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Type 'q()' to quit R. > x <- c(33,32,31,29,49,48,33,23,24,24,25,27,24,21,15,21,49,48,35,36,51,50,61,63,61,62,58,65,93,94,86,88,102,107,121,127,125,128,117,127,160,162,153,160,177,178,196,212,212,211,204,216,248,250,240,249,275,277,286,302,290,290,277,285,311,300,291,299,332,337,343,360,353,351,341,348,381,358,353,358,399,409,407,419,418,421,414,424,463,437,430,436,474,489,482,492,502,500,493,504,538,516,502,501,541,571,559,569,576,573,562,570,597,573,562,556,600,630,624,634) > 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$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ > #Source of accompanying publication: > #Technical description: > par1 <- as.numeric(par1) > if (par2 == 'Single') K <- 1 > if (par2 == 'Double') K <- 2 > if (par2 == 'Triple') K <- par1 > nx <- length(x) > nxmK <- nx - K > x <- ts(x, frequency = par1) > if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) > if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) > if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) > fit Holt-Winters exponential smoothing with trend and multiplicative seasonal component. Call: HoltWinters(x = x, seasonal = par3) Smoothing parameters: alpha: 0.1165086 beta : 0.1139601 gamma: 0.92312 Coefficients: [,1] a 482.354158 b 4.158067 s1 1.311996 s2 1.291626 s3 1.254364 s4 1.260789 s5 1.313013 s6 1.249991 s7 1.214377 s8 1.192881 s9 1.277518 s10 1.331139 s11 1.305098 s12 1.314015 > myresid <- x - fit$fitted[,'xhat'] > postscript(file="/var/www/html/freestat/rcomp/tmp/1p5n61280159319.ps",horizontal=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/www/html/freestat/rcomp/tmp/2he581280159319.ps",horizontal=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/www/html/freestat/rcomp/tmp/3he581280159319.ps",horizontal=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/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/freestat/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$gamma) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/www/html/freestat/rcomp/tmp/4oy5c1280159320.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Observed',header=TRUE) > a<-table.element(a,'Fitted',header=TRUE) > a<-table.element(a,'Residuals',header=TRUE) > a<-table.row.end(a) > for (i in 1:nxmK) { + a<-table.row.start(a) + a<-table.element(a,i+K,header=TRUE) + a<-table.element(a,x[i+K]) + a<-table.element(a,fit$fitted[i,'xhat']) + a<-table.element(a,myresid[i]) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/www/html/freestat/rcomp/tmp/5ry3i1280159320.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/www/html/freestat/rcomp/tmp/62pl31280159320.tab") > > try(system("convert tmp/1p5n61280159319.ps tmp/1p5n61280159319.png",intern=TRUE)) character(0) > try(system("convert tmp/2he581280159319.ps tmp/2he581280159319.png",intern=TRUE)) character(0) > try(system("convert tmp/3he581280159319.ps tmp/3he581280159319.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.379 0.698 1.654