R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(0.0266,0.0324,0.0305,0.0298,0.0201,0.0174,0.0118,0.0140,0.0128,0.0134,0.0111,0.0094,0.0121,0.0092,0.0134,0.0135,0.0147,0.0111,0.0160,0.0147,0.0164,0.0167,0.0156,0.0172,0.0160,0.0156,0.0131,0.0110,0.0158,0.0188,0.0161,0.0173,0.0163,0.0143,0.0209,0.0189,0.0172,0.0178,0.0200,0.0252,0.0209,0.0213,0.0232,0.0242,0.0241,0.0225,0.0172,0.0204,0.0233,0.0201,0.0196,0.0133,0.0173,0.0187,0.0168,0.0158,0.0169,0.0178,0.0191,0.0185,0.0186,0.0204,0.0208,0.0194,0.0191,0.0134,0.0130,0.0138,0.0124,0.0130,0.0179,0.0224,0.0264,0.0279,0.0308,0.0388,0.0370,0.0461,0.0507,0.0522,0.0493,0.0515,0.0480,0.0390,0.0354,0.0334,0.0280,0.0160,0.0153,0.0069,-0.0010,-0.0066,-0.0020,-0.0062,-0.0058,-0.0031,-0.0025,-0.0009,0.0013,0.0094,0.0105,0.0158,0.0202,0.0216,0.0206,0.0256,0.0254,0.0253,0.0260,0.0272,0.0281,0.0292,0.0287,0.0289,0.0327,0.0333,0.0314,0.0303,0.0309,0.0339)
> par3 = 'additive'
> par2 = 'Single'
> 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 without trend and without seasonal component.

Call:
 HoltWinters(x = x, beta = F, gamma = F) 

Smoothing parameters:
 alpha:  0.9999567 
 beta :  FALSE 
 gamma:  FALSE 

Coefficients:
        [,1]
a 0.03389987
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/rcomp/tmp/1ht591323887285.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/2xl8m1323887285.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/33lh31323887285.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/rcomp/tmp/4ujd21323887285.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/rcomp/tmp/5h2st1323887285.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/rcomp/tmp/6efse1323887285.tab") 
> 
> try(system("convert tmp/1ht591323887285.ps tmp/1ht591323887285.png",intern=TRUE))
character(0)
> try(system("convert tmp/2xl8m1323887285.ps tmp/2xl8m1323887285.png",intern=TRUE))
character(0)
> try(system("convert tmp/33lh31323887285.ps tmp/33lh31323887285.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.300   0.070   1.369