Structural time series model

*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, 02 Dec 2009 09:07:15 -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/02/t125977012155k41kcayq9tyrl.htm/, Retrieved Wed, 02 Dec 2009 17:08:48 +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/02/t125977012155k41kcayq9tyrl.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 «

108.5 112.3 116.6 115.5 120.1 132.9 128.1 129.3 132.5 131 124.9 120.8 122 122.1 127.4 135.2 137.3 135 136 138.4 134.7 138.4 133.9 133.6 141.2 151.8 155.4 156.6 161.6 160.7 156 159.5 168.7 169.9 169.9 185.9 190.8 195.8 211.9 227.1 251.3 256.7 251.9 251.2 270.3 267.2 243 229.9 187.2 178.2 175.2 192.4 187 184 194.1 212.7 217.5 200.5 205.9 196.5 206.3

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 1 108.5 108.5 0 0 0 2 112.3 112.107990567052 0.299520333464632 0.19200943294768 0.234351320027692 3 116.6 116.409030079065 0.887614852216326 0.190969920935322 0.406095837952912 4 115.5 115.308612515095 0.506970831336137 0.191387484905296 -0.196432614080234 5 120.1 119.909283573374 1.40574594768484 0.190716426625717 0.397420833309356 6 132.9 132.710710205320 4.09845149806786 0.189289794679854 1.09442172247909 7 128.1 127.909870095453 1.90980717082471 0.190129904547208 -0.849289434139052 8 129.3 129.109819929010 1.73136342564871 0.19018007098989 -0.067500890602942 9 132.5 132.309897317013 2.10503379961536 0.190102682987361 0.139380176174126 10 131 130.809756006955 1.18172212395556 0.190243993044685 -0.341747259421099 11 124.9 124.709543947020 -0.690029537920745 0.190456052980489 -0.689855260765352 12 120.8 120.609470218456 -1.5683058003174 0.190529781543639 -0.322941913658471 13 122 122.651708053429 -0.67070203984092 -0.651708053428792 0.39704415205166 14 122.1 122.039447201094 -0.656336288331872 0.0605527989058466 0.00463021949165108 15 127.4 127.346371066669 0.885032913320507 0.0536289333313029 0.563633530939744 16 135.2 135.152331300144 2.67264666215725 0.0476686998559181 0.654463099242995 17 137.3 137.251965243614 2.52469290278928 0.0480347563857951 -0.0542031281548969 18 135 134.949677716785 1.27853089963487 0.0503222832147156 -0.456699678648379 19 136 135.949579760849 1.20660186550826 0.0504202391509342 -0.0263661848720782 20 138.4 138.349891088549 1.51476131455073 0.0501089114514825 0.112970838502852 21 134.7 134.648881952614 0.168274310860272 0.0511180473862879 -0.49365021666894 22 138.4 138.349388930855 1.08016412983750 0.0506110691450223 0.334328967300456 23 133.9 133.848794722423 -0.360608970948542 0.0512052775769712 -0.528244758194134 24 133.6 133.548799510041 -0.344960143717595 0.0512004899585639 0.00573754075203173 25 141.2 140.408161017566 1.48702368351126 0.79183898243404 0.736730848354184 26 151.8 151.730651166420 3.94672563081249 0.0693488335802398 0.837608783247037 27 155.4 155.3303832955 3.85704099781783 0.0696167044999834 -0.0328123753762335 28 156.6 156.528861133309 3.17032954811392 0.0711388666909328 -0.251484976370749 29 161.6 161.529638533126 3.64299402716278 0.0703614668742037 0.173189197355598 30 160.7 160.628206806302 2.46967955106439 0.0717931936984147 -0.430040013420672 31 156 155.926530764534 0.618226640712535 0.073469235465853 -0.67869832266883 32 159.5 159.427030480674 1.36234170148878 0.0729695193255008 0.272798850669425 33 168.7 168.628038652596 3.38605334067904 0.0719613474040545 0.741945776264576 34 169.9 169.827830060818 2.82161933494502 0.0721699391821734 -0.206941845093007 35 169.9 169.827630339277 2.0930927609312 0.0723696607226506 -0.267108022297403 36 185.9 185.828360549885 5.68375487178261 0.0716394501150607 1.31649613388155 37 190.8 191.579724418513 5.70103908380125 -0.779724418513252 0.00674254824636057 38 195.8 195.745383403916 5.31380287164402 0.054616596083769 -0.134786750952614 39 211.9 211.851555468646 8.10246397156012 0.0484445313535728 1.02083549291497 40 227.1 227.054567436321 9.93634429333901 0.0454325636789757 0.67180158286185 41 251.3 251.259056998838 13.6205930622158 0.0409430011624472 1.35017346216786 42 256.7 256.657137735176 11.4976355660279 0.0428622648238606 -0.778172340319613 43 251.9 251.854315262646 7.28921867515689 0.0456847373538225 -1.54278319793577 44 251.2 251.153288922094 5.22633731974211 0.0467110779061335 -0.756290805500648 45 270.3 270.254611024232 8.80852017045513 0.0453889757680056 1.31334238926104 46 267.2 267.153769200972 5.73378946609652 0.0462307990276661 -1.12731660280892 47 243 242.952199505244 -1.99491949928063 0.0478004947564810 -2.83367806576953 48 229.9 229.851767521988 -4.86216410919509 0.0482324780116287 -1.05126185453105 49 187.2 190.846821033877 -13.6130873322921 -3.64682103387687 -3.36178761805418 50 178.2 177.863188963842 -13.4535500646630 0.336811036157823 0.0561944119767591 51 175.2 174.867937333590 -10.7516442018882 0.332062666410322 0.989400902380608 52 192.4 192.077353771140 -3.53053077142593 0.322646228859826 2.64577173900073 53 187 186.676886637842 -4.01336692661487 0.323113362157837 -0.176963386407946 54 184 183.677074463347 -3.75167838099818 0.322925536653252 0.0959274445987369 55 194.1 193.778978905259 -0.174954146833104 0.321021094741323 1.31124736495429 56 212.7 212.380893727223 4.67282383617023 0.319106272777386 1.77731521856663 57 217.5 217.180903348730 4.70566049649699 0.319096651270350 0.0120390754466365 58 200.5 200.179685200108 -0.898627503394373 0.320314799892371 -2.0547615681818 59 205.9 205.579947419136 0.727633176955665 0.320052580863928 0.596258950010388 60 196.5 196.179634654342 -1.88723883633122 0.320365345657877 -0.958732070721639 61 206.3 208.772903583346 1.82976239899704 -2.47290358334623 1.41479136733123

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/1lnwi1259770033.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/1lnwi1259770033.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/2ipud1259770033.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/2ipud1259770033.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/3gx4x1259770033.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/3gx4x1259770033.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/4dcg41259770033.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/4dcg41259770033.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/5jptt1259770033.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125977012155k41kcayq9tyrl/5jptt1259770033.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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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