R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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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(428800
+ ,424800
+ ,403400
+ ,398400
+ ,393500
+ ,380500
+ ,398300
+ ,387300
+ ,370400
+ ,372800
+ ,444600
+ ,449900
+ ,458100
+ ,424800
+ ,420600
+ ,400100
+ ,393000
+ ,387100
+ ,377500
+ ,400400
+ ,391400
+ ,363600
+ ,431000
+ ,441700
+ ,448500
+ ,415600
+ ,408000
+ ,416600
+ ,409300
+ ,387600
+ ,394500
+ ,407600
+ ,378500
+ ,359600
+ ,435700
+ ,433800
+ ,427700
+ ,413300
+ ,379500
+ ,379300
+ ,353700
+ ,378200
+ ,380600
+ ,394000
+ ,374000
+ ,375000
+ ,437600
+ ,443900
+ ,488800
+ ,463900
+ ,440000
+ ,453800
+ ,451600
+ ,453400
+ ,461400
+ ,509100
+ ,540600
+ ,555100
+ ,677400
+ ,694600
+ ,750100
+ ,733900
+ ,709300
+ ,720500
+ ,693200
+ ,687200
+ ,686800
+ ,720900
+ ,653100
+ ,624700
+ ,690000
+ ,717800
+ ,736500
+ ,699900
+ ,675600
+ ,635600
+ ,632500
+ ,594900
+ ,604000
+ ,620800
+ ,578400
+ ,571200
+ ,627400
+ ,657700
+ ,674100
+ ,672800
+ ,615300
+ ,609100
+ ,607600
+ ,566900
+ ,572700
+ ,589200
+ ,534800
+ ,543100
+ ,591100
+ ,624800
+ ,665300
+ ,642600
+ ,608700
+ ,594500
+ ,563800
+ ,596100
+ ,597600
+ ,633100
+ ,591000
+ ,584200
+ ,655800
+ ,670700
+ ,699700
+ ,712900
+ ,652000
+ ,635100
+ ,603100
+ ,610100
+ ,602000
+ ,597600
+ ,585400
+ ,567100
+ ,620600
+ ,646200
+ ,644800
+ ,645200
+ ,644800
+ ,593000
+ ,569100
+ ,518800
+ ,538700
+ ,554600
+ ,507900
+ ,488400
+ ,563300
+ ,592400
+ ,598100
+ ,546300
+ ,516100
+ ,518500
+ ,477400
+ ,483400
+ ,469400
+ ,501300
+ ,457400
+ ,446700
+ ,501900
+ ,550400
+ ,593700
+ ,548900
+ ,534200
+ ,550500
+ ,541800
+ ,569300
+ ,587400
+ ,627700
+ ,607000
+ ,629500
+ ,704600
+ ,767700
+ ,812200
+ ,824600
+ ,856300
+ ,812200
+ ,764100
+ ,801700
+ ,806000
+ ,867200
+ ,801600
+ ,817500
+ ,920900
+ ,959700
+ ,997700
+ ,949100
+ ,910900
+ ,920400
+ ,914200
+ ,926300
+ ,906400
+ ,926100
+ ,902500
+ ,895300
+ ,979900
+ ,1009700
+ ,1043800
+ ,979800
+ ,921600
+ ,923500
+ ,914500
+ ,891700
+ ,916000
+ ,931700
+ ,902400
+ ,893700
+ ,941500
+ ,980100
+ ,1006900
+ ,949200
+ ,883200
+ ,849900
+ ,839200
+ ,803900
+ ,797900
+ ,830800
+ ,753300
+ ,764100
+ ,807600
+ ,853700
+ ,886200
+ ,815700
+ ,743000
+ ,753600
+ ,724800
+ ,709600
+ ,721900)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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=0, beta=0)
> if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
> 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:  0.7221018 
 beta :  0.1660564 
 gamma:  0.5262852 

Coefficients:
           [,1]
a   748238.7542
b    -6493.6035
s1     377.5733
s2  -42900.1098
s3  -40494.1839
s4   24651.7215
s5   61473.5308
s6   81153.7691
s7   28468.6458
s8   -9580.4377
s9  -12194.5803
s10 -33026.5105
s11 -38330.8616
s12 -27760.7853
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/rcomp/tmp/1r1j81243942865.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2t9wl1243942865.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/30wsm1243942865.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/www/html/rcomp/tmp/4342q1243942865.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/www/html/rcomp/tmp/58qxb1243942865.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/www/html/rcomp/tmp/6yrro1243942865.tab") 
> 
> system("convert tmp/1r1j81243942865.ps tmp/1r1j81243942865.png")
> system("convert tmp/2t9wl1243942865.ps tmp/2t9wl1243942865.png")
> system("convert tmp/30wsm1243942865.ps tmp/30wsm1243942865.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.342   0.587   1.923