R version 2.10.1 (2009-12-14)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(100.4,97.7,97,96.5,98.4,106.3,103.1,102.4,95,98.1,106.1,99.1,101.2,95.5,99.8,97.1,97.5,96.8,97.7,100.9,94.3,99.5,100.8,97,99.2,101,102.3,97,91.2,97.6,95.7,100.5,94.4,102.9,105.1,98.8,100.7,99.6,107.7,102.9,101.6,102.7,110.5,109.8,94.3,102.5,105,102.3,107.7,100.3,99.5,95,97.7,96.3,97.8,106.4,96.1,106.2,114.7,111.9,121,117.7,115.4,114.3,109.5,108.1,108.2,99.1,101.2,98.1,95.5,97.9,98.2,98.7,95.6,95.8,94.4,96.5,103.3,104.3,104.5,102.3,103.8,103.1,102.2,106.3,102.1,94,102.6,102.6,106.7,107.9,109.3,105.9,109.1,108.5,111.7,109.8,109.1,108.5,108.5,106.2,117.1,109.8,115.2,115.9,119.2,121,118.6,117.6,114.6,110.6,102.5,101.6,107.4,105.8,102.8,104,100.4,100.6)
> 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:  0.6455193 
 beta :  0 
 gamma:  0.6302229 

Coefficients:
          [,1]
a   98.4939230
b   -0.1856061
s1   3.1480016
s2   1.9748743
s3  -0.1238050
s4  -2.7947149
s5  -3.4741706
s6  -2.5999377
s7   3.6658826
s8   1.7838508
s9   0.5913651
s10  0.1467115
s11  1.6215343
s12  2.2846779
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/yougetitorg/rcomp/tmp/1u9sc1295190952.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/yougetitorg/rcomp/tmp/25nik1295190952.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/yougetitorg/rcomp/tmp/3lj0c1295190952.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/yougetitorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/yougetitorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4r8jk1295190952.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/5nj8b1295190952.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/6t1cf1295190952.tab") 
> 
> try(system("convert tmp/1u9sc1295190952.ps tmp/1u9sc1295190952.png",intern=TRUE))
character(0)
> try(system("convert tmp/25nik1295190952.ps tmp/25nik1295190952.png",intern=TRUE))
character(0)
> try(system("convert tmp/3lj0c1295190952.ps tmp/3lj0c1295190952.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.230   0.680   1.579