R version 2.10.1 (2009-12-14)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(101.02,101.15,101.51,101.75,101.8,101.8,101.8,101.82,101.99,102.25,102.34,102.35,102.35,102.39,102.49,102.67,102.68,102.7,102.71,102.72,102.83,102.92,103.04,103.08,103.09,103.11,103.18,103.18,103.22,103.25,103.25,103.25,103.47,103.57,103.66,103.7,103.7,103.75,103.85,104.02,104.13,104.17,104.18,104.2,104.5,104.78,104.88,104.89,104.9,104.95,105.24,105.35,105.44,105.46,105.47,105.48,105.75,106.1,106.19,106.23,106.24,106.25,106.35,106.48,106.52,106.55,106.55,106.56,106.89,107.09,107.24,107.28,107.3,107.31,107.47,107.35,107.31,107.32,107.32,107.34,107.53,107.72,107.75,107.79,107.81,107.9,107.8,107.86,107.8,107.74,107.75,107.83,107.8,107.81,107.86,107.83)
> 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:  0.9350373 
 beta :  0 
 gamma:  1 

Coefficients:
             [,1]
a   107.771072298
b     0.074586247
s1    0.005621739
s2   -0.045972165
s3   -0.028211396
s4    0.044196926
s5    0.030587292
s6   -0.008133404
s7   -0.068774376
s8   -0.141340632
s9   -0.059455874
s10   0.078566372
s11   0.112137564
s12   0.058927702
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/yougetitorg/rcomp/tmp/1p6r11295195222.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/yougetitorg/rcomp/tmp/21t0v1295195222.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/yougetitorg/rcomp/tmp/3t46l1295195222.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/yougetitorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/yougetitorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/yougetitorg/rcomp/tmp/4c6v51295195222.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/yougetitorg/rcomp/tmp/5jzbm1295195222.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/yougetitorg/rcomp/tmp/6fjgc1295195222.tab") 
> 
> try(system("convert tmp/1p6r11295195222.ps tmp/1p6r11295195222.png",intern=TRUE))
character(0)
> try(system("convert tmp/21t0v1295195222.ps tmp/21t0v1295195222.png",intern=TRUE))
character(0)
> try(system("convert tmp/3t46l1295195222.ps tmp/3t46l1295195222.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.090   0.670   1.444