R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(8.64
+ ,8.89
+ ,8.87
+ ,8.81
+ ,8.87
+ ,9.06
+ ,9.12
+ ,8.66
+ ,8.17
+ ,8.04
+ ,7.71
+ ,7.55
+ ,7.52
+ ,7.38
+ ,7.52
+ ,7.31
+ ,6.92
+ ,7.09
+ ,7.05
+ ,7.37
+ ,7.05
+ ,6.79
+ ,6.35
+ ,6.44
+ ,6.89
+ ,7.16
+ ,7.46
+ ,7.91
+ ,7.86
+ ,8.02
+ ,8.38
+ ,8.50
+ ,8.40
+ ,8.24
+ ,8.33
+ ,8.28
+ ,8.15
+ ,8.06
+ ,7.79
+ ,7.28
+ ,7.52
+ ,7.23
+ ,7.13
+ ,7.21
+ ,6.99
+ ,6.77
+ ,6.69
+ ,6.39
+ ,6.85
+ ,6.74
+ ,6.56
+ ,6.62
+ ,6.71
+ ,6.67
+ ,6.54
+ ,6.14
+ ,6.13
+ ,5.86
+ ,5.88
+ ,5.75
+ ,5.53
+ ,5.86
+ ,5.90
+ ,5.95
+ ,5.69
+ ,5.53
+ ,5.71
+ ,5.60
+ ,5.73
+ ,5.60
+ ,5.41
+ ,5.13
+ ,5.00
+ ,5.04
+ ,5.10
+ ,4.96
+ ,4.90
+ ,4.80
+ ,4.48
+ ,4.29
+ ,4.27
+ ,4.18
+ ,4.02
+ ,3.82
+ ,4.13
+ ,4.16
+ ,3.98
+ ,4.26
+ ,4.70
+ ,4.96
+ ,5.13
+ ,5.35
+ ,5.41
+ ,5.42
+ ,5.51
+ ,5.75
+ ,5.67
+ ,5.46
+ ,5.56
+ ,5.56
+ ,5.54
+ ,5.53
+ ,5.65
+ ,5.58
+ ,5.57
+ ,5.36
+ ,5.23
+ ,5.11
+ ,5.07
+ ,5.04
+ ,5.34
+ ,5.43
+ ,5.31
+ ,5.12
+ ,4.97
+ ,5.00
+ ,4.64
+ ,4.80
+ ,5.10
+ ,5.11
+ ,5.12
+ ,5.36
+ ,5.26
+ ,5.27
+ ,5.10
+ ,4.94
+ ,4.68
+ ,4.41
+ ,4.60
+ ,4.53
+ ,4.18
+ ,4.00
+ ,3.87
+ ,4.09
+ ,4.13
+ ,3.74
+ ,3.81
+ ,4.11
+ ,4.14
+ ,3.99
+ ,4.28
+ ,4.37
+ ,4.24
+ ,4.19
+ ,4.01
+ ,3.95
+ ,4.30
+ ,4.37
+ ,4.40
+ ,4.29
+ ,4.12
+ ,4.07
+ ,3.93
+ ,3.79
+ ,3.67
+ ,3.53
+ ,3.69
+ ,3.69
+ ,3.48
+ ,3.31
+ ,3.16
+ ,3.25
+ ,3.14
+ ,3.19
+ ,3.43
+ ,3.45
+ ,3.31
+ ,3.51
+ ,3.53
+ ,3.83
+ ,4.02
+ ,3.99
+ ,4.11
+ ,3.96
+ ,3.83
+ ,3.71
+ ,3.81
+ ,3.73
+ ,3.99
+ ,4.17
+ ,4.00
+ ,4.10
+ ,4.24
+ ,4.45
+ ,4.62
+ ,4.49
+ ,4.45
+ ,4.49
+ ,4.36
+ ,4.32
+ ,4.45
+ ,4.13
+ ,4.14
+ ,4.30
+ ,4.42
+ ,4.67
+ ,4.96
+ ,4.73
+ ,4.52
+ ,4.36
+ ,4.15
+ ,3.92
+ ,3.88
+ ,4.20
+ ,3.95
+ ,3.78
+ ,3.69
+ ,3.77
+ ,3.66
+ ,3.53
+ ,3.50
+ ,3.14
+ ,3.42
+ ,3.30
+ ,2.81
+ ,3.15
+ ,3.37
+ ,4.05
+ ,4.00
+ ,4.20
+ ,4.21
+ ,4.24
+ ,4.24
+ ,4.17
+ ,4.12
+ ,4.35
+ ,3.98
+ ,3.62
+ ,4.39
+ ,5.01
+ ,4.07
+ ,3.70
+ ,3.59
+ ,3.44
+ ,3.33
+ ,2.98
+ ,3.14
+ ,2.55
+ ,2.49
+ ,2.53
+ ,2.43)
> par3 = 'additive'
> par2 = 'Single'
> par1 = '12'
> par3 <- 'additive'
> par2 <- 'Single'
> 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 without trend and without seasonal component.

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

Smoothing parameters:
 alpha:  0.9999224 
 beta :  FALSE 
 gamma:  FALSE 

Coefficients:
      [,1]
a 2.430008
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1im0b1353592076.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2zzyx1353592076.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/345h31353592076.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/wessaorg/rcomp/tmp/4f8k81353592076.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/wessaorg/rcomp/tmp/5z1e11353592076.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/wessaorg/rcomp/tmp/6r4x81353592076.tab") 
> 
> try(system("convert tmp/1im0b1353592076.ps tmp/1im0b1353592076.png",intern=TRUE))
character(0)
> try(system("convert tmp/2zzyx1353592076.ps tmp/2zzyx1353592076.png",intern=TRUE))
character(0)
> try(system("convert tmp/345h31353592076.ps tmp/345h31353592076.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.932   0.583   4.471