WS 9 Review 3 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: Thu, 10 Dec 2009 11:55:45 -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/10/t1260471386pb54r8x8wn4ny88.htm/, Retrieved Thu, 10 Dec 2009 19:56:33 +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/10/t1260471386pb54r8x8wn4ny88.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 «

283.042 276.687 277.915 277.128 277.103 275.037 270.150 267.140 264.993 287.259 291.186 292.300 288.186 281.477 282.656 280.190 280.408 276.836 275.216 274.352 271.311 289.802 290.726 292.300 278.506 269.826 265.861 269.034 264.176 255.198 253.353 246.057 235.372 258.556 260.993 254.663 250.643 243.422 247.105 248.541 245.039 237.080 237.085 225.554 226.839 247.934 248.333 246.969 245.098 246.263 255.765 264.319 268.347 273.046 273.963 267.430 271.993 292.710 295.881 293.299

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 1 283.042 283.042 0 0 0 2 276.687 279.643099949226 -2.92361682846477 -2.95609994922578 -1.60260866952763 3 277.915 276.140559463114 -3.26175628566210 1.77444053688619 -0.125865216510943 4 277.128 275.559759426404 -1.65533158744298 1.56824057359594 0.625674700662030 5 277.103 276.338883741368 -0.180007006998245 0.764116258632077 0.536882429936485 6 275.037 275.60117321584 -0.51149442481712 -0.564173215840185 -0.120727948617283 7 270.15 271.60358070987 -2.58377139671973 -1.45358070987009 -0.761464920927339 8 267.14 267.303320934953 -3.60804292510288 -0.163320934952686 -0.376027613640751 9 264.993 264.329183977815 -3.22942193172469 0.663816022184723 0.138895032605294 10 287.259 278.896504964221 7.39846997122516 8.36249503577857 3.89920571124566 11 291.186 291.461100071561 10.4826558430896 -0.275100071561301 1.13156009519430 12 292.3 295.863621442826 6.85348046703138 -3.56362144282566 -1.33148594559240 13 288.186 292.255746405733 0.659880772553535 -4.06974640573311 -2.31104249620351 14 281.477 286.251855201344 -3.29403221142526 -4.77485520134415 -1.46225990329933 15 282.656 281.892745223988 -3.90720772337637 0.763254776012354 -0.222981966516256 16 280.19 279.177391289139 -3.22641961421955 1.01260871086094 0.253176943380808 17 280.408 278.155724777872 -1.94890680913889 2.25227522212757 0.472296549723932 18 276.836 275.44314718552 -2.3901821268414 1.39285281447971 -0.161077836539959 19 275.216 273.85075963422 -1.93187859289896 1.36524036577975 0.167747256630069 20 274.352 274.118593889419 -0.666967996970173 0.233406110580757 0.464367161811322 21 271.311 277.005124913504 1.38092983527905 -5.69412491350405 0.751506378766255 22 289.802 282.616787170681 3.82032419108576 7.18521282931867 0.894942062131855 23 290.726 288.395970810411 4.94872345148285 2.33002918958949 0.414038742564155 24 292.3 292.35330596947 4.37838610119883 -0.0533059694697586 -0.209592664946352 25 278.506 285.316536319926 -2.19633091444993 -6.81053631992616 -2.42343573801538 26 269.826 276.256467579431 -6.14771431710252 -6.43046757943118 -1.45003376242421 27 265.861 266.634641590441 -8.12879440977871 -0.773641590440527 -0.724380148669477 28 269.034 265.086978257636 -4.3924438531557 3.9470217423637 1.37611885262853 29 264.176 261.384315302726 -3.99864143943873 2.79168469727378 0.145243433947237 30 255.198 254.689111649302 -5.54084907698173 0.508888350698388 -0.565358817642569 31 253.353 251.237668901975 -4.34973827492976 2.11533109802521 0.435929106413505 32 246.057 247.567923625875 -3.96258950990762 -1.51092362587526 0.141949478481996 33 235.372 243.730269033852 -3.89139064501295 -8.3582690338519 0.0261260507276766 34 258.556 248.955687365365 1.30715314276691 9.60031263463508 1.90760936506891 35 260.993 256.290579633762 4.74320958488971 4.70242036623771 1.26134079557061 36 254.663 253.667085475468 0.543443375764997 0.995914524532434 -1.54329364666324 37 250.643 253.641545189888 0.218748236195865 -2.99854518988786 -0.119323540000477 38 243.422 250.621368195597 -1.62730637310546 -7.1993681955969 -0.676709885244777 39 247.105 249.983560617877 -1.06592851870523 -2.87856061787672 0.205616875082688 40 248.541 246.003758049731 -2.71543378950017 2.53724195026863 -0.606230501450016 41 245.039 241.424549571363 -3.77324081855548 3.61445042863657 -0.389366177369497 42 237.08 236.939737742876 -4.17786799784796 0.140262257124481 -0.148538252076744 43 237.085 233.95956975557 -3.49776021738589 3.12543024443020 0.249143942575550 44 225.554 228.694666217751 -4.49947570767945 -3.14066621775122 -0.367107800009838 45 226.839 234.702560242164 1.45475009444517 -7.86356024216446 2.18424387096914 46 247.934 239.935409873783 3.59631437949716 7.99859012621723 0.78606664695112 47 248.333 241.837933750243 2.6358952621466 6.49506624975652 -0.352698905034626 48 246.969 245.163425907907 3.0271714506196 1.80557409209291 0.143736203847724 49 245.098 247.574727806296 2.67755544773851 -2.47672780629557 -0.128339536551380 50 246.263 252.688653132227 4.05883059350544 -6.42565313222742 0.506263793426672 51 255.765 257.312633909106 4.37833178738536 -1.54763390910607 0.117099126771383 52 264.319 261.029390743114 4.00478444917048 3.28960925688568 -0.137195330543637 53 268.347 264.245999316680 3.55907301537736 4.10100068332029 -0.163895920974508 54 273.046 271.033684397402 5.38764542366191 2.01231560259847 0.671488106668861 55 273.963 272.762415832025 3.31660379504582 1.20058416797530 -0.75918263216 56 267.43 275.194322775954 2.81665594756149 -7.76432277595415 -0.183216475363602 57 271.993 280.186083401745 4.04463347747718 -8.19308340174468 0.450382121364642 58 292.71 284.211792784952 4.03394963943675 8.4982072150479 -0.00392200071173293 59 295.881 289.068561433317 4.49877102502402 6.81243856668293 0.170729131214369 60 293.299 292.135336776130 3.68914657189752 1.16366322386956 -0.2973494716982

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/1riqv1260471343.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/1riqv1260471343.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/27v431260471343.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/27v431260471343.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/3vs1i1260471343.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/3vs1i1260471343.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/4lzrp1260471343.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/4lzrp1260471343.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/5vpav1260471343.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260471386pb54r8x8wn4ny88/5vpav1260471343.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')

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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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