R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(0.8800,1.0300,0.6900,0.7100,1.1100,1.0500,1.0300,0.6500,0.5900,0.7700,0.9000,1.2600,0.9600,0.8300,0.8700,0.7900,1.1200,0.8800,0.6400,0.6400,0.5800,0.5000,0.9900,1.0700,0.8900,0.8900,0.8300,0.8600,0.9000,1.1200,0.8800,0.8800,0.8900,0.8200,0.8800,0.8100,0.8800,0.7600,1.1300,0.8500,1.4500,1.5500,0.7100,0.8100,0.8300,0.7300,0.9000,0.9400,1.7800,0.8800,1.0400,0.8300,1.4100,0.9600,1.3000,0.8300,1.4000,0.9100,0.8700,0.9700,1.1900,1.2300,1.3300,1.1700,1.0900,0.6300,0.8900,0.6300,1.5100,0.9700,0.8400,0.9200,0.9500,0.7300,1.0200,0.7900,1.2700,0.9500,0.7500,0.5200,0.9500,0.8200,0.7600,1.2400,0.9400,1.0400,1.8100,0.9500,1.3900,0.8600,1.1500,1.5100,0.6000,0.7200,1.1000,1.6200,1.8400,1.7300,1.3600,1.0700,1.0000,1.4900,0.9000,1.4300,1.5400,0.8100,1.6100,1.3000,1.4000,1.0300,0.7900,1.1100,1.1500,1.0300,1.5900,1.1100,1.3300,0.9300,1.0700,1.1400,1.1200,0.8600,0.8200,1.0200,1.0700,1.3100,0.9800,0.8900,0.8000,0.8000,0.7800,0.9700)
> 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: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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=0, beta=0)
> if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
> if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
> fit
Holt-Winters exponential smoothing without trend and with additive seasonal component.

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

Smoothing parameters:
 alpha:  0.1232153 
 beta :  0 
 gamma:  0.1722167 

Coefficients:
           [,1]
a    0.96405700
s1   0.16649005
s2  -0.02462520
s3   0.03335548
s4  -0.07053026
s5   0.14769389
s6   0.06322660
s7   0.02481600
s8  -0.08730384
s9  -0.04369859
s10 -0.22707706
s11 -0.04773372
s12  0.12835175
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/freestat/rcomp/tmp/180441250618238.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/218ss1250618238.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/3twon1250618238.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4nin61250618238.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/52rcw1250618238.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/6v5ow1250618238.tab") 
> 
> system("convert tmp/180441250618238.ps tmp/180441250618238.png")
> system("convert tmp/218ss1250618238.ps tmp/218ss1250618238.png")
> system("convert tmp/3twon1250618238.ps tmp/3twon1250618238.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.347   0.761   1.466