R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(1.6,2,2.6,3,2.6,2.9,2.5,2.4,1.5,1.1,0.6,0.9,1.1,1.5,1.7,1.2,0.4,-0.7,-1.4,-1.6,-1.2,-0.4,-0.2,-0.3,-0.5,0,-0.5,0.2,0.7,1.6,2.6,3.3,3.3,3.2,3.5,3.9,4.5,4.6,6.6,7.1,8.9,8.8,8.5,7.6,7.5,7.5,6.1,6.3,8.4,7.1,5.6,4.2,2.1,1.2,0.9,1.4,1.7,1.7,1.9,1.3,-0.7,0.3,0.8,0.9,1.1,2.5,2.7,3.3,4.2,3.8,3.8,3.2,2.9,1.9,1.7,1.6,1.7,1.2,0.7,-0.2,-1.5,-1.2,-1,0,-0.6,0.7,1.3,0.8,1,0.5,0.3,1,1,1.1,1.5,1.5,2,1.7,0.6,1.2,1.5,2.1,3.2,3.9,4.6,4.2,4.4,3.7,3.7,2.8,2.9,3.9,3.1,3,2.8,2.4,2.1,3.1,3,3.1,3.3,3.3,3.8,3.1,3.9,4,4.4,3.7,3.6,3.4,2.8,2.8,2.6,3.3,2.4,1.6,0.7,0,-1.1,-1.2,-1.3,-1.6,-1.3,-1.6,-1.1,-1,0.3,1.2,0.7,1.1,2.1,2.5,2.3,2.3,2.6,3.2,2.2,2.7,2.2,1.4,2.4,2,1.3,1.1,1.4,1.8,1.9,1.6)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> 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:  0.8737744 
 beta :  0.01385323 
 gamma:  1 

Coefficients:
           [,1]
a    2.06531708
b   -0.02067273
s1  -0.54368887
s2  -0.04576534
s3   0.38147603
s4   0.67823839
s5   0.82411218
s6   0.42779464
s7   0.22224699
s8   0.24985159
s9   0.23651378
s10  0.11144848
s11 -0.18806450
s12 -0.46531708
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1rc571356290082.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/222rg1356290082.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/39jaj1356290082.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4m2fm1356290082.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/5dack1356290082.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/60xdu1356290082.tab") 
> 
> try(system("convert tmp/1rc571356290082.ps tmp/1rc571356290082.png",intern=TRUE))
character(0)
> try(system("convert tmp/222rg1356290082.ps tmp/222rg1356290082.png",intern=TRUE))
character(0)
> try(system("convert tmp/39jaj1356290082.ps tmp/39jaj1356290082.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.234   0.281   2.557