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(93.2
+ ,96
+ ,95.2
+ ,77.1
+ ,70.9
+ ,64.8
+ ,70.1
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+ ,79.5
+ ,100.6
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+ ,102.8
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+ ,94.4
+ ,113
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+ ,132.7
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+ ,157.7
+ ,137.2
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+ ,98.7
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+ ,151.7
+ ,129.4
+ ,174.1
+ ,197
+ ,193.9
+ ,164.1
+ ,142.8
+ ,157.9
+ ,159.2
+ ,162.2
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+ ,169.4
+ ,168.8
+ ,158.1
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+ ,149.3
+ ,143.4
+ ,142.2
+ ,188.4
+ ,166.2
+ ,199.2
+ ,182.7
+ ,145.2
+ ,182.1
+ ,158.7
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+ ,139.6
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+ ,198.6
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+ ,179.7
+ ,157
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+ ,156.6
+ ,166.7
+ ,156.8
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+ ,160.7
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+ ,166.5
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+ ,151.2
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+ ,148.2
+ ,153.5
+ ,145.1
+ ,183.7
+ ,210.5
+ ,203.3
+ ,153.3
+ ,144.3
+ ,169.6
+ ,143.7
+ ,160.1
+ ,135.6
+ ,141.8
+ ,159.9
+ ,145.7
+ ,183.5
+ ,198.2
+ ,186.8
+ ,172
+ ,150.6
+ ,163.3
+ ,153.7
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+ ,135.5
+ ,148.5
+ ,148.4
+ ,133.6
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+ ,208.6
+ ,197.3
+ ,164.4
+ ,148.1
+ ,152
+ ,144.1
+ ,155
+ ,124.5
+ ,153
+ ,146
+ ,138
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+ ,147
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+ ,150
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+ ,145
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+ ,137
+ ,129
+ ,128
+ ,140
+ ,143
+ ,151
+ ,177
+ ,184
+ ,151
+ ,134
+ ,164
+ ,126
+ ,131
+ ,125
+ ,127
+ ,143
+ ,143
+ ,160
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+ ,138
+ ,136
+ ,152
+ ,127
+ ,151
+ ,130
+ ,119
+ ,153)
> par3 = 'multiplicative'
> par2 = 'Double'
> 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 without seasonal component.

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

Smoothing parameters:
 alpha:  0.6920957 
 beta :  0.00660408 
 gamma:  FALSE 

Coefficients:
          [,1]
a 144.02420839
b   0.09031428
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/rcomp/tmp/1wz1x1275894895.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/2jnbu1275894895.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/3jnbu1275894895.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4xx9l1275894895.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/51yp81275894895.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/6t77t1275894895.tab") 
> 
> try(system("convert tmp/1wz1x1275894895.ps tmp/1wz1x1275894895.png",intern=TRUE))
character(0)
> try(system("convert tmp/2jnbu1275894895.ps tmp/2jnbu1275894895.png",intern=TRUE))
character(0)
> try(system("convert tmp/3jnbu1275894895.ps tmp/3jnbu1275894895.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.100   0.840   3.175