ROW]
[ROW][C]13[/C][C]103.44[/C][C]103.293242011366[/C][C]-0.0605653637776451[/C][C]0.146757988633870[/C][C]-1.73779670925153[/C][/ROW]
[ROW][C]14[/C][C]103.32[/C][C]103.331042251593[/C][C]-0.0519801085368243[/C][C]-0.0110422515933838[/C][C]0.555141601417225[/C][/ROW]
[ROW][C]15[/C][C]103.3[/C][C]103.311022702522[/C][C]-0.0494380504621622[/C][C]-0.0110227025217995[/C][C]0.211408498502653[/C][/ROW]
[ROW][C]16[/C][C]103.26[/C][C]103.271017400811[/C][C]-0.0486704764988985[/C][C]-0.0110174008112351[/C][C]0.0623290479251919[/C][/ROW]
[ROW][C]17[/C][C]103.14[/C][C]103.151054148554[/C][C]-0.0545820478318245[/C][C]-0.0110541485537382[/C][C]-0.470664016636422[/C][/ROW]
[ROW][C]18[/C][C]103.11[/C][C]103.121042550360[/C][C]-0.0525127744926746[/C][C]-0.0110425503598981[/C][C]0.162088201379941[/C][/ROW]
[ROW][C]19[/C][C]102.91[/C][C]102.921106203583[/C][C]-0.0650887714572062[/C][C]-0.0111062035831994[/C][C]-0.971916856400752[/C][/ROW]
[ROW][C]20[/C][C]103.23[/C][C]103.240954328097[/C][C]-0.0319019609830202[/C][C]-0.0109543280968609[/C][C]2.53640811558381[/C][/ROW]
[ROW][C]21[/C][C]103.23[/C][C]103.240942840120[/C][C]-0.0291284056495086[/C][C]-0.0109428401203158[/C][C]0.21003656624671[/C][/ROW]
[ROW][C]22[/C][C]103.14[/C][C]103.150962840525[/C][C]-0.0344591376692731[/C][C]-0.0109628405248079[/C][C]-0.40062819514297[/C][/ROW]
[ROW][C]23[/C][C]102.91[/C][C]102.921021428520[/C][C]-0.0516863719727084[/C][C]-0.0110214285201618[/C][C]-1.2865862156552[/C][/ROW]
[ROW][C]24[/C][C]102.42[/C][C]102.431141128595[/C][C]-0.0904939968173886[/C][C]-0.0111411285950175[/C][C]-2.88324803452654[/C][/ROW]
[ROW][C]25[/C][C]102.1[/C][C]102.041870481085[/C][C]-0.115736024969886[/C][C]0.05812951891548[/C][C]-2.14835894388426[/C][/ROW]
[ROW][C]26[/C][C]102.07[/C][C]102.073119677213[/C][C]-0.102383469934942[/C][C]-0.00311967721273393[/C][C]0.881819353261513[/C][/ROW]
[ROW][C]27[/C][C]102.06[/C][C]102.063117251125[/C][C]-0.094121432454439[/C][C]-0.00311725112524153[/C][C]0.60740502226227[/C][/ROW]
[ROW][C]28[/C][C]101.98[/C][C]101.983116912324[/C][C]-0.0928555399991643[/C][C]-0.00311691232419478[/C][C]0.0928351410039142[/C][/ROW]
[ROW][C]29[/C][C]101.83[/C][C]101.833118160191[/C][C]-0.0979881685703347[/C][C]-0.00311816019072596[/C][C]-0.375634958031822[/C][/ROW]
[ROW][C]30[/C][C]101.75[/C][C]101.753117802721[/C][C]-0.096369889170432[/C][C]-0.00311780272060873[/C][C]0.118234496644265[/C][/ROW]
[ROW][C]31[/C][C]101.56[/C][C]101.563119495771[/C][C]-0.104804432737705[/C][C]-0.00311949577064302[/C][C]-0.615381067835623[/C][/ROW]
[ROW][C]32[/C][C]101.66[/C][C]101.663116126409[/C][C]-0.0863345323848052[/C][C]-0.00311612640918814[/C][C]1.34599737485727[/C][/ROW]
[ROW][C]33[/C][C]101.65[/C][C]101.653114983941[/C][C]-0.0794441640191125[/C][C]-0.00311498394129133[/C][C]0.501656293120192[/C][/ROW]
[ROW][C]34[/C][C]101.61[/C][C]101.613114446924[/C][C]-0.0758810333994267[/C][C]-0.00311444692445935[/C][C]0.259209976183802[/C][/ROW]
[ROW][C]35[/C][C]101.52[/C][C]101.523114621774[/C][C]-0.0771572452658088[/C][C]-0.00311462177353093[/C][C]-0.0927808640347435[/C][/ROW]
[ROW][C]36[/C][C]101.31[/C][C]101.313116118117[/C][C]-0.0891710819846183[/C][C]-0.00311611811704867[/C][C]-0.8729356750975[/C][/ROW]
[ROW][C]37[/C][C]101.19[/C][C]101.164255139333[/C][C]-0.0944947635939917[/C][C]0.0257448606668044[/C][C]-0.416615268446897[/C][/ROW]
[ROW][C]38[/C][C]101.11[/C][C]101.111885695164[/C][C]-0.0906823212614798[/C][C]-0.00188569516434792[/C][C]0.259491666821823[/C][/ROW]
[ROW][C]39[/C][C]101.1[/C][C]101.101891691181[/C][C]-0.0833773850690747[/C][C]-0.00189169118054432[/C][C]0.530149371816324[/C][/ROW]
[ROW][C]40[/C][C]101.07[/C][C]101.071895291033[/C][C]-0.0785435153969892[/C][C]-0.00189529103318753[/C][C]0.350729359183862[/C][/ROW]
[ROW][C]41[/C][C]100.98[/C][C]100.981894588374[/C][C]-0.0795812144845533[/C][C]-0.00189458837432693[/C][C]-0.0752769647514083[/C][/ROW]
[ROW][C]42[/C][C]100.93[/C][C]100.931896238314[/C][C]-0.0769014032168808[/C][C]-0.00189623831407626[/C][C]0.194367357401417[/C][/ROW]
[ROW][C]43[/C][C]100.92[/C][C]100.921899631758[/C][C]-0.0708399077083481[/C][C]-0.00189963175764587[/C][C]0.439581847152546[/C][/ROW]
[ROW][C]44[/C][C]101.02[/C][C]101.021907512070[/C][C]-0.0553595680164641[/C][C]-0.00190751206959326[/C][C]1.12251338795001[/C][/ROW]
[ROW][C]45[/C][C]101.01[/C][C]101.011909414759[/C][C]-0.0512490306604136[/C][C]-0.00190941475868671[/C][C]0.298036319387071[/C][/ROW]
[ROW][C]46[/C][C]100.97[/C][C]100.971909843856[/C][C]-0.0502295554935866[/C][C]-0.00190984385588771[/C][C]0.0739118026397467[/C][/ROW]
[ROW][C]47[/C][C]100.89[/C][C]100.891908811178[/C][C]-0.0529277497666185[/C][C]-0.00190881117785979[/C][C]-0.195606237866223[/C][/ROW]
[ROW][C]48[/C][C]100.62[/C][C]100.621901963855[/C][C]-0.0726027157772648[/C][C]-0.00190196385523712[/C][C]-1.42626624398634[/C][/ROW]
[ROW][C]49[/C][C]100.53[/C][C]100.512961758190[/C][C]-0.0758756655620918[/C][C]0.0170382418103744[/C][C]-0.249921541121885[/C][/ROW]
[ROW][C]50[/C][C]100.48[/C][C]100.481172369972[/C][C]-0.071893471025049[/C][C]-0.00117236997202315[/C][C]0.275517192751225[/C][/ROW]
[ROW][C]51[/C][C]100.48[/C][C]100.481178342147[/C][C]-0.0653758733014334[/C][C]-0.00117834214649636[/C][C]0.472369066887793[/C][/ROW]
[ROW][C]52[/C][C]100.47[/C][C]100.471182513954[/C][C]-0.0603556698666559[/C][C]-0.00118251395444556[/C][C]0.36384159413811[/C][/ROW]
[ROW][C]53[/C][C]100.52[/C][C]100.521190074026[/C][C]-0.0503511181441277[/C][C]-0.00119007402650279[/C][C]0.725080618390734[/C][/ROW]
[ROW][C]54[/C][C]100.49[/C][C]100.491191341815[/C][C]-0.0485061319441162[/C][C]-0.00119134181538184[/C][C]0.133714907349267[/C][/ROW]
[ROW][C]55[/C][C]100.47[/C][C]100.471192956636[/C][C]-0.0459218215221221[/C][C]-0.00119295663560042[/C][C]0.187296545105111[/C][/ROW]
[ROW][C]56[/C][C]100.44[/C][C]100.441193776809[/C][C]-0.0444783759456416[/C][C]-0.00119377680910751[/C][C]0.104612640271396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113425&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113425&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	104.31	104.31	0	0	0
2	103.88	103.902294705550	-0.0235502905421562	-0.0222947055497816	-1.68396802191647
3	103.88	103.902212705130	-0.0230627915483656	-0.0222127051305003	0.160576516216919
4	103.86	103.882202348102	-0.0229743379049404	-0.0222023481025030	0.0207960922739162
5	103.89	103.912029756396	-0.0210390066673808	-0.0220297563956681	0.358271067967188
6	103.98	104.001683756457	-0.0161992955968004	-0.0216837564565165	0.748215093703513
7	103.98	104.001635802637	-0.0153894375142909	-0.0216358026373737	0.108789580305062
8	104.29	104.310726263410	0.00274825088015736	-0.0207262634095379	2.17859634360554
9	104.29	104.310733478046	0.0025810502502226	-0.0207334780458504	-0.0183507695207754
10	104.24	104.260862496924	-0.000853205935104232	-0.0208624969238806	-0.350259632538984
11	103.98	104.001454362635	-0.0187878521408545	-0.0214543626347393	-1.72266317912536
12	103.54	103.562346559576	-0.0493539922474934	-0.0223465595762711	-2.79492399348178
13	103.44	103.293242011366	-0.0605653637776451	0.146757988633870	-1.73779670925153
14	103.32	103.331042251593	-0.0519801085368243	-0.0110422515933838	0.555141601417225
15	103.3	103.311022702522	-0.0494380504621622	-0.0110227025217995	0.211408498502653
16	103.26	103.271017400811	-0.0486704764988985	-0.0110174008112351	0.0623290479251919
17	103.14	103.151054148554	-0.0545820478318245	-0.0110541485537382	-0.470664016636422
18	103.11	103.121042550360	-0.0525127744926746	-0.0110425503598981	0.162088201379941
19	102.91	102.921106203583	-0.0650887714572062	-0.0111062035831994	-0.971916856400752
20	103.23	103.240954328097	-0.0319019609830202	-0.0109543280968609	2.53640811558381
21	103.23	103.240942840120	-0.0291284056495086	-0.0109428401203158	0.21003656624671
22	103.14	103.150962840525	-0.0344591376692731	-0.0109628405248079	-0.40062819514297
23	102.91	102.921021428520	-0.0516863719727084	-0.0110214285201618	-1.2865862156552
24	102.42	102.431141128595	-0.0904939968173886	-0.0111411285950175	-2.88324803452654
25	102.1	102.041870481085	-0.115736024969886	0.05812951891548	-2.14835894388426
26	102.07	102.073119677213	-0.102383469934942	-0.00311967721273393	0.881819353261513
27	102.06	102.063117251125	-0.094121432454439	-0.00311725112524153	0.60740502226227
28	101.98	101.983116912324	-0.0928555399991643	-0.00311691232419478	0.0928351410039142
29	101.83	101.833118160191	-0.0979881685703347	-0.00311816019072596	-0.375634958031822
30	101.75	101.753117802721	-0.096369889170432	-0.00311780272060873	0.118234496644265
31	101.56	101.563119495771	-0.104804432737705	-0.00311949577064302	-0.615381067835623
32	101.66	101.663116126409	-0.0863345323848052	-0.00311612640918814	1.34599737485727
33	101.65	101.653114983941	-0.0794441640191125	-0.00311498394129133	0.501656293120192
34	101.61	101.613114446924	-0.0758810333994267	-0.00311444692445935	0.259209976183802
35	101.52	101.523114621774	-0.0771572452658088	-0.00311462177353093	-0.0927808640347435
36	101.31	101.313116118117	-0.0891710819846183	-0.00311611811704867	-0.8729356750975
37	101.19	101.164255139333	-0.0944947635939917	0.0257448606668044	-0.416615268446897
38	101.11	101.111885695164	-0.0906823212614798	-0.00188569516434792	0.259491666821823
39	101.1	101.101891691181	-0.0833773850690747	-0.00189169118054432	0.530149371816324
40	101.07	101.071895291033	-0.0785435153969892	-0.00189529103318753	0.350729359183862
41	100.98	100.981894588374	-0.0795812144845533	-0.00189458837432693	-0.0752769647514083
42	100.93	100.931896238314	-0.0769014032168808	-0.00189623831407626	0.194367357401417
43	100.92	100.921899631758	-0.0708399077083481	-0.00189963175764587	0.439581847152546
44	101.02	101.021907512070	-0.0553595680164641	-0.00190751206959326	1.12251338795001
45	101.01	101.011909414759	-0.0512490306604136	-0.00190941475868671	0.298036319387071
46	100.97	100.971909843856	-0.0502295554935866	-0.00190984385588771	0.0739118026397467
47	100.89	100.891908811178	-0.0529277497666185	-0.00190881117785979	-0.195606237866223
48	100.62	100.621901963855	-0.0726027157772648	-0.00190196385523712	-1.42626624398634
49	100.53	100.512961758190	-0.0758756655620918	0.0170382418103744	-0.249921541121885
50	100.48	100.481172369972	-0.071893471025049	-0.00117236997202315	0.275517192751225
51	100.48	100.481178342147	-0.0653758733014334	-0.00117834214649636	0.472369066887793
52	100.47	100.471182513954	-0.0603556698666559	-0.00118251395444556	0.36384159413811
53	100.52	100.521190074026	-0.0503511181441277	-0.00119007402650279	0.725080618390734
54	100.49	100.491191341815	-0.0485061319441162	-0.00119134181538184	0.133714907349267
55	100.47	100.471192956636	-0.0459218215221221	-0.00119295663560042	0.187296545105111
56	100.44	100.441193776809	-0.0444783759456416	-0.00119377680910751	0.104612640271396

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