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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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(8.82000
+ ,8.80000
+ ,8.82000
+ ,8.58000
+ ,8.54000
+ ,8.42000
+ ,8.43000
+ ,8.44000
+ ,8.09000
+ ,7.69000
+ ,7.56000
+ ,7.54000
+ ,7.40000
+ ,7.39000
+ ,7.37000
+ ,7.31000
+ ,7.35000
+ ,7.26000
+ ,7.37000
+ ,7.35000
+ ,7.33000
+ ,7.32000
+ ,7.31000
+ ,7.33000
+ ,7.32000
+ ,7.27000
+ ,7.48000
+ ,7.70000
+ ,7.77000
+ ,7.80000
+ ,7.84000
+ ,7.81000
+ ,7.78000
+ ,7.82000
+ ,7.80000
+ ,7.81000
+ ,7.80000
+ ,7.66000
+ ,7.41000
+ ,7.35000
+ ,7.39000
+ ,7.32000
+ ,7.32000
+ ,7.30000
+ ,7.29000
+ ,7.26000
+ ,7.22000
+ ,7.21000
+ ,7.21000
+ ,7.21000
+ ,7.20000
+ ,7.19000
+ ,7.18000
+ ,7.12000
+ ,7.12000
+ ,7.07000
+ ,7.08000
+ ,7.05000
+ ,7.06000
+ ,7.07000
+ ,7.08000
+ ,7.08000
+ ,7.09000
+ ,7.07000
+ ,7.06000
+ ,6.99000
+ ,6.99000
+ ,6.99000
+ ,6.98000
+ ,6.96000
+ ,6.95000
+ ,6.91000
+ ,6.91000
+ ,6.87000
+ ,6.91000
+ ,6.89000
+ ,6.88000
+ ,6.90000
+ ,6.91000
+ ,6.85000
+ ,6.86000
+ ,6.82000
+ ,6.80000
+ ,6.83000
+ ,6.84000
+ ,6.89000
+ ,7.14000
+ ,7.21000
+ ,7.25000
+ ,7.31000
+ ,7.30000
+ ,7.48000
+ ,7.49000
+ ,7.40000
+ ,7.44000
+ ,7.42000
+ ,7.14000
+ ,7.24000
+ ,7.33000
+ ,7.61000
+ ,7.66000
+ ,7.69000
+ ,7.70000
+ ,7.68000
+ ,7.71000
+ ,7.71000
+ ,7.72000
+ ,7.68000
+ ,7.72000
+ ,7.74000
+ ,7.76000
+ ,7.90000
+ ,7.97000
+ ,7.96000
+ ,7.95000
+ ,7.97000
+ ,7.93000
+ ,7.99000
+ ,7.96000
+ ,7.92000
+ ,7.97000
+ ,7.98000
+ ,8.00000
+ ,8.04000
+ ,8.17000
+ ,8.29000
+ ,8.26000
+ ,8.30000
+ ,8.32000
+ ,8.28000
+ ,8.27000
+ ,8.32000)
> par3 = 'additive'
> par2 = 'Double'
> 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 without seasonal component.

Call:
 HoltWinters(x = x, gamma = F) 

Smoothing parameters:
 alpha:  1 
 beta :  0.1788142 
 gamma:  FALSE 

Coefficients:
        [,1]
a 8.32000000
b 0.02200378
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/rcomp/tmp/1kyih1264535347.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2eni61264535347.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3xawb1264535347.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4lk091264535347.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/55jj01264535347.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/6fdc61264535347.tab") 
> 
> try(system("convert tmp/1kyih1264535347.ps tmp/1kyih1264535347.png",intern=TRUE))
character(0)
> try(system("convert tmp/2eni61264535347.ps tmp/2eni61264535347.png",intern=TRUE))
character(0)
> try(system("convert tmp/3xawb1264535347.ps tmp/3xawb1264535347.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.987   0.515   1.327