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(413491
+ ,399153
+ ,385939
+ ,373917
+ ,364635
+ ,364696
+ ,418358
+ ,428212
+ ,423730
+ ,420677
+ ,417428
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+ ,391116
+ ,443814
+ ,460373
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+ ,515476
+ ,520862
+ ,519517
+ ,511805
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+ ,570158
+ ,591665
+ ,593572
+ ,586346
+ ,586063
+ ,591504
+ ,594033
+ ,585597
+ ,572450
+ ,562917
+ ,554675
+ ,553997
+ ,601310
+ ,622255
+ ,616735
+ ,606480
+ ,595079
+ ,598588
+ ,599917
+ ,591573
+ ,575489
+ ,567223
+ ,555338
+ ,555252
+ ,608249
+ ,630859
+ ,628632
+ ,624435
+ ,609670
+ ,615830
+ ,621170
+ ,604212
+ ,584348
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+ ,555234
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+ ,536322
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+ ,575093
+ ,580112
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+ ,563250
+ ,551531
+ ,537034
+ ,544686
+ ,600991
+ ,604378
+ ,586111
+ ,563668
+ ,548604
+ ,551174
+ ,555654)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> 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:  0.6619994 
 beta :  0.1215102 
 gamma:  1 

Coefficients:
          [,1]
a   547560.322
b    -1659.258
s1   -3696.812
s2  -15192.780
s3  -22323.939
s4  -34568.491
s5  -26459.298
s6   25364.085
s7   30275.550
s8   16231.489
s9    3272.346
s10  -3221.445
s11   5698.944
s12   8093.678
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/rcomp/tmp/1ddy61322561003.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/277651322561003.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/380fx1322561003.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4jgnq1322561004.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/57bia1322561004.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/687ld1322561004.tab") 
> 
> try(system("convert tmp/1ddy61322561003.ps tmp/1ddy61322561003.png",intern=TRUE))
character(0)
> try(system("convert tmp/277651322561003.ps tmp/277651322561003.png",intern=TRUE))
character(0)
> try(system("convert tmp/380fx1322561003.ps tmp/380fx1322561003.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.510   0.040   1.549