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*The author of this computation has been verified*

R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Wed, 02 Dec 2009 13:13:08 -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/02/t1259784990hq7vp4bwgetjtn4.htm/, Retrieved Sun, 28 Apr 2024 14:05:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62569, Retrieved Sun, 28 Apr 2024 14:05:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

ws 8 Ad hoc forecasting link 3

Estimated Impact

150

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]
-   PD      [Structural Time Series Models] [ws 8 Ad hoc forec...] [2009-12-02 20:13:08] [88e98f4c87ea17c4967db8279bda8533] [Current]
-   PD        [Structural Time Series Models] [Workshop 9] [2009-12-04 12:11:14] [4fe1472705bb0a32f118ba3ca90ffa8e] 
-    D          [Structural Time Series Models] [WS9] [2009-12-11 12:50:35] [4fe1472705bb0a32f118ba3ca90ffa8e] 
-   PD        [Structural Time Series Models] [ws9: decomposition 3] [2009-12-04 17:22:48] [bd8e774728cf1f2f4e6868fd314defe3] 

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Dataseries X:

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Histogram

Boxplots

8.2
8.0
7.5
6.8
6.5
6.6
7.6
8.0
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7.0
7.1
7.2
7.1
6.9
7.0
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9
7.7
7.4
7.5
8.0
8.1

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=62569&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=62569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62569&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' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	8.2	8.2	0	0	0
2	8	8.00127622385071	-0.198829249170883	-0.00127622385071316	-0.598073118941194
3	7.5	7.50424229625797	-0.491527403456245	-0.00424229625796986	-0.885821392637681
4	6.8	6.80220081746625	-0.697066633095816	-0.00220081746624831	-0.616165908322563
5	6.5	6.4930882979517	-0.318123204097619	0.0069117020482963	1.13637371559309
6	6.6	6.59498743817802	0.0921636486981209	0.00501256182198041	1.23035153817779
7	7.6	7.58747819215078	0.971613735735346	0.0125218078492171	2.63725884597568
8	8	8.01242865401694	0.437626846235962	-0.0124286540169404	-1.60129798047321
9	8.1	8.10340957322805	0.0990190273909277	-0.00340957322805405	-1.01540323736988
10	7.7	7.7065893312022	-0.385322600241157	-0.00658933120220374	-1.45242380512738
11	7.5	7.49533324515493	-0.215292384816175	0.00466675484507046	0.509879635333864
12	7.6	7.5957828454469	0.0931280948839882	0.00421715455310197	0.924878683038533
13	7.8	7.79928214402348	0.200924128988881	0.000717855976524546	0.323324515103376
14	7.8	7.80444061393912	0.00964705742520267	-0.0044406139391238	-0.574999884941081
15	7.8	7.79444672469474	-0.00925141985035046	0.00555327530525888	-0.0570613182610372
16	7.5	7.51435346712922	-0.269238884920420	-0.0143534671292197	-0.77916967657956
17	7.5	7.48010809146576	-0.0436389865141169	0.0198919085342391	0.676552831522696
18	7.1	7.13215460746487	-0.335818745667748	-0.0321546074648676	-0.876175770310857
19	7.5	7.45861478957107	0.300044902656793	0.0413852104289313	1.90680213012571
20	7.5	7.52253000560251	0.0733345084034039	-0.0225300056025130	-0.67984982701803
21	7.6	7.58931255003648	0.0670438990805684	0.0106874499635243	-0.0188640212074657
22	7.7	7.70467232543183	0.113432482805563	-0.00467232543183108	0.139108182310275
23	7.7	7.70394827098096	0.00382924482361731	-0.00394827098095685	-0.328673714573005
24	7.9	7.89502798938089	0.183609644851946	0.00497201061911532	0.539118450313555
25	8.1	8.09550708102145	0.199803675938381	0.00449291897854567	0.0485739614297106
26	8.2	8.21278592288984	0.120544419390146	-0.0127859228898438	-0.238031560638894
27	8.2	8.18338269996662	-0.0219584806524405	0.0166173000333839	-0.429224444701056
28	8.2	8.22861227231093	0.0418715276638166	-0.0286122723109273	0.191300548247779
29	7.9	7.86607042662083	-0.342220157664370	0.0339295733791663	-1.15186763919896
30	7.3	7.36709203350069	-0.49112352211264	-0.0670920335006883	-0.446524587838063
31	6.9	6.84864872298369	-0.517074370481081	0.0513512770163114	-0.0778203766124455
32	6.6	6.6114610289264	-0.251214990431378	-0.0114610289263976	0.797248188001727
33	6.7	6.68509100878294	0.0573492672457816	0.0149089912170651	0.925309847789275
34	6.9	6.89303681878207	0.200398378425854	0.0069631812179319	0.428969809946214
35	7	7.01469536849558	0.125604268032079	-0.0146953684955780	-0.224289628416851
36	7.1	7.09862466899692	0.0860185355373725	0.00137533100307608	-0.118708251487739
37	7.2	7.1939345874963	0.0948428468455854	0.00606541250370479	0.0264700572836137
38	7.1	7.10911781559053	-0.0758552673534938	-0.0091178155905304	-0.512242098679318
39	6.9	6.90130145026726	-0.200379065112696	-0.00130145026726123	-0.374438460525143
40	7	7.00139617516327	0.0833206926798958	-0.00139617516327404	0.85041307684321
41	6.8	6.77256789963946	-0.211245394818097	0.0274321003605378	-0.88335907896211
42	6.4	6.46170274177889	-0.305269897498116	-0.0617027417788883	-0.281957637067885
43	6.7	6.63508630895394	0.146505530258980	0.0649136910460583	1.35476580623548
44	6.6	6.63099025249448	0.00436244281857145	-0.0309902524944815	-0.426252887802726
45	6.4	6.40375519643981	-0.214226655247958	-0.00375519643980783	-0.655496042739364
46	6.3	6.28485310606508	-0.124255940044097	0.0151468939349188	0.269800492435974
47	6.2	6.21010238213756	-0.077530824101797	-0.0101023821375598	0.140117581690292
48	6.5	6.49191442191504	0.26161845268534	0.00808557808496397	1.01702941557067
49	6.8	6.78757128238072	0.293740538137197	0.0124287176192758	0.0963598020491305
50	6.8	6.8048908537256	0.0328243948144305	-0.00489085372559283	-0.782622561453217
51	6.4	6.44274390155025	-0.338339181198148	-0.0427439015502456	-1.11493471421101
52	6.1	6.08404278979504	-0.357490041728859	0.0159572102049574	-0.0574170355480497
53	5.8	5.75080416684335	-0.334695040411939	0.0491958331566479	0.0683555586832608
54	6.1	6.16511387239222	0.369442766061553	-0.0651138723922228	2.11156204883655
55	7.2	7.11400569602106	0.914196608647263	0.085994303978942	1.63358397877916
56	7.3	7.34637447608622	0.273200751966980	-0.0463744760862209	-1.92219252827409
57	6.9	6.9333497561851	-0.371925562088877	-0.0333497561851056	-1.93457840208780
58	6.1	6.09046053945314	-0.814684917103662	0.0095394605468556	-1.32772870375830
59	5.8	5.80466258506902	-0.317468537609233	-0.00466258506901974	1.49103566216011
60	6.2	6.17598923858834	0.330042526748548	0.0240107614116598	1.94174225265400
61	7.1	7.0652782640628	0.85574128072645	0.0347217359372012	1.57700003230341
62	7.7	7.69685792091581	0.645020681608193	0.00314207908419144	-0.631918632022108
63	7.9	7.95582038480998	0.283185326341197	-0.055820384809978	-1.08625998222228
64	7.7	7.67962744384338	-0.241547994978146	0.0203725561566161	-1.57344633658481
65	7.4	7.37856118066919	-0.297347152107841	0.0214388193308141	-0.167318389716091
66	7.5	7.5989708923728	0.188119406854844	-0.0989708923728049	1.45582258909089
67	8	7.89333388825534	0.287741156002331	0.106666111744657	0.298741052108636
68	8.1	8.12413026988492	0.234345957665361	-0.0241302698849243	-0.160119375331914

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 8.2 & 8.2 & 0 & 0 & 0 \tabularnewline
2 & 8 & 8.00127622385071 & -0.198829249170883 & -0.00127622385071316 & -0.598073118941194 \tabularnewline
3 & 7.5 & 7.50424229625797 & -0.491527403456245 & -0.00424229625796986 & -0.885821392637681 \tabularnewline
4 & 6.8 & 6.80220081746625 & -0.697066633095816 & -0.00220081746624831 & -0.616165908322563 \tabularnewline
5 & 6.5 & 6.4930882979517 & -0.318123204097619 & 0.0069117020482963 & 1.13637371559309 \tabularnewline
6 & 6.6 & 6.59498743817802 & 0.0921636486981209 & 0.00501256182198041 & 1.23035153817779 \tabularnewline
7 & 7.6 & 7.58747819215078 & 0.971613735735346 & 0.0125218078492171 & 2.63725884597568 \tabularnewline
8 & 8 & 8.01242865401694 & 0.437626846235962 & -0.0124286540169404 & -1.60129798047321 \tabularnewline
9 & 8.1 & 8.10340957322805 & 0.0990190273909277 & -0.00340957322805405 & -1.01540323736988 \tabularnewline
10 & 7.7 & 7.7065893312022 & -0.385322600241157 & -0.00658933120220374 & -1.45242380512738 \tabularnewline
11 & 7.5 & 7.49533324515493 & -0.215292384816175 & 0.00466675484507046 & 0.509879635333864 \tabularnewline
12 & 7.6 & 7.5957828454469 & 0.0931280948839882 & 0.00421715455310197 & 0.924878683038533 \tabularnewline
13 & 7.8 & 7.79928214402348 & 0.200924128988881 & 0.000717855976524546 & 0.323324515103376 \tabularnewline
14 & 7.8 & 7.80444061393912 & 0.00964705742520267 & -0.0044406139391238 & -0.574999884941081 \tabularnewline
15 & 7.8 & 7.79444672469474 & -0.00925141985035046 & 0.00555327530525888 & -0.0570613182610372 \tabularnewline
16 & 7.5 & 7.51435346712922 & -0.269238884920420 & -0.0143534671292197 & -0.77916967657956 \tabularnewline
17 & 7.5 & 7.48010809146576 & -0.0436389865141169 & 0.0198919085342391 & 0.676552831522696 \tabularnewline
18 & 7.1 & 7.13215460746487 & -0.335818745667748 & -0.0321546074648676 & -0.876175770310857 \tabularnewline
19 & 7.5 & 7.45861478957107 & 0.300044902656793 & 0.0413852104289313 & 1.90680213012571 \tabularnewline
20 & 7.5 & 7.52253000560251 & 0.0733345084034039 & -0.0225300056025130 & -0.67984982701803 \tabularnewline
21 & 7.6 & 7.58931255003648 & 0.0670438990805684 & 0.0106874499635243 & -0.0188640212074657 \tabularnewline
22 & 7.7 & 7.70467232543183 & 0.113432482805563 & -0.00467232543183108 & 0.139108182310275 \tabularnewline
23 & 7.7 & 7.70394827098096 & 0.00382924482361731 & -0.00394827098095685 & -0.328673714573005 \tabularnewline
24 & 7.9 & 7.89502798938089 & 0.183609644851946 & 0.00497201061911532 & 0.539118450313555 \tabularnewline
25 & 8.1 & 8.09550708102145 & 0.199803675938381 & 0.00449291897854567 & 0.0485739614297106 \tabularnewline
26 & 8.2 & 8.21278592288984 & 0.120544419390146 & -0.0127859228898438 & -0.238031560638894 \tabularnewline
27 & 8.2 & 8.18338269996662 & -0.0219584806524405 & 0.0166173000333839 & -0.429224444701056 \tabularnewline
28 & 8.2 & 8.22861227231093 & 0.0418715276638166 & -0.0286122723109273 & 0.191300548247779 \tabularnewline
29 & 7.9 & 7.86607042662083 & -0.342220157664370 & 0.0339295733791663 & -1.15186763919896 \tabularnewline
30 & 7.3 & 7.36709203350069 & -0.49112352211264 & -0.0670920335006883 & -0.446524587838063 \tabularnewline
31 & 6.9 & 6.84864872298369 & -0.517074370481081 & 0.0513512770163114 & -0.0778203766124455 \tabularnewline
32 & 6.6 & 6.6114610289264 & -0.251214990431378 & -0.0114610289263976 & 0.797248188001727 \tabularnewline
33 & 6.7 & 6.68509100878294 & 0.0573492672457816 & 0.0149089912170651 & 0.925309847789275 \tabularnewline
34 & 6.9 & 6.89303681878207 & 0.200398378425854 & 0.0069631812179319 & 0.428969809946214 \tabularnewline
35 & 7 & 7.01469536849558 & 0.125604268032079 & -0.0146953684955780 & -0.224289628416851 \tabularnewline
36 & 7.1 & 7.09862466899692 & 0.0860185355373725 & 0.00137533100307608 & -0.118708251487739 \tabularnewline
37 & 7.2 & 7.1939345874963 & 0.0948428468455854 & 0.00606541250370479 & 0.0264700572836137 \tabularnewline
38 & 7.1 & 7.10911781559053 & -0.0758552673534938 & -0.0091178155905304 & -0.512242098679318 \tabularnewline
39 & 6.9 & 6.90130145026726 & -0.200379065112696 & -0.00130145026726123 & -0.374438460525143 \tabularnewline
40 & 7 & 7.00139617516327 & 0.0833206926798958 & -0.00139617516327404 & 0.85041307684321 \tabularnewline
41 & 6.8 & 6.77256789963946 & -0.211245394818097 & 0.0274321003605378 & -0.88335907896211 \tabularnewline
42 & 6.4 & 6.46170274177889 & -0.305269897498116 & -0.0617027417788883 & -0.281957637067885 \tabularnewline
43 & 6.7 & 6.63508630895394 & 0.146505530258980 & 0.0649136910460583 & 1.35476580623548 \tabularnewline
44 & 6.6 & 6.63099025249448 & 0.00436244281857145 & -0.0309902524944815 & -0.426252887802726 \tabularnewline
45 & 6.4 & 6.40375519643981 & -0.214226655247958 & -0.00375519643980783 & -0.655496042739364 \tabularnewline
46 & 6.3 & 6.28485310606508 & -0.124255940044097 & 0.0151468939349188 & 0.269800492435974 \tabularnewline
47 & 6.2 & 6.21010238213756 & -0.077530824101797 & -0.0101023821375598 & 0.140117581690292 \tabularnewline
48 & 6.5 & 6.49191442191504 & 0.26161845268534 & 0.00808557808496397 & 1.01702941557067 \tabularnewline
49 & 6.8 & 6.78757128238072 & 0.293740538137197 & 0.0124287176192758 & 0.0963598020491305 \tabularnewline
50 & 6.8 & 6.8048908537256 & 0.0328243948144305 & -0.00489085372559283 & -0.782622561453217 \tabularnewline
51 & 6.4 & 6.44274390155025 & -0.338339181198148 & -0.0427439015502456 & -1.11493471421101 \tabularnewline
52 & 6.1 & 6.08404278979504 & -0.357490041728859 & 0.0159572102049574 & -0.0574170355480497 \tabularnewline
53 & 5.8 & 5.75080416684335 & -0.334695040411939 & 0.0491958331566479 & 0.0683555586832608 \tabularnewline
54 & 6.1 & 6.16511387239222 & 0.369442766061553 & -0.0651138723922228 & 2.11156204883655 \tabularnewline
55 & 7.2 & 7.11400569602106 & 0.914196608647263 & 0.085994303978942 & 1.63358397877916 \tabularnewline
56 & 7.3 & 7.34637447608622 & 0.273200751966980 & -0.0463744760862209 & -1.92219252827409 \tabularnewline
57 & 6.9 & 6.9333497561851 & -0.371925562088877 & -0.0333497561851056 & -1.93457840208780 \tabularnewline
58 & 6.1 & 6.09046053945314 & -0.814684917103662 & 0.0095394605468556 & -1.32772870375830 \tabularnewline
59 & 5.8 & 5.80466258506902 & -0.317468537609233 & -0.00466258506901974 & 1.49103566216011 \tabularnewline
60 & 6.2 & 6.17598923858834 & 0.330042526748548 & 0.0240107614116598 & 1.94174225265400 \tabularnewline
61 & 7.1 & 7.0652782640628 & 0.85574128072645 & 0.0347217359372012 & 1.57700003230341 \tabularnewline
62 & 7.7 & 7.69685792091581 & 0.645020681608193 & 0.00314207908419144 & -0.631918632022108 \tabularnewline
63 & 7.9 & 7.95582038480998 & 0.283185326341197 & -0.055820384809978 & -1.08625998222228 \tabularnewline
64 & 7.7 & 7.67962744384338 & -0.241547994978146 & 0.0203725561566161 & -1.57344633658481 \tabularnewline
65 & 7.4 & 7.37856118066919 & -0.297347152107841 & 0.0214388193308141 & -0.167318389716091 \tabularnewline
66 & 7.5 & 7.5989708923728 & 0.188119406854844 & -0.0989708923728049 & 1.45582258909089 \tabularnewline
67 & 8 & 7.89333388825534 & 0.287741156002331 & 0.106666111744657 & 0.298741052108636 \tabularnewline
68 & 8.1 & 8.12413026988492 & 0.234345957665361 & -0.0241302698849243 & -0.160119375331914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62569&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]8.2[/C][C]8.2[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]8[/C][C]8.00127622385071[/C][C]-0.198829249170883[/C][C]-0.00127622385071316[/C][C]-0.598073118941194[/C][/ROW]
[ROW][C]3[/C][C]7.5[/C][C]7.50424229625797[/C][C]-0.491527403456245[/C][C]-0.00424229625796986[/C][C]-0.885821392637681[/C][/ROW]
[ROW][C]4[/C][C]6.8[/C][C]6.80220081746625[/C][C]-0.697066633095816[/C][C]-0.00220081746624831[/C][C]-0.616165908322563[/C][/ROW]
[ROW][C]5[/C][C]6.5[/C][C]6.4930882979517[/C][C]-0.318123204097619[/C][C]0.0069117020482963[/C][C]1.13637371559309[/C][/ROW]
[ROW][C]6[/C][C]6.6[/C][C]6.59498743817802[/C][C]0.0921636486981209[/C][C]0.00501256182198041[/C][C]1.23035153817779[/C][/ROW]
[ROW][C]7[/C][C]7.6[/C][C]7.58747819215078[/C][C]0.971613735735346[/C][C]0.0125218078492171[/C][C]2.63725884597568[/C][/ROW]
[ROW][C]8[/C][C]8[/C][C]8.01242865401694[/C][C]0.437626846235962[/C][C]-0.0124286540169404[/C][C]-1.60129798047321[/C][/ROW]
[ROW][C]9[/C][C]8.1[/C][C]8.10340957322805[/C][C]0.0990190273909277[/C][C]-0.00340957322805405[/C][C]-1.01540323736988[/C][/ROW]
[ROW][C]10[/C][C]7.7[/C][C]7.7065893312022[/C][C]-0.385322600241157[/C][C]-0.00658933120220374[/C][C]-1.45242380512738[/C][/ROW]
[ROW][C]11[/C][C]7.5[/C][C]7.49533324515493[/C][C]-0.215292384816175[/C][C]0.00466675484507046[/C][C]0.509879635333864[/C][/ROW]
[ROW][C]12[/C][C]7.6[/C][C]7.5957828454469[/C][C]0.0931280948839882[/C][C]0.00421715455310197[/C][C]0.924878683038533[/C][/ROW]
[ROW][C]13[/C][C]7.8[/C][C]7.79928214402348[/C][C]0.200924128988881[/C][C]0.000717855976524546[/C][C]0.323324515103376[/C][/ROW]
[ROW][C]14[/C][C]7.8[/C][C]7.80444061393912[/C][C]0.00964705742520267[/C][C]-0.0044406139391238[/C][C]-0.574999884941081[/C][/ROW]
[ROW][C]15[/C][C]7.8[/C][C]7.79444672469474[/C][C]-0.00925141985035046[/C][C]0.00555327530525888[/C][C]-0.0570613182610372[/C][/ROW]
[ROW][C]16[/C][C]7.5[/C][C]7.51435346712922[/C][C]-0.269238884920420[/C][C]-0.0143534671292197[/C][C]-0.77916967657956[/C][/ROW]
[ROW][C]17[/C][C]7.5[/C][C]7.48010809146576[/C][C]-0.0436389865141169[/C][C]0.0198919085342391[/C][C]0.676552831522696[/C][/ROW]
[ROW][C]18[/C][C]7.1[/C][C]7.13215460746487[/C][C]-0.335818745667748[/C][C]-0.0321546074648676[/C][C]-0.876175770310857[/C][/ROW]
[ROW][C]19[/C][C]7.5[/C][C]7.45861478957107[/C][C]0.300044902656793[/C][C]0.0413852104289313[/C][C]1.90680213012571[/C][/ROW]
[ROW][C]20[/C][C]7.5[/C][C]7.52253000560251[/C][C]0.0733345084034039[/C][C]-0.0225300056025130[/C][C]-0.67984982701803[/C][/ROW]
[ROW][C]21[/C][C]7.6[/C][C]7.58931255003648[/C][C]0.0670438990805684[/C][C]0.0106874499635243[/C][C]-0.0188640212074657[/C][/ROW]
[ROW][C]22[/C][C]7.7[/C][C]7.70467232543183[/C][C]0.113432482805563[/C][C]-0.00467232543183108[/C][C]0.139108182310275[/C][/ROW]
[ROW][C]23[/C][C]7.7[/C][C]7.70394827098096[/C][C]0.00382924482361731[/C][C]-0.00394827098095685[/C][C]-0.328673714573005[/C][/ROW]
[ROW][C]24[/C][C]7.9[/C][C]7.89502798938089[/C][C]0.183609644851946[/C][C]0.00497201061911532[/C][C]0.539118450313555[/C][/ROW]
[ROW][C]25[/C][C]8.1[/C][C]8.09550708102145[/C][C]0.199803675938381[/C][C]0.00449291897854567[/C][C]0.0485739614297106[/C][/ROW]
[ROW][C]26[/C][C]8.2[/C][C]8.21278592288984[/C][C]0.120544419390146[/C][C]-0.0127859228898438[/C][C]-0.238031560638894[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]8.18338269996662[/C][C]-0.0219584806524405[/C][C]0.0166173000333839[/C][C]-0.429224444701056[/C][/ROW]
[ROW][C]28[/C][C]8.2[/C][C]8.22861227231093[/C][C]0.0418715276638166[/C][C]-0.0286122723109273[/C][C]0.191300548247779[/C][/ROW]
[ROW][C]29[/C][C]7.9[/C][C]7.86607042662083[/C][C]-0.342220157664370[/C][C]0.0339295733791663[/C][C]-1.15186763919896[/C][/ROW]
[ROW][C]30[/C][C]7.3[/C][C]7.36709203350069[/C][C]-0.49112352211264[/C][C]-0.0670920335006883[/C][C]-0.446524587838063[/C][/ROW]
[ROW][C]31[/C][C]6.9[/C][C]6.84864872298369[/C][C]-0.517074370481081[/C][C]0.0513512770163114[/C][C]-0.0778203766124455[/C][/ROW]
[ROW][C]32[/C][C]6.6[/C][C]6.6114610289264[/C][C]-0.251214990431378[/C][C]-0.0114610289263976[/C][C]0.797248188001727[/C][/ROW]
[ROW][C]33[/C][C]6.7[/C][C]6.68509100878294[/C][C]0.0573492672457816[/C][C]0.0149089912170651[/C][C]0.925309847789275[/C][/ROW]
[ROW][C]34[/C][C]6.9[/C][C]6.89303681878207[/C][C]0.200398378425854[/C][C]0.0069631812179319[/C][C]0.428969809946214[/C][/ROW]
[ROW][C]35[/C][C]7[/C][C]7.01469536849558[/C][C]0.125604268032079[/C][C]-0.0146953684955780[/C][C]-0.224289628416851[/C][/ROW]
[ROW][C]36[/C][C]7.1[/C][C]7.09862466899692[/C][C]0.0860185355373725[/C][C]0.00137533100307608[/C][C]-0.118708251487739[/C][/ROW]
[ROW][C]37[/C][C]7.2[/C][C]7.1939345874963[/C][C]0.0948428468455854[/C][C]0.00606541250370479[/C][C]0.0264700572836137[/C][/ROW]
[ROW][C]38[/C][C]7.1[/C][C]7.10911781559053[/C][C]-0.0758552673534938[/C][C]-0.0091178155905304[/C][C]-0.512242098679318[/C][/ROW]
[ROW][C]39[/C][C]6.9[/C][C]6.90130145026726[/C][C]-0.200379065112696[/C][C]-0.00130145026726123[/C][C]-0.374438460525143[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]7.00139617516327[/C][C]0.0833206926798958[/C][C]-0.00139617516327404[/C][C]0.85041307684321[/C][/ROW]
[ROW][C]41[/C][C]6.8[/C][C]6.77256789963946[/C][C]-0.211245394818097[/C][C]0.0274321003605378[/C][C]-0.88335907896211[/C][/ROW]
[ROW][C]42[/C][C]6.4[/C][C]6.46170274177889[/C][C]-0.305269897498116[/C][C]-0.0617027417788883[/C][C]-0.281957637067885[/C][/ROW]
[ROW][C]43[/C][C]6.7[/C][C]6.63508630895394[/C][C]0.146505530258980[/C][C]0.0649136910460583[/C][C]1.35476580623548[/C][/ROW]
[ROW][C]44[/C][C]6.6[/C][C]6.63099025249448[/C][C]0.00436244281857145[/C][C]-0.0309902524944815[/C][C]-0.426252887802726[/C][/ROW]
[ROW][C]45[/C][C]6.4[/C][C]6.40375519643981[/C][C]-0.214226655247958[/C][C]-0.00375519643980783[/C][C]-0.655496042739364[/C][/ROW]
[ROW][C]46[/C][C]6.3[/C][C]6.28485310606508[/C][C]-0.124255940044097[/C][C]0.0151468939349188[/C][C]0.269800492435974[/C][/ROW]
[ROW][C]47[/C][C]6.2[/C][C]6.21010238213756[/C][C]-0.077530824101797[/C][C]-0.0101023821375598[/C][C]0.140117581690292[/C][/ROW]
[ROW][C]48[/C][C]6.5[/C][C]6.49191442191504[/C][C]0.26161845268534[/C][C]0.00808557808496397[/C][C]1.01702941557067[/C][/ROW]
[ROW][C]49[/C][C]6.8[/C][C]6.78757128238072[/C][C]0.293740538137197[/C][C]0.0124287176192758[/C][C]0.0963598020491305[/C][/ROW]
[ROW][C]50[/C][C]6.8[/C][C]6.8048908537256[/C][C]0.0328243948144305[/C][C]-0.00489085372559283[/C][C]-0.782622561453217[/C][/ROW]
[ROW][C]51[/C][C]6.4[/C][C]6.44274390155025[/C][C]-0.338339181198148[/C][C]-0.0427439015502456[/C][C]-1.11493471421101[/C][/ROW]
[ROW][C]52[/C][C]6.1[/C][C]6.08404278979504[/C][C]-0.357490041728859[/C][C]0.0159572102049574[/C][C]-0.0574170355480497[/C][/ROW]
[ROW][C]53[/C][C]5.8[/C][C]5.75080416684335[/C][C]-0.334695040411939[/C][C]0.0491958331566479[/C][C]0.0683555586832608[/C][/ROW]
[ROW][C]54[/C][C]6.1[/C][C]6.16511387239222[/C][C]0.369442766061553[/C][C]-0.0651138723922228[/C][C]2.11156204883655[/C][/ROW]
[ROW][C]55[/C][C]7.2[/C][C]7.11400569602106[/C][C]0.914196608647263[/C][C]0.085994303978942[/C][C]1.63358397877916[/C][/ROW]
[ROW][C]56[/C][C]7.3[/C][C]7.34637447608622[/C][C]0.273200751966980[/C][C]-0.0463744760862209[/C][C]-1.92219252827409[/C][/ROW]
[ROW][C]57[/C][C]6.9[/C][C]6.9333497561851[/C][C]-0.371925562088877[/C][C]-0.0333497561851056[/C][C]-1.93457840208780[/C][/ROW]
[ROW][C]58[/C][C]6.1[/C][C]6.09046053945314[/C][C]-0.814684917103662[/C][C]0.0095394605468556[/C][C]-1.32772870375830[/C][/ROW]
[ROW][C]59[/C][C]5.8[/C][C]5.80466258506902[/C][C]-0.317468537609233[/C][C]-0.00466258506901974[/C][C]1.49103566216011[/C][/ROW]
[ROW][C]60[/C][C]6.2[/C][C]6.17598923858834[/C][C]0.330042526748548[/C][C]0.0240107614116598[/C][C]1.94174225265400[/C][/ROW]
[ROW][C]61[/C][C]7.1[/C][C]7.0652782640628[/C][C]0.85574128072645[/C][C]0.0347217359372012[/C][C]1.57700003230341[/C][/ROW]
[ROW][C]62[/C][C]7.7[/C][C]7.69685792091581[/C][C]0.645020681608193[/C][C]0.00314207908419144[/C][C]-0.631918632022108[/C][/ROW]
[ROW][C]63[/C][C]7.9[/C][C]7.95582038480998[/C][C]0.283185326341197[/C][C]-0.055820384809978[/C][C]-1.08625998222228[/C][/ROW]
[ROW][C]64[/C][C]7.7[/C][C]7.67962744384338[/C][C]-0.241547994978146[/C][C]0.0203725561566161[/C][C]-1.57344633658481[/C][/ROW]
[ROW][C]65[/C][C]7.4[/C][C]7.37856118066919[/C][C]-0.297347152107841[/C][C]0.0214388193308141[/C][C]-0.167318389716091[/C][/ROW]
[ROW][C]66[/C][C]7.5[/C][C]7.5989708923728[/C][C]0.188119406854844[/C][C]-0.0989708923728049[/C][C]1.45582258909089[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]7.89333388825534[/C][C]0.287741156002331[/C][C]0.106666111744657[/C][C]0.298741052108636[/C][/ROW]
[ROW][C]68[/C][C]8.1[/C][C]8.12413026988492[/C][C]0.234345957665361[/C][C]-0.0241302698849243[/C][C]-0.160119375331914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62569&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	8.2	8.2	0	0	0
2	8	8.00127622385071	-0.198829249170883	-0.00127622385071316	-0.598073118941194
3	7.5	7.50424229625797	-0.491527403456245	-0.00424229625796986	-0.885821392637681
4	6.8	6.80220081746625	-0.697066633095816	-0.00220081746624831	-0.616165908322563
5	6.5	6.4930882979517	-0.318123204097619	0.0069117020482963	1.13637371559309
6	6.6	6.59498743817802	0.0921636486981209	0.00501256182198041	1.23035153817779
7	7.6	7.58747819215078	0.971613735735346	0.0125218078492171	2.63725884597568
8	8	8.01242865401694	0.437626846235962	-0.0124286540169404	-1.60129798047321
9	8.1	8.10340957322805	0.0990190273909277	-0.00340957322805405	-1.01540323736988
10	7.7	7.7065893312022	-0.385322600241157	-0.00658933120220374	-1.45242380512738
11	7.5	7.49533324515493	-0.215292384816175	0.00466675484507046	0.509879635333864
12	7.6	7.5957828454469	0.0931280948839882	0.00421715455310197	0.924878683038533
13	7.8	7.79928214402348	0.200924128988881	0.000717855976524546	0.323324515103376
14	7.8	7.80444061393912	0.00964705742520267	-0.0044406139391238	-0.574999884941081
15	7.8	7.79444672469474	-0.00925141985035046	0.00555327530525888	-0.0570613182610372
16	7.5	7.51435346712922	-0.269238884920420	-0.0143534671292197	-0.77916967657956
17	7.5	7.48010809146576	-0.0436389865141169	0.0198919085342391	0.676552831522696
18	7.1	7.13215460746487	-0.335818745667748	-0.0321546074648676	-0.876175770310857
19	7.5	7.45861478957107	0.300044902656793	0.0413852104289313	1.90680213012571
20	7.5	7.52253000560251	0.0733345084034039	-0.0225300056025130	-0.67984982701803
21	7.6	7.58931255003648	0.0670438990805684	0.0106874499635243	-0.0188640212074657
22	7.7	7.70467232543183	0.113432482805563	-0.00467232543183108	0.139108182310275
23	7.7	7.70394827098096	0.00382924482361731	-0.00394827098095685	-0.328673714573005
24	7.9	7.89502798938089	0.183609644851946	0.00497201061911532	0.539118450313555
25	8.1	8.09550708102145	0.199803675938381	0.00449291897854567	0.0485739614297106
26	8.2	8.21278592288984	0.120544419390146	-0.0127859228898438	-0.238031560638894
27	8.2	8.18338269996662	-0.0219584806524405	0.0166173000333839	-0.429224444701056
28	8.2	8.22861227231093	0.0418715276638166	-0.0286122723109273	0.191300548247779
29	7.9	7.86607042662083	-0.342220157664370	0.0339295733791663	-1.15186763919896
30	7.3	7.36709203350069	-0.49112352211264	-0.0670920335006883	-0.446524587838063
31	6.9	6.84864872298369	-0.517074370481081	0.0513512770163114	-0.0778203766124455
32	6.6	6.6114610289264	-0.251214990431378	-0.0114610289263976	0.797248188001727
33	6.7	6.68509100878294	0.0573492672457816	0.0149089912170651	0.925309847789275
34	6.9	6.89303681878207	0.200398378425854	0.0069631812179319	0.428969809946214
35	7	7.01469536849558	0.125604268032079	-0.0146953684955780	-0.224289628416851
36	7.1	7.09862466899692	0.0860185355373725	0.00137533100307608	-0.118708251487739
37	7.2	7.1939345874963	0.0948428468455854	0.00606541250370479	0.0264700572836137
38	7.1	7.10911781559053	-0.0758552673534938	-0.0091178155905304	-0.512242098679318
39	6.9	6.90130145026726	-0.200379065112696	-0.00130145026726123	-0.374438460525143
40	7	7.00139617516327	0.0833206926798958	-0.00139617516327404	0.85041307684321
41	6.8	6.77256789963946	-0.211245394818097	0.0274321003605378	-0.88335907896211
42	6.4	6.46170274177889	-0.305269897498116	-0.0617027417788883	-0.281957637067885
43	6.7	6.63508630895394	0.146505530258980	0.0649136910460583	1.35476580623548
44	6.6	6.63099025249448	0.00436244281857145	-0.0309902524944815	-0.426252887802726
45	6.4	6.40375519643981	-0.214226655247958	-0.00375519643980783	-0.655496042739364
46	6.3	6.28485310606508	-0.124255940044097	0.0151468939349188	0.269800492435974
47	6.2	6.21010238213756	-0.077530824101797	-0.0101023821375598	0.140117581690292
48	6.5	6.49191442191504	0.26161845268534	0.00808557808496397	1.01702941557067
49	6.8	6.78757128238072	0.293740538137197	0.0124287176192758	0.0963598020491305
50	6.8	6.8048908537256	0.0328243948144305	-0.00489085372559283	-0.782622561453217
51	6.4	6.44274390155025	-0.338339181198148	-0.0427439015502456	-1.11493471421101
52	6.1	6.08404278979504	-0.357490041728859	0.0159572102049574	-0.0574170355480497
53	5.8	5.75080416684335	-0.334695040411939	0.0491958331566479	0.0683555586832608
54	6.1	6.16511387239222	0.369442766061553	-0.0651138723922228	2.11156204883655
55	7.2	7.11400569602106	0.914196608647263	0.085994303978942	1.63358397877916
56	7.3	7.34637447608622	0.273200751966980	-0.0463744760862209	-1.92219252827409
57	6.9	6.9333497561851	-0.371925562088877	-0.0333497561851056	-1.93457840208780
58	6.1	6.09046053945314	-0.814684917103662	0.0095394605468556	-1.32772870375830
59	5.8	5.80466258506902	-0.317468537609233	-0.00466258506901974	1.49103566216011
60	6.2	6.17598923858834	0.330042526748548	0.0240107614116598	1.94174225265400
61	7.1	7.0652782640628	0.85574128072645	0.0347217359372012	1.57700003230341
62	7.7	7.69685792091581	0.645020681608193	0.00314207908419144	-0.631918632022108
63	7.9	7.95582038480998	0.283185326341197	-0.055820384809978	-1.08625998222228
64	7.7	7.67962744384338	-0.241547994978146	0.0203725561566161	-1.57344633658481
65	7.4	7.37856118066919	-0.297347152107841	0.0214388193308141	-0.167318389716091
66	7.5	7.5989708923728	0.188119406854844	-0.0989708923728049	1.45582258909089
67	8	7.89333388825534	0.287741156002331	0.106666111744657	0.298741052108636
68	8.1	8.12413026988492	0.234345957665361	-0.0241302698849243	-0.160119375331914

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 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;

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