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Type 'q()' to quit R. > x <- c(94.72,95.76,96.14,97.11,97.19,97.43,97.43,97.56,97.66,97.75,97.82,97.82,97.82,98.35,98.19,98.19,98.21,98.22,98.26,98.23,98.26,98.5,98.51,98.51,98.51,98.89,99.55,99.9,100.12,100.09,100.09,100.09,100.46,100.71,100.79,100.79,100.93,101.15,101.53,101.91,102.18,102.24,102.2,102.32,102.43,102.45,102.84,102.96,102.96,103.1,103.4,103.74,103.97,104.29,104.33,104.46,104.9,105.31,105.63,105.68,105.87,106.34,106.6,107.1,107.06,107.4,107.4,107.43,107.75,107.84,107.97,108.04) > par3 = 'additive' > par2 = 'Triple' > par1 = '12' > par3 <- 'additive' > par2 <- 'Triple' > par1 <- '12' > #'GNU S' R Code compiled by R2WASP v. 1.2.327 () > #Author: root > #To cite this work: Wessa P., (2013), Exponential Smoothing (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ > #Source of accompanying publication: > # > par1 <- as.numeric(par1) > if (par2 == 'Single') K <- 1 > if (par2 == 'Double') K <- 2 > if (par2 == 'Triple') K <- par1 > nx <- length(x) > nxmK <- nx - K > x <- ts(x, frequency = par1) > if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) > if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) > if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) > fit Holt-Winters exponential smoothing with trend and additive seasonal component. Call: HoltWinters(x = x, seasonal = par3) Smoothing parameters: alpha: 0.8326499 beta : 0.04599874 gamma: 1 Coefficients: [,1] a 108.16526261 b 0.19112945 s1 -0.14696193 s2 0.14351971 s3 0.23289333 s4 0.23738492 s5 0.04924015 s6 -0.01554298 s7 -0.06017425 s8 -0.01810949 s9 0.09136595 s10 0.04555073 s11 0.01778310 s12 -0.12526261 > myresid <- x - fit$fitted[,'xhat'] > postscript(file="/var/wessaorg/rcomp/tmp/1om161493734757.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/2cwv91493734757.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/3ep5c1493734757.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$gamma) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/43b8p1493734757.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Observed',header=TRUE) > a<-table.element(a,'Fitted',header=TRUE) > a<-table.element(a,'Residuals',header=TRUE) > a<-table.row.end(a) > for (i in 1:nxmK) { + a<-table.row.start(a) + a<-table.element(a,i+K,header=TRUE) + a<-table.element(a,x[i+K]) + a<-table.element(a,fit$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/5b5f71493734757.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/67ymb1493734757.tab") > > try(system("convert tmp/1om161493734757.ps tmp/1om161493734757.png",intern=TRUE)) character(0) > try(system("convert tmp/2cwv91493734757.ps tmp/2cwv91493734757.png",intern=TRUE)) character(0) > try(system("convert tmp/3ep5c1493734757.ps tmp/3ep5c1493734757.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 2.168 0.192 2.506