R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(547612,563280,581302,572273,518654,520579,530577,540324,547970,555654,551174,548604,563668,586111,604378,600991,544686,537034,551531,563250,574761,580112,575093,557560,564478,580523,596594,586570,536214,523597,536535,536322,532638,528222,516141,501866,506174,517945,533590,528379,477580,469357,490243,492622,507561,516922,514258,509846,527070,541657,564591,555362,498662,511038,525919,531673,548854,560576,557274,565742,587625,619916,625809,619567,572942,572775,574205,579799,590072,593408,597141,595404,612117,628232,628884,620735,569028,567456,573100,584428,589379,590865,595454,594167,611324,612613,610763,593530,542722,536662,543599,555332,560854,562325,554788,547344,565464,577992,579714,569323,506971,500857,509127,509933,517009,519164,512238,509239,518585,522975,525192,516847,455626,454724,461251,470439,474605,476049,471067,470984,502831,512927,509673,484015,431328,436087,442867,447988,460070,467037,460170,464196,485025)
> par3 = 'multiplicative'
> par2 = 'Triple'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2010), Exponential Smoothing (v1.0.4) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> 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 multiplicative seasonal component.

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

Smoothing parameters:
 alpha:  1 
 beta :  0.1138148 
 gamma:  0.2163014 

Coefficients:
            [,1]
a   4.819161e+05
b   1.040300e+03
s1  1.043119e+00
s2  1.071679e+00
s3  1.061654e+00
s4  9.587772e-01
s5  9.430344e-01
s6  9.668736e-01
s7  9.817373e-01
s8  9.921818e-01
s9  1.002179e+00
s10 9.900264e-01
s11 9.822871e-01
s12 1.006451e+00
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1zg681322658854.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2grqb1322658854.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3m4s31322658854.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/46xgw1322658854.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/5fnju1322658854.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/6itc91322658854.tab") 
> 
> try(system("convert tmp/1zg681322658854.ps tmp/1zg681322658854.png",intern=TRUE))
character(0)
> try(system("convert tmp/2grqb1322658854.ps tmp/2grqb1322658854.png",intern=TRUE))
character(0)
> try(system("convert tmp/3m4s31322658854.ps tmp/3m4s31322658854.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.362   0.163   1.590