R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(95320.00
+ ,94965.00
+ ,94605.00
+ ,93860.00
+ ,101230.00
+ ,100840.00
+ ,95320.00
+ ,91650.00
+ ,92005.00
+ ,92005.00
+ ,92400.00
+ ,93110.00
+ ,94215.00
+ ,94215.00
+ ,93505.00
+ ,91650.00
+ ,101230.00
+ ,102690.00
+ ,100485.00
+ ,95320.00
+ ,97530.00
+ ,94215.00
+ ,95710.00
+ ,96425.00
+ ,97170.00
+ ,95320.00
+ ,95710.00
+ ,93110.00
+ ,101230.00
+ ,103795.00
+ ,101590.00
+ ,97530.00
+ ,101945.00
+ ,97170.00
+ ,101590.00
+ ,101230.00
+ ,102335.00
+ ,98275.00
+ ,102690.00
+ ,102335.00
+ ,108960.00
+ ,107465.00
+ ,101590.00
+ ,98630.00
+ ,102690.00
+ ,97170.00
+ ,101230.00
+ ,101945.00
+ ,103440.00
+ ,100130.00
+ ,101945.00
+ ,103050.00
+ ,107110.00
+ ,103795.00
+ ,99380.00
+ ,94605.00
+ ,99025.00
+ ,86875.00
+ ,92755.00
+ ,96065.00
+ ,99380.00
+ ,94605.00
+ ,94605.00
+ ,94605.00
+ ,97170.00
+ ,93505.00
+ ,88695.00
+ ,84670.00
+ ,87590.00
+ ,76190.00
+ ,83175.00
+ ,87235.00
+ ,87980.00
+ ,83920.00
+ ,84275.00
+ ,83175.00
+ ,86875.00
+ ,84275.00
+ ,79150.00
+ ,75445.00
+ ,81710.00
+ ,68105.00
+ ,76940.00
+ ,80965.00
+ ,80965.00
+ ,76190.00
+ ,71775.00
+ ,71420.00
+ ,75445.00
+ ,71775.00
+ ,64795.00
+ ,59985.00
+ ,65150.00
+ ,53005.00
+ ,64045.00
+ ,69920.00
+ ,71775.00
+ ,67715.00
+ ,62585.00
+ ,66255.00
+ ,67715.00
+ ,66610.00
+ ,55565.00
+ ,50440.00
+ ,54105.00
+ ,43065.00
+ ,54465.00
+ ,58525.00
+ ,61835.00
+ ,56315.00
+ ,51150.00
+ ,54105.00
+ ,55565.00
+ ,52645.00
+ ,41605.00
+ ,36795.00
+ ,41210.00
+ ,29065.00
+ ,42315.00
+ ,50440.00)
> 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: 0.6590048
 beta : 0
 gamma: FALSE

Coefficients:
      [,1]
a 46407.68
b  -355.00
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/13j1z1439761444.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2ah6t1439761444.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/38tss1439761444.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/46xc01439761444.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/5qdix1439761444.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/6t2uh1439761444.tab") 
> 
> try(system("convert tmp/13j1z1439761444.ps tmp/13j1z1439761444.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ah6t1439761444.ps tmp/2ah6t1439761444.png",intern=TRUE))
character(0)
> try(system("convert tmp/38tss1439761444.ps tmp/38tss1439761444.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.379   0.235   1.607