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(3221816.00
+ ,3209817.00
+ ,3197649.00
+ ,3172468.00
+ ,3421574.00
+ ,3408392.00
+ ,3221816.00
+ ,3097770.00
+ ,3109769.00
+ ,3109769.00
+ ,3123120.00
+ ,3147118.00
+ ,3184467.00
+ ,3184467.00
+ ,3160469.00
+ ,3097770.00
+ ,3421574.00
+ ,3470922.00
+ ,3396393.00
+ ,3221816.00
+ ,3296514.00
+ ,3184467.00
+ ,3234998.00
+ ,3259165.00
+ ,3284346.00
+ ,3221816.00
+ ,3234998.00
+ ,3147118.00
+ ,3421574.00
+ ,3508271.00
+ ,3433742.00
+ ,3296514.00
+ ,3445741.00
+ ,3284346.00
+ ,3433742.00
+ ,3421574.00
+ ,3458923.00
+ ,3321695.00
+ ,3470922.00
+ ,3458923.00
+ ,3682848.00
+ ,3632317.00
+ ,3433742.00
+ ,3333694.00
+ ,3470922.00
+ ,3284346.00
+ ,3421574.00
+ ,3445741.00
+ ,3496272.00
+ ,3384394.00
+ ,3445741.00
+ ,3483090.00
+ ,3620318.00
+ ,3508271.00
+ ,3359044.00
+ ,3197649.00
+ ,3347045.00
+ ,2936375.00
+ ,3135119.00
+ ,3246997.00
+ ,3359044.00
+ ,3197649.00
+ ,3197649.00
+ ,3197649.00
+ ,3284346.00
+ ,3160469.00
+ ,2997891.00
+ ,2861846.00
+ ,2960542.00
+ ,2575222.00
+ ,2811315.00
+ ,2948543.00
+ ,2973724.00
+ ,2836496.00
+ ,2848495.00
+ ,2811315.00
+ ,2936375.00
+ ,2848495.00
+ ,2675270.00
+ ,2550041.00
+ ,2761798.00
+ ,2301949.00
+ ,2600572.00
+ ,2736617.00
+ ,2736617.00
+ ,2575222.00
+ ,2425995.00
+ ,2413996.00
+ ,2550041.00
+ ,2425995.00
+ ,2190071.00
+ ,2027493.00
+ ,2202070.00
+ ,1791569.00
+ ,2164721.00
+ ,2363296.00
+ ,2425995.00
+ ,2288767.00
+ ,2115373.00
+ ,2239419.00
+ ,2288767.00
+ ,2251418.00
+ ,1878097.00
+ ,1704872.00
+ ,1828749.00
+ ,1455597.00
+ ,1840917.00
+ ,1978145.00
+ ,2090023.00
+ ,1903447.00
+ ,1728870.00
+ ,1828749.00
+ ,1878097.00
+ ,1779401.00
+ ,1406249.00
+ ,1243671.00
+ ,1392898.00
+ ,982397.00
+ ,1430247.00
+ ,1704872.00)
> 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: 0.405343
 beta : 0.06451955
 gamma: 1

Coefficients:
          [,1]
a   1482782.55
b    -32342.41
s1   244518.88
s2    64959.60
s3   -93591.85
s4    17727.43
s5    86888.06
s6    24314.99
s7  -295306.66
s8  -397149.59
s9  -183507.85
s10 -516129.50
s11  -32862.01
s12  222089.45
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/18r171439142310.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/249oy1439142310.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/34c4m1439142310.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/43x9j1439142310.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/54jcz1439142310.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/6wng11439142310.tab") 
> 
> try(system("convert tmp/18r171439142310.ps tmp/18r171439142310.png",intern=TRUE))
character(0)
> try(system("convert tmp/249oy1439142310.ps tmp/249oy1439142310.png",intern=TRUE))
character(0)
> try(system("convert tmp/34c4m1439142310.ps tmp/34c4m1439142310.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.398   0.215   1.621