R version 3.3.2 (2016-10-31) -- "Sincere Pumpkin Patch"
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Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(1.56,1.56,1.54,1.54,1.54,1.54,1.57,1.58,1.57,1.57,1.57,1.57,1.56,1.58,1.58,1.58,1.58,1.53,1.48,1.48,1.48,1.48,1.48,1.57,1.57,1.57,1.60,1.60,1.65,1.71,1.71,1.71,1.74,1.78,1.84,1.84,1.76,1.72,1.66,1.65,1.66,1.66,1.66,1.61,1.55,1.56,1.55,1.55,1.61,1.54,1.48,1.42,1.42,1.42,1.43,1.46,1.50,1.47,1.43,1.42,1.39,1.37,1.38,1.51,1.47,1.47,1.53,1.55,1.50,1.52,1.53,1.53,1.52,1.60,1.52,1.64,1.63,1.69,1.73,1.69,1.61,1.52,1.55,1.56,1.56,1.56,1.54,1.53,1.54,1.48,1.38,1.34,1.28,1.28,1.30,1.31,1.31,1.31,1.32,1.31,1.27,1.24,1.24,1.24,1.24,1.24,1.24,1.24,1.23,1.26,1.28,1.32,1.40,1.41,1.37,1.33,1.33,1.34,1.34,1.38,1.43,1.39,1.33,1.33,1.34,1.38,1.37,1.38,1.31,1.38,1.30,1.30,1.29,1.31,1.31,1.32,1.31,1.30,1.31,1.33,1.34,1.42,1.42,1.36,1.36,1.34,1.34,1.33,1.31,1.25,1.23,1.17,1.19,1.19,1.19,1.19)
> par3 = 'additive'
> par2 = 'Double'
> par1 = '12'
> par3 <- 'additive'
> par2 <- 'Double'
> par1 <- '12'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), Exponential Smoothing (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/
> #Source of accompanying publication: 
> #
> 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
 gamma: FALSE

Coefficients:
  [,1]
a 1.19
b 0.00
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1m6b51483978252.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2cuf71483978252.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3px4q1483978252.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4lcr91483978252.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/5f6si1483978252.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/65l371483978252.tab") 
> 
> try(system("convert tmp/1m6b51483978252.ps tmp/1m6b51483978252.png",intern=TRUE))
character(0)
> try(system("convert tmp/2cuf71483978252.ps tmp/2cuf71483978252.png",intern=TRUE))
character(0)
> try(system("convert tmp/3px4q1483978252.ps tmp/3px4q1483978252.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.669   0.112   1.799