R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: x86_64-redhat-linux-gnu (64-bit)

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> x <- c(206010
+ ,198112
+ ,194519
+ ,185705
+ ,180173
+ ,176142
+ ,203401
+ ,221902
+ ,197378
+ ,185001
+ ,176356
+ ,180449
+ ,180144
+ ,173666
+ ,165688
+ ,161570
+ ,156145
+ ,153730
+ ,182698
+ ,200765
+ ,176512
+ ,166618
+ ,158644
+ ,159585
+ ,163095
+ ,159044
+ ,155511
+ ,153745
+ ,150569
+ ,150605
+ ,179612
+ ,194690
+ ,189917
+ ,184128
+ ,175335
+ ,179566
+ ,181140
+ ,177876
+ ,175041
+ ,169292
+ ,166070
+ ,166972
+ ,206348
+ ,215706
+ ,202108
+ ,195411
+ ,193111
+ ,195198
+ ,198770
+ ,194163
+ ,190420
+ ,189733
+ ,186029
+ ,191531
+ ,232571
+ ,243477
+ ,227247
+ ,217859
+ ,208679
+ ,213188
+ ,216234
+ ,213586
+ ,209465
+ ,204045
+ ,200237
+ ,203666
+ ,241476
+ ,260307
+ ,243324
+ ,244460
+ ,233575
+ ,237217
+ ,235243
+ ,230354
+ ,227184
+ ,221678
+ ,217142
+ ,219452
+ ,256446
+ ,265845
+ ,248624
+ ,241114
+ ,229245
+ ,231805
+ ,219277
+ ,219313
+ ,212610
+ ,214771
+ ,211142
+ ,211457
+ ,240048
+ ,240636
+ ,230580
+ ,208795
+ ,197922
+ ,194596
+ ,194581
+ ,185686
+ ,178106
+ ,172608
+ ,167302
+ ,168053
+ ,202300
+ ,202388
+ ,182516
+ ,173476
+ ,166444
+ ,171297
+ ,169701
+ ,164182
+ ,161914
+ ,159612
+ ,151001
+ ,158114
+ ,186530
+ ,187069
+ ,174330
+ ,169362
+ ,166827
+ ,178037
+ ,186413
+ ,189226
+ ,191563
+ ,188906
+ ,186005
+ ,195309
+ ,223532
+ ,226899
+ ,214126
+ ,206903
+ ,204442
+ ,220375
+ ,214320
+ ,212588
+ ,205816
+ ,202196
+ ,195722
+ ,198563
+ ,229139
+ ,229527
+ ,211868
+ ,203555
+ ,195770)
> par20 = ''
> par19 = ''
> par18 = ''
> par17 = ''
> par16 = ''
> par15 = ''
> par14 = ''
> par13 = ''
> par12 = ''
> par11 = ''
> par10 = ''
> par9 = ''
> par8 = ''
> par7 = ''
> par6 = ''
> par5 = ''
> par4 = ''
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> ylab = ''
> xlab = ''
> main = ''
> #'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#output/
> #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:  0.7867217 
 beta :  0.1557372 
 gamma:  1 

Coefficients:
          [,1]
a   197311.838
b    -1381.874
s1    2722.351
s2   -2241.738
s3   -5155.396
s4   -9165.970
s5  -11968.960
s6  -16764.897
s7  -12249.923
s8   17861.652
s9   22696.707
s10  11397.422
s11   5246.744
s12  -1541.838
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/wessaorg/rcomp/tmp/1eblz1293661987.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/wessaorg/rcomp/tmp/2eblz1293661987.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/wessaorg/rcomp/tmp/3eblz1293661987.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/www/wessaorg/rcomp/tmp/4slj81293661987.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/wessaorg/rcomp/tmp/5emiw1293661987.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/wessaorg/rcomp/tmp/66dzh1293661987.tab") 
> 
> try(system("convert tmp/1eblz1293661987.ps tmp/1eblz1293661987.png",intern=TRUE))
character(0)
> try(system("convert tmp/2eblz1293661987.ps tmp/2eblz1293661987.png",intern=TRUE))
character(0)
> try(system("convert tmp/3eblz1293661987.ps tmp/3eblz1293661987.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
   1.28    0.18    1.51