x <- c(126.81,125.8,123.07,119.52,118.03,117.27,117.27,116.69,115.38,114.31,113.33,111.79,111.79,110.92,109.37,107.04,104.72,104.14,104.14,102.95,102.13,101.01,100.07,99.4,99.4,99.34,97.72,96.26,95.77,95.04,95.04,94.55,94,93.14,91.21,90.3,90.3,89.74,89.07,89.06,88.97,88.78,88.78,88.23,87.91,87.79,87.89,88,88,87.08,85.75,84.29,84.39,83.72,83.72,81.76,81.53,80.55,79.83,78.98,78.98,78.27,77.41,76.75,76.38,74.96,74.96,74.46,74.04,73.22,72.97,72.91,72.91,73.27,72.93,72.67,71.94,71.9,71.89,71.72,70.85,69.82,69.61,69.48) par3 = 'multiplicative' par2 = 'Double' par1 = '12' par3 <- 'multiplicative' par2 <- 'Double' 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$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ #Source of accompanying publication: # par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] postscript(file="/var/wessaorg/rcomp/tmp/1q4fr1386924072.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() postscript(file="/var/wessaorg/rcomp/tmp/2pbbs1386924072.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() postscript(file="/var/wessaorg/rcomp/tmp/3sck11386924072.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() #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$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file="/var/wessaorg/rcomp/tmp/4surk1386924073.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$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/5ms8j1386924073.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/6d94t1386924073.tab") try(system("convert tmp/1q4fr1386924072.ps tmp/1q4fr1386924072.png",intern=TRUE)) try(system("convert tmp/2pbbs1386924072.ps tmp/2pbbs1386924072.png",intern=TRUE)) try(system("convert tmp/3sck11386924072.ps tmp/3sck11386924072.png",intern=TRUE))