R version 2.12.1 (2010-12-16)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(26.663
+ ,23.598
+ ,26.931
+ ,24.740
+ ,25.806
+ ,24.364
+ ,24.477
+ ,23.901
+ ,23.175
+ ,23.227
+ ,21.672
+ ,21.870
+ ,21.439
+ ,21.089
+ ,23.709
+ ,21.669
+ ,21.752
+ ,20.761
+ ,23.479
+ ,23.824
+ ,23.105
+ ,23.110
+ ,21.759
+ ,22.073
+ ,21.937
+ ,20.035
+ ,23.590
+ ,21.672
+ ,22.222
+ ,22.123
+ ,23.950
+ ,23.504
+ ,22.238
+ ,23.142
+ ,21.059
+ ,21.573
+ ,21.548
+ ,20.000
+ ,22.424
+ ,20.615
+ ,21.761
+ ,22.874
+ ,24.104
+ ,23.748
+ ,23.262
+ ,22.907
+ ,21.519
+ ,22.025
+ ,22.604
+ ,20.894
+ ,24.677
+ ,23.673
+ ,25.320
+ ,23.583
+ ,24.671
+ ,24.454
+ ,24.122
+ ,24.252
+ ,22.084
+ ,22.991
+ ,23.287
+ ,23.049
+ ,25.076
+ ,24.037
+ ,24.430
+ ,24.667
+ ,26.451
+ ,25.618
+ ,25.014
+ ,25.110
+ ,22.964
+ ,23.981
+ ,23.798
+ ,22.270
+ ,24.775
+ ,22.646
+ ,23.988
+ ,24.737
+ ,26.276
+ ,25.816
+ ,25.210
+ ,25.199
+ ,23.162
+ ,24.707
+ ,24.364
+ ,22.644
+ ,25.565
+ ,24.062
+ ,25.431
+ ,24.635
+ ,27.009
+ ,26.606
+ ,26.268
+ ,26.462
+ ,25.246
+ ,25.180
+ ,24.657
+ ,23.304
+ ,26.982
+ ,26.199
+ ,27.210
+ ,26.122
+ ,26.706
+ ,26.878
+ ,26.152
+ ,26.379
+ ,24.712
+ ,25.688
+ ,24.990
+ ,24.239
+ ,26.721
+ ,23.475
+ ,24.767
+ ,26.219
+ ,28.361
+ ,28.599
+ ,27.914
+ ,27.784
+ ,25.693
+ ,26.881
+ ,26.217
+ ,24.218
+ ,27.914
+ ,26.975
+ ,28.527
+ ,27.139
+ ,28.982
+ ,28.169
+ ,28.056
+ ,29.136
+ ,26.291
+ ,26.987
+ ,26.589
+ ,24.848
+ ,27.543
+ ,26.896
+ ,28.878
+ ,27.390
+ ,28.065
+ ,28.141
+ ,29.048
+ ,28.484
+ ,26.634
+ ,27.735
+ ,27.132
+ ,24.924
+ ,28.963
+ ,26.589
+ ,27.931
+ ,28.009
+ ,29.229
+ ,28.759
+ ,28.405
+ ,27.945
+ ,25.912
+ ,26.619
+ ,26.076
+ ,25.286
+ ,27.660
+ ,25.951
+ ,26.398
+ ,25.565
+ ,28.865
+ ,30.000
+ ,29.261
+ ,29.012
+ ,26.992
+ ,27.897)
> 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: 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 additive seasonal component.

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

Smoothing parameters:
 alpha:  0.4823655 
 beta :  0.02988495 
 gamma:  0.563186 

Coefficients:
           [,1]
a   28.04366357
b    0.04199921
s1  -0.78546221
s2  -2.19944507
s3   0.87813012
s4  -0.65164728
s5   0.63427267
s6   0.21182821
s7   2.23177191
s8   2.17167733
s9   1.52077678
s10  1.16900861
s11 -0.97500043
s12 -0.18636055
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/rcomp/tmp/15ngn1322918419.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/26zaq1322918419.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/3w6x31322918419.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/rcomp/tmp/4a33v1322918419.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/rcomp/tmp/532aj1322918419.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/rcomp/tmp/602ux1322918419.tab") 
> 
> try(system("convert tmp/15ngn1322918419.ps tmp/15ngn1322918419.png",intern=TRUE))
character(0)
> try(system("convert tmp/26zaq1322918419.ps tmp/26zaq1322918419.png",intern=TRUE))
character(0)
> try(system("convert tmp/3w6x31322918419.ps tmp/3w6x31322918419.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.904   0.248   2.133