R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(29054.50
+ ,28543.50
+ ,28032.00
+ ,27009.50
+ ,37356.00
+ ,36844.50
+ ,29054.50
+ ,23881.50
+ ,24392.50
+ ,24392.50
+ ,24904.00
+ ,25982.00
+ ,22859.00
+ ,19731.00
+ ,17169.50
+ ,17169.50
+ ,27009.50
+ ,28032.00
+ ,20242.00
+ ,11429.50
+ ,16091.50
+ ,16091.50
+ ,19731.00
+ ,21831.50
+ ,21320.00
+ ,16091.50
+ ,18708.50
+ ,17681.00
+ ,26493.50
+ ,24392.50
+ ,16091.50
+ ,9891.00
+ ,15580.00
+ ,17169.50
+ ,18708.50
+ ,20753.50
+ ,16602.50
+ ,13019.00
+ ,14558.00
+ ,15069.00
+ ,28543.50
+ ,28543.50
+ ,20753.50
+ ,19731.00
+ ,22859.00
+ ,21320.00
+ ,25471.00
+ ,30644.00
+ ,31671.50
+ ,24392.50
+ ,22342.50
+ ,20242.00
+ ,34283.50
+ ,35311.00
+ ,32694.00
+ ,35311.00
+ ,34794.50
+ ,30644.00
+ ,35311.00
+ ,40484.00
+ ,42584.50
+ ,36333.50
+ ,32182.50
+ ,35311.00
+ ,48785.00
+ ,52936.00
+ ,51913.50
+ ,53958.00
+ ,53447.00
+ ,48274.00
+ ,57086.50
+ ,59187.00
+ ,62259.50
+ ,52936.00
+ ,49296.50
+ ,53447.00
+ ,63337.50
+ ,72150.00
+ ,70049.50
+ ,70049.50
+ ,71077.00
+ ,67488.00
+ ,76817.00
+ ,76817.00
+ ,75227.50
+ ,66410.00
+ ,67999.50
+ ,69027.00
+ ,75789.50
+ ,84602.00
+ ,78350.50
+ ,81479.00
+ ,78862.00
+ ,77328.00
+ ,89269.00
+ ,86652.00
+ ,83012.50
+ ,77839.50
+ ,83012.50
+ ,85629.50
+ ,88752.50
+ ,92903.00
+ ,88752.50
+ ,91314.00
+ ,88190.50
+ ,87679.50
+ ,100642.50
+ ,101720.50
+ ,97570.00
+ ,90291.50
+ ,96492.00
+ ,99104.00
+ ,102232.00
+ ,106894.00
+ ,102232.00
+ ,105871.50
+ ,104282.00
+ ,98592.50
+ ,110533.00
+ ,110533.00)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> par3 <- 'additive'
> par2 <- 'Triple'
> 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 additive seasonal component.

Call:
HoltWinters(x = x, seasonal = par3)

Smoothing parameters:
 alpha: 0.6536165
 beta : 0.05293179
 gamma: 1

Coefficients:
           [,1]
a   105813.8495
b     1026.6615
s1     606.8713
s2   -5977.8972
s3   -3136.4929
s4   -3261.4014
s5    1258.3986
s6    8195.6800
s7    4374.5625
s8    5930.9417
s9    1703.6467
s10  -3288.9800
s11   6880.9961
s12   4719.1505
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/11meb1470785318.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2qynd1470785318.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3fi2i1470785318.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4cvya1470785318.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/5xhs51470785318.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/64td21470785318.tab") 
> 
> try(system("convert tmp/11meb1470785318.ps tmp/11meb1470785318.png",intern=TRUE))
character(0)
> try(system("convert tmp/2qynd1470785318.ps tmp/2qynd1470785318.png",intern=TRUE))
character(0)
> try(system("convert tmp/3fi2i1470785318.ps tmp/3fi2i1470785318.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.472   0.135   1.624