R version 2.10.1 (2009-12-14)
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ISBN 3-900051-07-0

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> x <- c(103.6,103.5,110.9,115.8,117.8,121.1,128.7,112.7,111.3,116.2,109.8,137.9,98.7,100.5,128.7,98.7,115,121,125.9,117.3,115,113.8,115.7,145.5,101.7,106.9,116.4,114.6,122.5,120.4,116.5,117,114.3,111.5,117.8,141.5,102.6,103.8,119.8,113.6,121.8,123.9,122.7,120,111.6,117.6,121.3,143.7,107.1,107.7,126.4,111.5,127.9,124.9,122,124.9,113.9,120.8,123.3,143.5,107.1,106.5,114.6,122.2,120.2,123.1,127.1,118.5,116.1,120.6,115.7,146.5,108,106.6,122.2,115.8,115.6,124.5,121.7,118.7,113.7,113.4,115.1,143.9,101,103.4,121.5,111.9,117.4,124.3,122,119.7,115,112.2,115.3,142.6,104.1,105.3,124.4,113.9,124.8,131.8,125.6,125,119.7,116.1,120,148.1,109.2,109.4,135.1,114.9,129,138.5,125.6,130.4,120.3,126.2,127.6,150.9,114.6,118.6,131.4,124.5,136.8,136.8,136.6,131,125.8,129.4,124.8,157.1,116.6,114.2,128.4,127.3,133.5,137.2,137.7,131.2,127.7,133.9,124.3,160.6)
> 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:  0.1247829 
 beta :  0.01790396 
 gamma:  0.6420466 

Coefficients:
           [,1]
a   129.7227185
b     0.1331697
s1    0.9042213
s2    0.9004779
s3    1.0225945
s4    0.9832678
s5    1.0484177
s6    1.0764580
s7    1.0642252
s8    1.0243774
s9    0.9865844
s10   1.0216639
s11   0.9697122
s12   1.2302957
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/yougetitorg/rcomp/tmp/1svl71294395685.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/yougetitorg/rcomp/tmp/200r61294395685.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/yougetitorg/rcomp/tmp/3ky1j1294395685.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/yougetitorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/yougetitorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/yougetitorg/rcomp/tmp/4enzb1294395685.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/yougetitorg/rcomp/tmp/5rses1294395685.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/yougetitorg/rcomp/tmp/67k351294395685.tab") 
> 
> try(system("convert tmp/1svl71294395685.ps tmp/1svl71294395685.png",intern=TRUE))
character(0)
> try(system("convert tmp/200r61294395685.ps tmp/200r61294395685.png",intern=TRUE))
character(0)
> try(system("convert tmp/3ky1j1294395685.ps tmp/3ky1j1294395685.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.450   0.790   2.154