R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(21571.00
+ ,21493.00
+ ,21422.00
+ ,21272.00
+ ,22747.00
+ ,22676.00
+ ,21571.00
+ ,20831.00
+ ,20909.00
+ ,20909.00
+ ,20980.00
+ ,21130.00
+ ,21051.00
+ ,21643.00
+ ,21864.00
+ ,21643.00
+ ,22455.00
+ ,21935.00
+ ,20759.00
+ ,20467.00
+ ,20467.00
+ ,20610.00
+ ,20026.00
+ ,20467.00
+ ,20097.00
+ ,20467.00
+ ,21051.00
+ ,21272.00
+ ,21792.00
+ ,21571.00
+ ,20246.00
+ ,19726.00
+ ,19506.00
+ ,19726.00
+ ,19363.00
+ ,19506.00
+ ,19064.00
+ ,19805.00
+ ,20168.00
+ ,20246.00
+ ,21643.00
+ ,21643.00
+ ,19805.00
+ ,19363.00
+ ,19363.00
+ ,19584.00
+ ,18622.00
+ ,18180.00
+ ,17668.00
+ ,17817.00
+ ,18480.00
+ ,17960.00
+ ,19363.00
+ ,19584.00
+ ,18180.00
+ ,17668.00
+ ,17375.00
+ ,17668.00
+ ,16855.00
+ ,16563.00
+ ,15388.00
+ ,15680.00
+ ,15751.00
+ ,15830.00
+ ,17226.00
+ ,17076.00
+ ,15388.00
+ ,14647.00
+ ,14355.00
+ ,14725.00
+ ,13322.00
+ ,12367.00
+ ,10601.00
+ ,10750.00
+ ,10750.00
+ ,10601.00
+ ,11854.00
+ ,11926.00
+ ,10451.00
+ ,10159.00
+ ,9568.00
+ ,10380.00
+ ,8905.00
+ ,8022.00
+ ,6333.00
+ ,6697.00
+ ,6255.00
+ ,6404.00
+ ,7509.00
+ ,7730.00
+ ,6996.00
+ ,6917.00
+ ,6917.00
+ ,7879.00
+ ,6184.00
+ ,5079.00
+ ,3163.00
+ ,4709.00
+ ,4488.00
+ ,4566.00
+ ,6333.00
+ ,6112.00
+ ,5300.00
+ ,5671.00
+ ,5671.00
+ ,6996.00
+ ,5450.00
+ ,4566.00
+ ,3163.00
+ ,5008.00
+ ,4859.00
+ ,4930.00
+ ,6476.00
+ ,6333.00
+ ,5813.00
+ ,5892.00
+ ,6255.00
+ ,7067.00
+ ,5813.00
+ ,4787.00)
> 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: 0.7917443
 beta : 0.01308421
 gamma: 1

Coefficients:
           [,1]
a    6467.97830
b    -103.30982
s1  -2077.07720
s2   -298.72632
s3    -28.19389
s4    376.28886
s5   1841.85028
s6   1568.44798
s7    363.39482
s8    -91.21032
s9   -385.76511
s10   154.53069
s11 -1264.06049
s12 -1680.97830
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1orbl1471289026.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2k37r1471289026.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3z3b41471289026.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/wessaorg/rcomp/tmp/4kyd71471289026.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/wessaorg/rcomp/tmp/57xkv1471289026.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/wessaorg/rcomp/tmp/6bpvb1471289026.tab") 
> 
> try(system("convert tmp/1orbl1471289026.ps tmp/1orbl1471289026.png",intern=TRUE))
character(0)
> try(system("convert tmp/2k37r1471289026.ps tmp/2k37r1471289026.png",intern=TRUE))
character(0)
> try(system("convert tmp/3z3b41471289026.ps tmp/3z3b41471289026.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.469   0.125   1.616