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(209704.00
+ ,208923.00
+ ,208131.00
+ ,206492.00
+ ,222706.00
+ ,221848.00
+ ,209704.00
+ ,201630.00
+ ,202411.00
+ ,202411.00
+ ,203280.00
+ ,204842.00
+ ,207273.00
+ ,207273.00
+ ,205711.00
+ ,201630.00
+ ,222706.00
+ ,225918.00
+ ,221067.00
+ ,209704.00
+ ,214566.00
+ ,207273.00
+ ,210562.00
+ ,212135.00
+ ,213774.00
+ ,209704.00
+ ,210562.00
+ ,204842.00
+ ,222706.00
+ ,228349.00
+ ,223498.00
+ ,214566.00
+ ,224279.00
+ ,213774.00
+ ,223498.00
+ ,222706.00
+ ,225137.00
+ ,216205.00
+ ,225918.00
+ ,225137.00
+ ,239712.00
+ ,236423.00
+ ,223498.00
+ ,216986.00
+ ,225918.00
+ ,213774.00
+ ,222706.00
+ ,224279.00
+ ,227568.00
+ ,220286.00
+ ,224279.00
+ ,226710.00
+ ,235642.00
+ ,228349.00
+ ,218636.00
+ ,208131.00
+ ,217855.00
+ ,191125.00
+ ,204061.00
+ ,211343.00
+ ,218636.00
+ ,208131.00
+ ,208131.00
+ ,208131.00
+ ,213774.00
+ ,205711.00
+ ,195129.00
+ ,186274.00
+ ,192698.00
+ ,167618.00
+ ,182985.00
+ ,191917.00
+ ,193556.00
+ ,184624.00
+ ,185405.00
+ ,182985.00
+ ,191125.00
+ ,185405.00
+ ,174130.00
+ ,165979.00
+ ,179762.00
+ ,149831.00
+ ,169268.00
+ ,178123.00
+ ,178123.00
+ ,167618.00
+ ,157905.00
+ ,157124.00
+ ,165979.00
+ ,157905.00
+ ,142549.00
+ ,131967.00
+ ,143330.00
+ ,116611.00
+ ,140899.00
+ ,153824.00
+ ,157905.00
+ ,148973.00
+ ,137687.00
+ ,145761.00
+ ,148973.00
+ ,146542.00
+ ,122243.00
+ ,110968.00
+ ,119031.00
+ ,94743.00
+ ,119823.00
+ ,128755.00
+ ,136037.00
+ ,123893.00
+ ,112530.00
+ ,119031.00
+ ,122243.00
+ ,115819.00
+ ,91531.00
+ ,80949.00
+ ,90662.00
+ ,63943.00
+ ,93093.00
+ ,110968.00)
> 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 102096.9
b   -781.0
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1bizv1439472238.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2tz571439472238.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3nfug1439472238.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4gzxw1439472238.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/5e6tx1439472238.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/6gdcb1439472238.tab") 
> 
> try(system("convert tmp/1bizv1439472238.ps tmp/1bizv1439472238.png",intern=TRUE))
character(0)
> try(system("convert tmp/2tz571439472238.ps tmp/2tz571439472238.png",intern=TRUE))
character(0)
> try(system("convert tmp/3nfug1439472238.ps tmp/3nfug1439472238.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.372   0.225   1.605