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Type 'q()' to quit R. > x <- c(34671,34355,34035,33373,39924,39577,34671,31409,31724,31724,32075,32706,34671,34035,35017,36631,45813,45813,43853,41888,43502,45466,45813,46795,49742,47777,47777,50724,58893,59555,57911,53982,56928,56928,57244,58893,60191,60853,60853,62817,70355,72315,72630,67724,70355,69373,67408,71653,72630,70986,71333,73613,82133,86372,86372,84412,87355,84412,82764,89004,89981,87670,93559,95870,102741,107301,106670,106319,108950,108630,104706,110594,112559,110594,118763,122692,131839,135448,134470,132505,134150,136114,129559,134785,138079,136750,145265,148207,160652,162932,159990,161634,162616,163598,157358,163247,166509,163247,172749,175692,188451,190416,191047,194340,194340,195638,189749,192696,194656,191047,201527,203491,216567,218878,222140,225087,225402,225749,219860,225749) > par3 = 'multiplicative' > par2 = 'Triple' > par1 = '12' > #'GNU S' R Code compiled by R2WASP v. 1.0.44 () > #Author: Prof. Dr. P. Wessa > #To cite this work: Wessa P., (2010), Exponential Smoothing (v1.0.4) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ > #Source of accompanying publication: > #Technical description: > par1 <- as.numeric(par1) > if (par2 == 'Single') K <- 1 > if (par2 == 'Double') K <- 2 > if (par2 == 'Triple') K <- par1 > nx <- length(x) > nxmK <- nx - K > x <- ts(x, frequency = par1) > if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) > if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) > if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) > fit Holt-Winters exponential smoothing with trend and multiplicative seasonal component. Call: HoltWinters(x = x, seasonal = par3) Smoothing parameters: alpha: 0.2142287 beta : 0.1078727 gamma: 1 Coefficients: [,1] a 2.156555e+05 b 2.486343e+03 s1 1.023104e+00 s2 9.929723e-01 s3 1.036647e+00 s4 1.037609e+00 s5 1.096476e+00 s6 1.100006e+00 s7 1.103985e+00 s8 1.105610e+00 s9 1.092854e+00 s10 1.080747e+00 s11 1.037060e+00 s12 1.046804e+00 > myresid <- x - fit$fitted[,'xhat'] > postscript(file="/var/wessaorg/rcomp/tmp/19p4v1313070623.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > op <- par(mfrow=c(2,1)) > plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') > plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') > par(op) > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/266gs1313070623.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > p <- predict(fit, par1, prediction.interval=TRUE) > np <- length(p[,1]) > plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/3chf11313070623.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > op <- par(mfrow = c(2,2)) > acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') > spectrum(myresid,main='Residals Periodogram') > cpgram(myresid,main='Residal Cumulative Periodogram') > qqnorm(myresid,main='Residual Normal QQ Plot') > qqline(myresid) > par(op) > dev.off() null device 1 > > #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/wessaorg/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'Parameter',header=TRUE) > a<-table.element(a,'Value',header=TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'alpha',header=TRUE) > a<-table.element(a,fit$alpha) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'beta',header=TRUE) > a<-table.element(a,fit$beta) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'gamma',header=TRUE) > a<-table.element(a,fit$gamma) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/4gog31313070623.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Observed',header=TRUE) > a<-table.element(a,'Fitted',header=TRUE) > a<-table.element(a,'Residuals',header=TRUE) > a<-table.row.end(a) > for (i in 1:nxmK) { + a<-table.row.start(a) + a<-table.element(a,i+K,header=TRUE) + a<-table.element(a,x[i+K]) + a<-table.element(a,fit$fitted[i,'xhat']) + a<-table.element(a,myresid[i]) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/5aqe31313070623.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Forecast',header=TRUE) > a<-table.element(a,'95% Lower Bound',header=TRUE) > a<-table.element(a,'95% Upper Bound',header=TRUE) > a<-table.row.end(a) > for (i in 1:np) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,p[i,'fit']) + a<-table.element(a,p[i,'lwr']) + a<-table.element(a,p[i,'upr']) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/66zon1313070623.tab") > > try(system("convert tmp/19p4v1313070623.ps tmp/19p4v1313070623.png",intern=TRUE)) character(0) > try(system("convert tmp/266gs1313070623.ps tmp/266gs1313070623.png",intern=TRUE)) character(0) > try(system("convert tmp/3chf11313070623.ps tmp/3chf11313070623.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.212 0.223 1.428