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(14.458,13.594,17.814,20.235,21.811,21.439,21.393,19.831,20.468,21.080,21.600,17.390,17.848,19.592,21.092,20.899,25.890,24.965,22.225,20.977,22.897,22.785,22.769,19.637,20.203,20.450,23.083,21.738,26.766,25.280,22.574,22.729,21.378,22.902,24.989,21.116,15.169,15.846,20.927,18.273,22.538,15.596,14.034,11.366,14.861,15.149,13.577,13.026,13.190,13.196,15.826,14.733,16.307,15.703,14.589,12.043,15.057,14.053,12.698,10.888,10.045,11.549,13.767,12.434,13.116,14.211,12.266,12.602,15.714,13.742,12.745,10.491,10.057,10.900,11.771,11.992,11.933,14.504,11.727,11.477,13.578,11.555,11.846,11.397,10.066,10.269,14.279,13.870,13.695,14.420,11.424,9.704,12.464,14.301,13.464,9.893,11.572,12.380,16.692,16.052,16.459,14.761,13.654,13.480,18.068,16.560,14.530,10.650,11.651,13.735,13.360,17.818,20.613,16.231,13.862,12.004,17.734,15.034,12.609,12.320,10.833,11.350,13.648,14.890,16.325,18.045,15.616,11.926,16.855,15.083,12.520,12.355)
> 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:  0.4804213 
 beta :  0.01992378 
 gamma:  0.4955172 

Coefficients:
             [,1]
a   14.3859483282
b    0.0006487139
s1  -2.8055130085
s2  -1.9681784328
s3   0.0777545472
s4   0.8540615295
s5   1.8318978352
s6   1.1007442395
s7  -1.0226923338
s8  -2.5323533331
s9   2.0257064850
s10  0.4457638728
s11 -1.0811282357
s12 -2.2394371654
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/rcomp/tmp/1e4q91293204709.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/27w7c1293204709.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/37w7c1293204709.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4gkfw1293204709.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/5rcxi1293204709.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/6hf2c1293204709.tab") 
> 
> try(system("convert tmp/1e4q91293204709.ps tmp/1e4q91293204709.png",intern=TRUE))
character(0)
> try(system("convert tmp/27w7c1293204709.ps tmp/27w7c1293204709.png",intern=TRUE))
character(0)
> try(system("convert tmp/37w7c1293204709.ps tmp/37w7c1293204709.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.994   0.562   2.476