R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: x86_64-redhat-linux-gnu (64-bit)

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> x <- c(13.2,13.8,16.2,14.7,13.9,16.0,14.4,12.3,15.9,15.9,15.5,15.1,14.5,15.1,17.4,16.2,15.6,17.2,14.9,13.8,17.5,16.2,17.5,16.6,16.2,16.6,19.6,15.9,18.0,18.3,16.3,14.9,18.2,18.4,18.5,16.0,17.4,17.2,19.6,17.2,18.3,19.3,18.1,16.2,18.4,20.5,19.0,16.5,18.7,19.0,19.2,20.5,19.3,20.6,20.1,16.1,20.4,19.7,15.6,14.4,13.9,14.3,15.3,14.4,13.8,15.7,14.7,12.5,16.2,16.1,16,15.8,15.2)
> par3 = 'additive'
> 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 additive seasonal component.

Call:
 HoltWinters(x = x, seasonal = par3) 

Smoothing parameters:
 alpha:  0.5827919 
 beta :  0.003477743 
 gamma:  0.1165807 

Coefficients:
           [,1]
a   16.14193455
b    0.08846678
s1  -0.47903959
s2   1.57835254
s3   0.34043614
s4  -0.15659230
s5   1.16966305
s6  -0.40734525
s7  -2.64902147
s8   0.82146046
s9   0.73991834
s10  0.09623682
s11 -0.58136459
s12 -0.87253881
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/wessaorg/rcomp/tmp/1ymcz1294263122.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/wessaorg/rcomp/tmp/28y5w1294263122.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/wessaorg/rcomp/tmp/39sf41294263122.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/www/wessaorg/rcomp/tmp/4eahv1294263122.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/wessaorg/rcomp/tmp/5l9le1294263122.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/wessaorg/rcomp/tmp/61x0y1294263122.tab") 
> try(system("convert tmp/1ymcz1294263122.ps tmp/1ymcz1294263122.png",intern=TRUE))
character(0)
> try(system("convert tmp/28y5w1294263122.ps tmp/28y5w1294263122.png",intern=TRUE))
character(0)
> try(system("convert tmp/39sf41294263122.ps tmp/39sf41294263122.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
   1.32    0.23    2.07