R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(5.2
+ ,7.9
+ ,8.7
+ ,8.9
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+ ,18.1
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+ ,13
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+ ,19
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+ ,15.9
+ ,13.6
+ ,9.2
+ ,2.8
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+ ,4.8
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+ ,7.8
+ ,9
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+ ,16.4
+ ,21.8
+ ,17.8
+ ,13.5
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+ ,7.1
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+ ,17.1
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+ ,12.9
+ ,10.9
+ ,5.3
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+ ,-0.2
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+ ,10.3
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+ ,6.2
+ ,7.7
+ ,9.3
+ ,15.6
+ ,16.3
+ ,16.6
+ ,17.4
+ ,15.3
+ ,9.7
+ ,3.7
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+ ,5.4
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+ ,18.3
+ ,16.8
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+ ,23
+ ,16.3
+ ,18.4
+ ,14.2
+ ,9.1
+ ,5.9
+ ,7.2
+ ,6.8
+ ,8
+ ,14.3
+ ,14.6
+ ,17.5
+ ,17.2
+ ,17.2
+ ,14.1
+ ,10.5
+ ,6.8
+ ,4.1
+ ,6.5
+ ,6.1
+ ,6.3
+ ,9.3
+ ,16.4
+ ,16.1
+ ,18
+ ,17.6
+ ,14
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+ ,6.9
+ ,2.8
+ ,0.7
+ ,3.6
+ ,6.7
+ ,12.5
+ ,14.4
+ ,16.5
+ ,18.7
+ ,19.4
+ ,15.8
+ ,11.3
+ ,9.7
+ ,2.9)
> 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:  0.1091090 
 beta :  0.02274475 
 gamma:  0.2455152 

Coefficients:
            [,1]
a   10.477669469
b    0.001426859
s1  -6.568389642
s2  -5.810574792
s3  -3.515777099
s4   0.722910244
s5   4.115438393
s6   6.463704601
s7   8.198709430
s8   7.733528281
s9   4.997400332
s10  1.071603419
s11 -2.670793263
s12 -6.749721861
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/rcomp/tmp/159171293402974.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2g1ia1293402974.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3g1ia1293402974.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/rcomp/tmp/4usgj1293402974.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/rcomp/tmp/5m2x31293402974.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/rcomp/tmp/6qkw91293402974.tab") 
> 
> try(system("convert tmp/159171293402974.ps tmp/159171293402974.png",intern=TRUE))
character(0)
> try(system("convert tmp/2g1ia1293402974.ps tmp/2g1ia1293402974.png",intern=TRUE))
character(0)
> try(system("convert tmp/3g1ia1293402974.ps tmp/3g1ia1293402974.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.559   0.624   3.269