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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: Tue, 07 Dec 2010 19:00:52 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes.htm/, Retrieved Tue, 07 Dec 2010 19:58:39 +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/2010/Dec/07/t1291748318k2kn01gb2lrhoes.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

103,48 103,93 103,89 104,4 104,79 104,77 105,13 105,26 104,96 104,75 105,01 105,15 105,2 105,77 105,78 106,26 106,13 106,12 106,57 106,44 106,54 107,1 108,1 108,4 108,84 109,62 110,42 110,67 111,66 112,28 112,87 112,18 112,36 112,16 111,49 111,25 111,36 111,74 111,1 111,33 111,25 111,04 110,97 111,31 111,02 111,07 111,36 111,54 112,05 112,52 112,94 113,33 113,78 113,77 113,82 113,89 114,25 114,41

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	103.48	103.48	0	0	0
2	103.93	103.873915011963	0.0671547068140572	0.0205163683230409	1.05673372968296
3	103.89	103.878658598222	0.0441107069774392	0.0204037216127486	-0.212745217106742
4	104.4	104.328896605387	0.212766643189411	0.018532748645815	1.29441439184492
5	104.79	104.746436345168	0.29987706478355	0.0178085281500633	0.642593675078283
6	104.77	104.784423137891	0.187752274708622	0.0183498153606676	-0.820063166157854
7	105.13	105.096267913576	0.240993750266082	0.0182115452968072	0.388621717198104
8	105.26	105.25235964382	0.204536778405807	0.0182610280463516	-0.265976068843939
9	104.96	104.998903709244	0.00780426151474636	0.0183989511065719	-1.43510339524529
10	104.75	104.762163590399	-0.0972581377454122	0.0184368095504773	-0.766372861116432
11	105.01	104.955252003452	0.0274920658456558	0.0184137520686329	0.909976860503057
12	105.15	105.115035893002	0.0843348039974786	0.0184083678840531	0.41463227353378
13	105.2	105.331371991286	0.138908704581269	-0.147259664919998	0.47449730748307
14	105.77	105.728992794546	0.240710806849184	0.0194658889661998	0.655989540727187
15	105.78	105.783925576531	0.161016128426702	0.0193336915853151	-0.582603370340138
16	106.26	106.20841822986	0.274454159091059	0.0187733441824657	0.822739281923393
17	106.13	106.151963334933	0.132256300814288	0.0193121816321711	-1.03451463989318
18	106.12	106.120936154171	0.0621249776487469	0.0194675510226062	-0.511135457885316
19	106.57	106.509832342419	0.202484848872294	0.0192999243132723	1.02359417310278
20	106.44	106.453065783842	0.0911115333383387	0.0193694853632611	-0.812346035400039
21	106.54	106.523246697419	0.082118914854446	0.0193723871055168	-0.0655943654371804
22	107.1	107.027794431137	0.263621836696443	0.0193422814761452	1.32394345266921
23	108.1	107.992896023293	0.565033073940443	0.0193166370618926	2.19860238118453
24	108.4	108.40039546851	0.497342984325434	0.019319588531805	-0.493756381673127
25	108.84	109.014559614347	0.546622951315751	-0.188909629601856	0.393645454873374
26	109.62	109.59859646102	0.561808997747749	0.0177516252565416	0.103005724369347
27	110.42	110.375253270046	0.654027280557182	0.01785156466381	0.673642701863089
28	110.67	110.693558228224	0.509582608789291	0.0183192319478328	-1.04969404269016
29	111.66	111.593366686826	0.677266744244495	0.0179028983905363	1.22104152281305
30	112.28	112.263041544135	0.674005486869827	0.0179076310698452	-0.0237757695965795
31	112.87	112.861515573975	0.641557894899944	0.0179330122335132	-0.236647995490579
32	112.18	112.311013757318	0.129413430779224	0.0181425174185119	-3.73561412849186
33	112.36	112.352813366424	0.0917694144341112	0.0181504731993205	-0.274586305285415
34	112.16	112.175509953511	-0.0238445254952432	0.0181630331419322	-0.843328331237461
35	111.49	111.547439850187	-0.283470880400788	0.0181775007011105	-1.89380913622189
36	111.25	111.235397803403	-0.295747606376388	0.0181778512986996	-0.0895509590826834
37	111.36	111.433201285786	-0.086226373888755	-0.134216965109667	1.62498585041849
38	111.74	111.688171024441	0.0543345130478958	0.0161280391596024	0.97392945897528
39	111.1	111.15732384563	-0.196911244102784	0.0159258200750152	-1.834638742933
40	111.33	111.275111774956	-0.0615566595291128	0.0155998830405733	0.98458133416731
41	111.25	111.232097947643	-0.0535886858845455	0.0155851718666258	0.0580468408749427
42	111.04	111.041486937155	-0.112453883813694	0.0156486864920975	-0.429209414913862
43	110.97	110.951540990476	-0.10278408806187	0.0156430628196737	0.0705269254169159
44	111.31	111.244845548901	0.0673940003617323	0.0155913052403021	1.24130311966288
45	111.02	111.03863009701	-0.0501671422770438	0.015609777377275	-0.8575273141104
46	111.07	111.047059169843	-0.0249895075574401	0.0156077438104045	0.183654572447691
47	111.36	111.308545394502	0.098105410768704	0.0156026440169899	0.89789931886991
48	111.54	111.511301351241	0.143072776227557	0.0156016892668165	0.328008536002872
49	112.05	112.118054533731	0.340523530686371	-0.125557139606325	1.50853262492872
50	112.52	112.503308664986	0.359112167686081	0.0118244391990438	0.130307665725181
51	112.94	112.920846428869	0.384201157154409	0.011840474552576	0.183163962727882
52	113.33	113.316712157356	0.389217196753956	0.0118308596560312	0.0365078715921515
53	113.78	113.761285223575	0.413003834460183	0.0117959045300156	0.173331500971737
54	113.77	113.804339507651	0.25406549185186	0.0119323906637665	-1.15897875629395
55	113.82	113.835866789549	0.158455743889951	0.0119766431916989	-0.697348796286899
56	113.89	113.890948369518	0.114040384266335	0.0119873938080219	-0.323973999545938
57	114.25	114.212104578002	0.203032499468324	0.0119762653798814	0.649137096645285
58	114.41	114.399926831239	0.196496912928743	0.0119766854838765	-0.0476729010209747

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/14jzp1291748448.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/14jzp1291748448.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/2fsga1291748448.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/2fsga1291748448.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/3fsga1291748448.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/3fsga1291748448.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/4p1gd1291748448.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/4p1gd1291748448.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/5iafy1291748448.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291748318k2kn01gb2lrhoes/5iafy1291748448.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

bitmap(file='test1.png')

plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')

grid()

dev.off()

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='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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