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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> x <- c(27.951,29.781,32.914,33.488,35.652,36.488,35.387,35.676,34.844,32.447,31.068,29.010,29.812,30.951,32.974,32.936,34.012,32.946,31.948,30.599,27.691,25.073,23.406,22.248,22.896,25.317,26.558,26.471,27.543,26.198,24.725,25.005,23.462,20.780,19.815,19.761,21.454,23.899,24.939,23.580,24.562,24.696,23.785,23.812,21.917,19.713,19.282,18.788,21.453,24.482,27.474,27.264,27.349,30.632,29.429,30.084,26.290,24.379,23.335,21.346,21.106,24.514,28.353,30.805,31.348,34.556,33.855,34.787,32.529,29.998,29.257,28.155,30.466,35.704,39.327,39.351,42.234,43.630,43.722,43.121,37.985,37.135,34.646,33.026,35.087,38.846,42.013,43.908,42.868,44.423,44.167,43.636,44.382,42.142,43.452,36.912,42.413,45.344,44.873,47.510,49.554,47.369,45.998,48.140,48.441,44.928,40.454,38.661,37.246,36.843,36.424,37.594,38.144,38.737,34.560,36.080,33.508,35.462,33.374,32.110,35.533,35.532,37.903,36.763,40.399,44.164,44.496,43.110,43.880,43.930,44.327)
> 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: 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 multiplicative seasonal component.

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

Smoothing parameters:
 alpha:  0.9459286 
 beta :  0.03904106 
 gamma:  0.7743588 

Coefficients:
          [,1]
a   47.9200450
b    0.3602228
s1   0.8706880
s2   0.9095422
s3   0.9584238
s4   1.0216281
s5   1.0409518
s6   1.0912671
s7   1.0991079
s8   1.0563623
s9   1.0606158
s10  1.0218504
s11  0.9656613
s12  0.9244778
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/rcomp/tmp/1pn9r1293474493.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2hwqu1293474493.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3hwqu1293474493.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4v66k1293474493.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/56f5n1293474493.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/69ymt1293474493.tab") 
> 
> try(system("convert tmp/1pn9r1293474493.ps tmp/1pn9r1293474493.png",intern=TRUE))
character(0)
> try(system("convert tmp/2hwqu1293474493.ps tmp/2hwqu1293474493.png",intern=TRUE))
character(0)
> try(system("convert tmp/3hwqu1293474493.ps tmp/3hwqu1293474493.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.987   0.560   2.283