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Paper 'Decomposition by structural time series models'

*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: Mon, 20 Dec 2010 18:19:34 +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/20/t129286944608sym98effrk3al.htm/, Retrieved Mon, 20 Dec 2010 19:24:07 +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/20/t129286944608sym98effrk3al.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 «

9,3 14,2 17,3 23 16,3 18,4 14,2 9,1 5,9 7,2 6,8 8 14,3 14,6 17,5 17,2 17,2 14,1 10,4 6,8 4,1 6,5 6,1 6,3 9,3 16,4 16,1 18 17,6 14 10,5 6,9 2,8 0,7 3,6 6,7 12,5 14,4 16,5 18,7 19,4 15,8 11,3 9,7 2,9 0,1 2,5 6,7 10,3 11,2 17,4 20,5 17 14,2 10,6 6,1

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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	9.3	9.3	0	0	0
2	14.2	13.4736505704315	4.10528827469964	0.0341811489468284	1.68788817435418
3	17.3	17.2954307702691	3.87381902117338	0.0348488777500524	-0.0892422670501881
4	23	22.7953445802416	5.21423320464757	0.0322877236448282	0.509928115872817
5	16.3	17.3813385696288	-3.56701612664088	0.0357082875956243	-3.31928107716536
6	18.4	17.9315460214604	-0.164585710011123	0.0358651880480432	1.28582435110197
7	14.2	14.5068164740025	-2.85875294813151	0.0357222557140473	-1.01816048760667
8	9.1	9.30995685826204	-4.79089331884082	0.0356951289081438	-0.730177046530401
9	5.9	5.73640706114873	-3.78492950094269	0.0356949597100448	0.380164645625416
10	7.2	6.66870415702367	0.113193227848089	0.0356895287162296	1.47314289402519
11	6.8	6.7659825299409	0.100041833914435	0.0356895348691232	-0.00497005451087878
12	8	7.85989162567289	0.921333932602784	0.0356895102183893	0.310375198168052
13	14.3	13.4485867875258	4.72109264248952	0.368312663052871	1.54882453246819
14	14.6	14.9259110002643	2.36626378775062	-0.0829124914284717	-0.849590760451241
15	17.5	17.5563796064935	2.58599970783584	-0.0837173849838232	0.0817094097148589
16	17.2	17.5470406895096	0.445429657382742	-0.0772596839675676	-0.804872088726869
17	17.2	17.3448569191145	-0.0893560378111895	-0.0768856075502051	-0.202078262502383
18	14.1	14.4696843140624	-2.39153556761987	-0.076987354812468	-0.870014716606215
19	10.4	10.6293139453037	-3.58887668960232	-0.0770853519865376	-0.452486321982249
20	6.8	6.89261888343265	-3.71103030858513	-0.0770883107293593	-0.0461631695082386
21	4.1	4.08244132690474	-2.96660127030685	-0.0770878415841244	0.281327813754573
22	6.5	6.05787163699064	1.11728876114332	-0.0770963523468533	1.54334636353314
23	6.1	6.27198608230061	0.370942145418384	-0.0770957674776677	-0.282052486648814
24	6.3	6.40236960764606	0.172154143899226	-0.0770957527653614	-0.0751241433633196
25	9.3	8.13374290892933	1.44892022873946	1.00392927389707	0.505961325380028
26	16.4	15.8956189251827	6.21046591975929	-0.0221772531843799	1.74806730522154
27	16.1	16.6747150620398	1.70140703799051	-0.0102881228118466	-1.68436453918366
28	18	18.0442907361596	1.42757350727018	-0.0096937841099987	-0.103109984803715
29	17.6	17.7859875759373	0.0351368718206689	-0.0089932503773615	-0.526173742409441
30	14	14.3715194464186	-2.81556075867516	-0.00908386898046829	-1.07730608851385
31	10.5	10.6086605345717	-3.59840861191378	-0.00912995371442475	-0.295845814747527
32	6.9	6.9187453757653	-3.67402704265202	-0.0091312710992513	-0.0285770217426683
33	2.8	2.85054458620149	-3.99975656934779	-0.00913141874720444	-0.123096723630126
34	0.7	0.532452665627751	-2.61009794370234	-0.00913350173375578	0.525167076433802
35	3.6	3.06846896338759	1.64244287730242	-0.0091358986383216	1.6070813318533
36	6.7	6.51915607574973	3.13670346047928	-0.00913597818123761	0.564697292667568
37	12.5	11.9879723736224	5.05123823723446	0.26861405482296	0.748990162653571
38	14.4	14.654991988634	3.21514326380093	-0.0447757597081732	-0.679503046031239
39	16.5	16.6679545416293	2.21811792558843	-0.042722230881625	-0.373391843239497
40	18.7	18.756112898119	2.11084037350763	-0.0425404037489694	-0.0404267496904691
41	19.4	19.5775170936669	1.04572260756571	-0.0421220121994161	-0.402493778657041
42	15.8	16.2967721221645	-2.52957745133131	-0.0422107515905544	-1.35114128314369
43	11.3	11.5728472303135	-4.34296811262106	-0.0422941022549466	-0.685298410837876
44	9.7	9.50340232652044	-2.46419852582633	-0.0422685460465063	0.710007341384477
45	2.9	3.33178318700323	-5.52786340039032	-0.0422696303466105	-1.15779220910008
46	0.1	-0.080045471502183	-3.77925868818571	-0.0422716768284112	0.660816698464737
47	2.5	1.93364796522073	1.00780330553977	-0.0422737835600121	1.80908268460161
48	6.7	6.38091307868192	3.8500367587607	-0.0422739016934459	1.07411087077608
49	10.3	9.889864978496	3.56962224557372	0.44578686329263	-0.108894999055899
50	11.2	11.4389686457123	1.99312776352447	-0.0546679883545291	-0.586108574789652
51	17.4	17.0792613359496	5.01593203915044	-0.0597760229065125	1.13390686985301
52	20.5	20.7036617298122	3.86704357078673	-0.0581786994249454	-0.433170802112864
53	17	17.7704874323238	-1.75056447306111	-0.0563687912403605	-2.12284350851554
54	14.2	14.4240643259263	-3.06934250130558	-0.0563956384633632	-0.498379497522009
55	10.6	10.7228080853074	-3.59154720066411	-0.0564153255901948	-0.197346445341313
56	6.1	6.24910627036739	-4.32053114938478	-0.0564234588509501	-0.275490921870606

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/122ze1292869170.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/122ze1292869170.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/2cbhh1292869170.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/2cbhh1292869170.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/3nkyj1292869170.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/3nkyj1292869170.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/4nkyj1292869170.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/4nkyj1292869170.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/5gtxm1292869170.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129286944608sym98effrk3al/5gtxm1292869170.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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