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: Fri, 04 Dec 2009 08:49:46 -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/04/t1259941823ois2kazam6sa337.htm/, Retrieved Fri, 04 Dec 2009 16:50:29 +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/04/t1259941823ois2kazam6sa337.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 «

6,3 6,2 6,1 6,3 6,5 6,6 6,5 6,2 6,2 5,9 6,1 6,1 6,1 6,1 6,1 6,4 6,7 6,9 7 7 6,8 6,4 5,9 5,5 5,5 5,6 5,8 5,9 6,1 6,1 6 6 5,9 5,5 5,6 5,4 5,2 5,2 5,2 5,5 5,8 5,8 5,5 5,3 5,1 5,2 5,8 5,8 5,5 5 4,9 5,3 6,1 6,5 6,8 6,6 6,4 6,4

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 'Gwilym Jenkins' @ 72.249.127.135 Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 6.3 6.3 0 0 0 2 6.2 6.20029716796157 -0.0997273913760922 -0.000297167961573839 -0.408489295620644 3 6.1 6.09979513470036 -0.100495243360923 0.000204865299644 -0.00315455903164451 4 6.3 6.2977542712815 0.194500442302507 0.00224572871850239 1.20650272869622 5 6.5 6.50056244598451 0.202713665487683 -0.00056244598451217 0.0335939443753683 6 6.6 6.60085242694527 0.101453906892288 -0.000852426945274272 -0.414174750832066 7 6.5 6.50139486682477 -0.0971738506217298 -0.00139486682476845 -0.812431313242722 8 6.2 6.20122037797162 -0.297867060449616 -0.00122037797162428 -0.820879468979458 9 6.2 6.19739745601969 -0.00716518778322905 0.00260254398030883 1.18903474146113 10 5.9 5.90282639286309 -0.291304249880994 -0.00282639286308901 -1.16219139953108 11 6.1 6.09577278145059 0.187442129164529 0.00422721854941176 1.95817822504077 12 6.1 6.10237558835989 0.00865832620058987 -0.00237558835988872 -0.731265165183998 13 6.1 6.0996405840477 -0.00260470068982178 0.000359415952302765 -0.0460731379892089 14 6.1 6.09809831207916 -0.0015542058861936 0.00190168792083857 0.00430205186249085 15 6.1 6.1029153458354 0.00469486711094491 -0.00291534583540403 0.0256578394536613 16 6.4 6.39424499109769 0.285270513823240 0.00575500890231338 1.14739140623323 17 6.7 6.70130836213141 0.306606247633500 -0.00130836213141272 0.087268661388703 18 6.9 6.90212650238412 0.203034133338359 -0.00212650238411872 -0.423632791071569 19 7 6.99776833237055 0.0978920113233735 0.00223166762944939 -0.430054457912472 20 7 7.00831592166869 0.0123777493686246 -0.008315921668692 -0.349772182215832 21 6.8 6.79326621756893 -0.210284393065206 0.00673378243107212 -0.910737246152639 22 6.4 6.41134286161733 -0.378326971685546 -0.0113428616173301 -0.687331190051569 23 5.9 5.89519003324078 -0.513265042694211 0.00480996675922306 -0.551926460204372 24 5.5 5.50019451632248 -0.397473728734047 -0.000194516322480695 0.473612059831032 25 5.5 5.49465719433266 -0.0137777565909232 0.00534280566734439 1.56957820207638 26 5.6 5.59373090296372 0.0967271380448915 0.0062690970362823 0.452416955990329 27 5.8 5.80674668407827 0.209852074922257 -0.00674668407826732 0.464098493181313 28 5.9 5.89852329004553 0.0951171887202256 0.00147670995447078 -0.469164425465421 29 6.1 6.09777884798091 0.196315844309289 0.00222115201908822 0.413933193440927 30 6.1 6.10433051306465 0.0119001181821761 -0.00433051306465253 -0.754300675425817 31 6 5.99991446133558 -0.101137111662663 8.55386644210451e-05 -0.462347213530348 32 6 6.00296433132393 0.000112641777257588 -0.00296433132392659 0.41413381032798 33 5.9 5.89434647535882 -0.105552577898710 0.00565352464118018 -0.432194041436554 34 5.5 5.51269607604272 -0.37386678661241 -0.0126960760427209 -1.09746426305425 35 5.6 5.58333742762385 0.0581108706386614 0.0166625723761448 1.76688394868857 36 5.4 5.41302376348706 -0.163873367966327 -0.0130237634870574 -0.90796494281159 37 5.2 5.19590335095372 -0.215615232430646 0.00409664904628482 -0.211663423911762 38 5.2 5.19428115474978 -0.00761995430960011 0.00571884525021697 0.851278105927362 39 5.2 5.20177504133049 0.00699657067112295 -0.00177504133049006 0.0599187143655675 40 5.5 5.49850349978326 0.287071001223696 0.00149650021673589 1.14524853621215 41 5.8 5.79535181471361 0.296521890400401 0.00464818528638515 0.0386572323901912 42 5.8 5.80539505310433 0.0195907458893417 -0.00539505310432997 -1.13270845750806 43 5.5 5.5105019898551 -0.284411449862545 -0.0105019898550986 -1.24343619640577 44 5.3 5.30200129586594 -0.211031054021123 -0.00200129586594092 0.300141992402568 45 5.1 5.07887731723402 -0.222720881797513 0.0211226827659831 -0.0478139726638196 46 5.2 5.221263236285 0.130215902004513 -0.0212632362849981 1.44358925216182 47 5.8 5.77043016141382 0.535203386883025 0.0295698385861810 1.65648848171649 48 5.8 5.82096959651487 0.0666979291113927 -0.0209695965148683 -1.91629208716602 49 5.5 5.50899350181228 -0.299324133513849 -0.00899350181227969 -1.49734206190159 50 5 4.991928494597 -0.509834519413333 0.00807150540300206 -0.861346783766708 51 4.9 4.89890080864346 -0.108373311863457 0.00109919135654351 1.64473864820553 52 5.3 5.29297322171802 0.375565339047456 0.007026778281981 1.97894098427504 53 6.1 6.08411931110482 0.775775708055115 0.0158806888951814 1.63698665582911 54 6.5 6.50460191986884 0.433598337150142 -0.00460191986883882 -1.39958013388923 55 6.8 6.8167387953026 0.316620496813262 -0.0167387953025987 -0.47846525350062 56 6.6 6.60588419853379 -0.191380760373913 -0.00588419853378606 -2.07783711048498 57 6.4 6.38068298955593 -0.223952571884354 0.0193170104440707 -0.133225890815008 58 6.4 6.43597540121338 0.0449831725585313 -0.0359754012133828 1.10000648024379

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/1ydlx1259941783.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/1ydlx1259941783.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/2za7y1259941783.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/2za7y1259941783.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/35roq1259941783.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/35roq1259941783.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/4ezht1259941783.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/4ezht1259941783.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/5miob1259941783.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941823ois2kazam6sa337/5miob1259941783.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 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')

Copyright

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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