R version 3.0.1 (2013-05-16) -- "Good Sport"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(58896,57616,56232,53708,79784,78524,58896,45848,47112,47112,48372,51040,54968,53708,45848,47112,83716,91572,70664,58896,61548,62828,69404,75856,77260,64088,65476,48372,96888,111200,78524,68016,74596,82452,94220,108656,108656,99412,95484,71928,111200,129564,113848,96888,99412,108656,121704,137420,126896,120444,120444,99412,129564,149188,133492,116516,121704,142612,151856,164888,154380,137420,133492,102080,122968,145260,120444,106008,120444,134756,142612,163624,153120,126896,129564,104744,125636,144000,122968,108656,121704,137420,134756,166168,160976,140068,141332,113848,130824,157048,137420,125636,145260,157048,147928,189724,179340,155784,149188,119056,136140,151856,132212,132212,154380,166168,159696,205420,193652,171484,162240,129564,141332,162240,146524,142612,160976,176672,159696,200228)
> par3 = 'multiplicative'
> par2 = 'Triple'
> par1 = '12'
> par3 <- 'multiplicative'
> par2 <- 'Triple'
> par1 <- '12'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), Exponential Smoothing (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/
> #Source of accompanying publication: 
> #
> 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 multiplicative seasonal component.

Call:
HoltWinters(x = x, seasonal = par3)

Smoothing parameters:
 alpha: 0.2040331
 beta : 0
 gamma: 1

Coefficients:
            [,1]
a   1.489703e+05
b   6.371463e+02
s1  1.313260e+00
s2  1.148501e+00
s3  1.079578e+00
s4  8.580155e-01
s5  9.415964e-01
s6  1.082847e+00
s7  9.739308e-01
s8  9.472203e-01
s9  1.071995e+00
s10 1.170965e+00
s11 1.064452e+00
s12 1.344080e+00
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/fisher/rcomp/tmp/1d7u11377058487.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/fisher/rcomp/tmp/2kc3u1377058487.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/fisher/rcomp/tmp/3ljpt1377058487.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/fisher/rcomp/tmp/4t3n11377058487.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/fisher/rcomp/tmp/5t9mt1377058487.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/fisher/rcomp/tmp/6fmup1377058487.tab") 
> 
> try(system("convert tmp/1d7u11377058487.ps tmp/1d7u11377058487.png",intern=TRUE))
character(0)
> try(system("convert tmp/2kc3u1377058487.ps tmp/2kc3u1377058487.png",intern=TRUE))
character(0)
> try(system("convert tmp/3ljpt1377058487.ps tmp/3ljpt1377058487.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.069   0.443   2.493