R version 2.12.1 (2010-12-16)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: x86_64-redhat-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

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(96.1,96.5,96.9,97.8,98.9,100.2,101.2,101,101.6,102.4,103.7,103.7,104.6,104.5,104.5,105.6,106.1,107.6,107.7,108.3,108.1,108.1,108,108.2,108.9,109.8,109.9,109.8,110.9,111.1,112.2,112.7,114.6,114.2,114.7,114.7,116,116.3,116.4,116.6,118.1,117.2,108.3,109.5,110.5,110.6,111.2,111.1,111,112.4,112.5,112.4,111.8,111.6,112.9,112.8,113.7,113.8,114,113.8,113.9,114.4,114.4,114.5,113.8,114.3,115,115.4,115.3,114.9,114.3,114.5,115.5,115.8,115.8,116,114.9,114.1,114.1,113.5,115,114.7,115.4,116.1,116.6,117.2,118.2,118,117.7,118.5,117.5,118,117.7,116.3,115,115.7,113.6,114.8,114.9,117.3,117.3,117.7,120,119.6,119.2,117.3,117.5,119,112.5,118.9,118.4,119.4,120.6,118.6,122,122.6,120.6,117.4,116.4,122.2,121,122.4,124.9,126.1,124.5,123.2,126.4,123.9,116,126.6,125.9,126.6,116.7,126.4,129,128.7,128.4,129.2,133.3,128.9,132.7,127.7,131.8,133.9)
> 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:  0.4883475 
 beta :  0.01228837 
 gamma:  FALSE 

Coefficients:
         [,1]
a 132.5170302
b   0.2902489
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/wessaorg/rcomp/tmp/1p59o1295220085.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/wessaorg/rcomp/tmp/29rbk1295220085.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/wessaorg/rcomp/tmp/325jp1295220085.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/www/wessaorg/rcomp/tmp/43pkc1295220085.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/wessaorg/rcomp/tmp/5vlzn1295220085.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/wessaorg/rcomp/tmp/6g7z41295220085.tab") 
> 
> try(system("convert tmp/1p59o1295220085.ps tmp/1p59o1295220085.png",intern=TRUE))
character(0)
> try(system("convert tmp/29rbk1295220085.ps tmp/29rbk1295220085.png",intern=TRUE))
character(0)
> try(system("convert tmp/325jp1295220085.ps tmp/325jp1295220085.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.340   0.130   1.513