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)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(2421.21,2378.63,2336.00,2250.79,3113.00,3070.38,2421.21,1990.13,2032.71,2032.71,2075.33,2165.17,1904.92,1644.25,1430.79,1430.79,2250.79,2336.00,1686.83,952.46,1340.96,1340.96,1644.25,1819.29,1776.67,1340.96,1559.04,1473.42,2207.79,2032.71,1340.96,824.25,1298.33,1430.79,1559.04,1729.46,1383.54,1084.92,1213.17,1255.75,2378.63,2378.63,1729.46,1644.25,1904.92,1776.67,2122.58,2553.67,2639.29,2032.71,1861.88,1686.83,2856.96,2942.58,2724.50,2942.58,2899.54,2553.67,2942.58,3373.67,3548.71,3027.79,2681.88,2942.58,4065.42,4411.33,4326.13,4496.50,4453.92,4022.83,4757.21,4932.25,5188.29,4411.33,4108.04,4453.92,5278.13,6012.50,5837.46,5837.46,5923.08,5624.00,6401.42,6401.42,6268.96,5534.17,5666.63,5752.25,6315.79,7050.17,6529.21,6789.92,6571.83,6444.00,7439.08,7221.00,6917.71,6486.63,6917.71,7135.79,7396.04,7741.92,7396.04,7609.50,7349.21,7306.63,8386.88,8476.71,8130.83,7524.29,8041.00,8258.67,8519.33,8907.83,8519.33,8822.63,8690.17,8216.04,9211.08,9211.08)
> 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: 0.6536108
 beta : 0.05293225
 gamma: 1

Coefficients:
          [,1]
a   8817.81137
b     85.55476
s1    50.57104
s2  -498.15711
s3  -261.36858
s4  -271.77930
s5   104.85908
s6   682.96607
s7   364.54268
s8   494.25259
s9   141.97814
s10 -274.07697
s11  573.42298
s12  393.26863
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/13dlz1471088732.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2lkgk1471088732.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3wtdd1471088732.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/405pm1471088732.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/5goez1471088732.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/6r7d91471088732.tab") 
> 
> try(system("convert tmp/13dlz1471088732.ps tmp/13dlz1471088732.png",intern=TRUE))
character(0)
> try(system("convert tmp/2lkgk1471088732.ps tmp/2lkgk1471088732.png",intern=TRUE))
character(0)
> try(system("convert tmp/3wtdd1471088732.ps tmp/3wtdd1471088732.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.449   0.149   1.617