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*The author of this computation has been verified*

R Software Module: /rwasp_structuraltimeseries.wasp (opens new window with default values)

Title produced by software: Structural Time Series Models

Date of computation: Wed, 09 Dec 2009 09:15:18 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii.htm/, Retrieved Wed, 09 Dec 2009 17:16:13 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

153.4 145 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179 190.6 190 181.6 174.8 180.5 196.8 193.8 197 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244 234.7 250.2 265.7 287.6 283.3 295.4 312.3 333.8 347.7 383.2 407.1 413.6 362.7 321.9 239.4 191 159.7 163.4 157.6 166.2 176.7 198.3 226.2 216.2 235.9 226.9

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	153.4	153.4	0	0	0
2	145	145.876191167459	-7.44134377868622	-0.041232530240796	-0.557950534988849
3	137.7	137.791193719566	-7.99195450904879	-0.0398729065246219	-0.0397493044432643
4	148.3	147.003485215649	6.86854273510676	-0.0565574451302474	1.05522810977596
5	152.2	152.373635982363	5.57296841526736	-0.0563948021853457	-0.0916881440644917
6	169.4	168.620760968549	14.8031708653358	-0.0559567353371608	0.653207893605105
7	168.6	169.727833670048	2.96004521014379	-0.0562167320232124	-0.838115427451734
8	161.1	161.993016572943	-6.28773277779368	-0.0562398245501543	-0.654446774325278
9	174.1	172.817389150323	8.50894960012367	-0.0562533969236409	1.04713164279455
10	179	179.220977744091	6.68846225306813	-0.0562526151651217	-0.128832251264188
11	190.6	190.311807905370	10.4951527359973	-0.0562528041658198	0.269391877582786
12	190	190.836360951728	1.87365858787821	-0.0562529569762432	-0.610125910298412
13	181.6	182.938653778518	-6.48111459570032	-0.582679721214916	-0.627341256815093
14	174.8	174.860704709527	-7.70792945736486	0.0323240020032319	-0.0840417131388031
15	180.5	179.560241812516	3.07890274373382	-0.00963164228381908	0.749056934503394
16	196.8	195.810782941204	14.4475557326564	-0.0337871215571341	0.80214830106102
17	193.8	195.021653927182	1.27646422051838	-0.0299470804210284	-0.93208399799127
18	197	196.976799209048	1.86335423195363	-0.0299028693092647	0.0415327406762524
19	216.3	215.060206884967	15.8892024854284	-0.0293202242738261	0.992580120109795
20	221.4	222.120174399738	8.25459899185731	-0.0293643167277498	-0.540285629075005
21	217.9	218.832431119834	-1.72595515304180	-0.0293498305701368	-0.706303868245136
22	229.7	228.813399308401	8.39691627123799	-0.0293580489453955	0.716375379228054
23	227.4	228.139096759735	0.5531101339685	-0.0293571517537865	-0.555090484024443
24	204.2	206.004465437042	-19.0647902955236	-0.0293577002260322	-1.38831960586255
25	196.6	195.003051588083	-12.1433736585019	0.970670268322744	0.509471571765212
26	198.8	197.797267133778	-0.289875233886651	0.0543044444348364	0.821434943482309
27	207.5	206.756990032806	7.74032777615458	0.0311256602890603	0.560382308394789
28	190.7	192.361294330894	-11.3746431385245	0.0612299935782609	-1.34975235316270
29	201.6	200.051105827534	5.10657504734081	0.0576686636780732	1.16633561543262
30	210.5	210.058624294885	9.34459482759583	0.0579052840527004	0.299914624446646
31	223.5	223.148920841059	12.5835579727666	0.0580050070096113	0.22921475523822
32	223.8	224.612106493327	2.96782973491725	0.0579638471243436	-0.680485867963241
33	231.2	230.883561117611	5.82444384379485	0.057960774111596	0.202156870978219
34	244	243.417116540052	11.6257533971697	0.0579572833314285	0.410547082700231
35	234.7	236.122394870615	-4.73462167408807	0.0579586702973887	-1.15779104661693
36	250.2	248.781167415319	10.3053008511142	0.0579589819436783	1.06434525893544
37	265.7	265.461227272232	15.7876099604038	-0.257289047453376	0.399569953009538
38	287.6	287.139981494835	20.5494542354446	0.067938579354525	0.331845793567933
39	283.3	284.943382235415	0.818325995602724	0.113214930425090	-1.38090746670211
40	295.4	294.607251802669	8.45878086852166	0.103655639860337	0.539754905519306
41	312.3	311.535112148441	15.7806327081183	0.102398824786656	0.518150260593486
42	333.8	333.234286690528	20.8985525614038	0.102625818350377	0.362183457773561
43	347.7	348.071737438764	15.6574577350208	0.102497631958868	-0.370901557770521
44	383.2	381.692019214542	31.1898066896142	0.102550447270045	1.09919329085371
45	407.1	407.424435919135	26.470850776141	0.102554479910365	-0.333951078366074
46	413.6	414.977574563639	10.1128703532823	0.102562299012752	-1.15762158183954
47	362.7	367.132139880492	-40.0031875070762	0.102565674062501	-3.54661325487644
48	321.9	322.184307513508	-44.2787805510905	0.102565603683433	-0.302575174699811
49	239.4	244.69135337561	-72.874940188163	-2.70385583171962	-2.07189404251916
50	191	189.435820702217	-58.4622989634655	0.356139455252289	1.00769419349876
51	159.7	157.346170983006	-35.5976922663954	0.312599188287056	1.60325199710515
52	163.4	160.129604881931	-2.43941747722193	0.278187741466031	2.34314407498757
53	157.6	157.348499499636	-2.73482896804113	0.278229801234249	-0.0209055951065479
54	166.2	165.100884909403	6.33368066687241	0.278563417531538	0.641758095721906
55	176.7	176.059491443347	10.3328854862313	0.278644548138784	0.28301557516907
56	198.3	197.177490856222	19.6587057997122	0.278670850872636	0.659969664214074
57	226.2	225.262086142016	26.9444973835265	0.278665686572093	0.515600908638063
58	216.2	218.554304103791	-2.15433671116012	0.278677223600816	-2.05926633270578
59	235.9	234.226556592164	13.2601648704251	0.278676362559669	1.09085347013727
60	226.9	228.135388232967	-3.47277104151221	0.278676134099501	-1.18415643272776

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/13lun1260375315.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/13lun1260375315.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/2d7qr1260375315.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/2d7qr1260375315.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/3tlt91260375315.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/3tlt91260375315.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/4bfs61260375315.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/4bfs61260375315.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/5zg5l1260375315.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375367leizxlmqs2ai6ii/5zg5l1260375315.ps (open in new window)

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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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