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Type 'q()' to quit R. > x <- c(101.5,100.7,110.6,96.8,100,104.8,86.8,92,100.2,106.6,102.1,93.7,97.6,96.9,105.6,102.8,101.7,104.2,92.7,91.9,106.5,112.3,102.8,96.5,101,98.9,105.1,103,99,104.3,94.6,90.4,108.9,111.4,100.8,102.5,98.2,98.7,113.3,104.6,99.3,111.8,97.3,97.7,115.6,111.9,107,107.1,100.6,99.2,108.4,103,99.8,115,90.8,95.9,114.4,108.2,112.6,109.1,105,105,118.5,103.7,112.5,116.6,96.6,101.9,116.5,119.3,115.4,108.5,111.5,108.8,121.8,109.6,112.2,119.6,104.1,105.3,115,124.1,116.8,107.5,115.6,116.2,116.3,119,111.9,118.6,106.9,103.2,118.6,118.7,102.8,100.6,94.9,94.5,102.9,95.3,92.5,102.7,91.5,89.5,104.2,105.2,99,95.5,90.5,96.1,113,101.9,101.4,113.6,96.6,97.8,114.9,112.5,108.4,107,103.5,107.5,122.3) > par3 = 'additive' > par2 = 'Single' > 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$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ > #Source of accompanying publication: > #Technical description: > par1 <- as.numeric(par1) > if (par2 == 'Single') K <- 1 > if (par2 == 'Double') K <- 2 > if (par2 == 'Triple') K <- par1 > nx <- length(x) > nxmK <- nx - K > x <- ts(x, frequency = par1) > if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) > if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) > if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) > fit Holt-Winters exponential smoothing without trend and without seasonal component. Call: HoltWinters(x = x, beta = F, gamma = F) Smoothing parameters: alpha: 0.2132569 beta : FALSE gamma: FALSE Coefficients: [,1] a 109.6562 > myresid <- x - fit$fitted[,'xhat'] > postscript(file="/var/wessaorg/rcomp/tmp/1n92j1322765090.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/2fqfo1322765090.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/3r0291322765090.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$gamma) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/4shjy1322765090.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Observed',header=TRUE) > a<-table.element(a,'Fitted',header=TRUE) > a<-table.element(a,'Residuals',header=TRUE) > a<-table.row.end(a) > for (i in 1:nxmK) { + a<-table.row.start(a) + a<-table.element(a,i+K,header=TRUE) + a<-table.element(a,x[i+K]) + a<-table.element(a,fit$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/55s3u1322765090.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/6tgzg1322765090.tab") > > try(system("convert tmp/1n92j1322765090.ps tmp/1n92j1322765090.png",intern=TRUE)) character(0) > try(system("convert tmp/2fqfo1322765090.ps tmp/2fqfo1322765090.png",intern=TRUE)) character(0) > try(system("convert tmp/3r0291322765090.ps tmp/3r0291322765090.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.275 0.165 1.441