R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(1.0137
+ ,0.9834
+ ,0.9643
+ ,0.9470
+ ,0.9060
+ ,0.9492
+ ,0.9397
+ ,0.9041
+ ,0.8721
+ ,0.8552
+ ,0.8564
+ ,0.8973
+ ,0.9383
+ ,0.9217
+ ,0.9095
+ ,0.8920
+ ,0.8742
+ ,0.8532
+ ,0.8607
+ ,0.9005
+ ,0.9111
+ ,0.9059
+ ,0.8883
+ ,0.8924
+ ,0.8833
+ ,0.8700
+ ,0.8758
+ ,0.8858
+ ,0.9170
+ ,0.9554
+ ,0.9922
+ ,0.9778
+ ,0.9808
+ ,0.9811
+ ,1.0014
+ ,1.0183
+ ,1.0622
+ ,1.0773
+ ,1.0807
+ ,1.0848
+ ,1.1582
+ ,1.1663
+ ,1.1372
+ ,1.1139
+ ,1.1222
+ ,1.1692
+ ,1.1702
+ ,1.2286
+ ,1.2613
+ ,1.2646
+ ,1.2262
+ ,1.1985
+ ,1.2007
+ ,1.2138
+ ,1.2266
+ ,1.2176
+ ,1.2218
+ ,1.2490
+ ,1.2991
+ ,1.3408
+ ,1.3119
+ ,1.3014
+ ,1.3201
+ ,1.2938
+ ,1.2694
+ ,1.2165
+ ,1.2037
+ ,1.2292
+ ,1.2256
+ ,1.2015
+ ,1.1786
+ ,1.1856
+ ,1.2103
+ ,1.1938
+ ,1.2020
+ ,1.2271
+ ,1.2770
+ ,1.2650
+ ,1.2684
+ ,1.2811
+ ,1.2727
+ ,1.2611
+ ,1.2881
+ ,1.3213
+ ,1.2999
+ ,1.3074
+ ,1.3242
+ ,1.3516
+ ,1.3511
+ ,1.3419
+ ,1.3716
+ ,1.3622
+ ,1.3896
+ ,1.4227
+ ,1.4684
+ ,1.4570
+ ,1.4718
+ ,1.4748
+ ,1.5527
+ ,1.5750
+ ,1.5557
+ ,1.5553
+ ,1.5770
+ ,1.4975
+ ,1.4369
+ ,1.3322
+ ,1.2732
+ ,1.3449
+ ,1.3239
+ ,1.2785
+ ,1.3050
+ ,1.3190
+ ,1.3650
+ ,1.4016
+ ,1.4088
+ ,1.4268
+ ,1.4562
+ ,1.4816
+ ,1.4914
+ ,1.4614
+ ,1.4272
+ ,1.3686
+ ,1.3569
+ ,1.3406
+ ,1.2565
+ ,1.2208
+ ,1.2770
+ ,1.2894
+ ,1.3067
+ ,1.3898
+ ,1.3661
+ ,1.3220
+ ,1.3360
+ ,1.3649
+ ,1.3999
+ ,1.4442
+ ,1.4349
+ ,1.4388
+ ,1.4264
+ ,1.4343
+ ,1.3770
+ ,1.3706
+ ,1.3556
+ ,1.3179
+ ,1.2905
+ ,1.3224
+ ,1.3201
+ ,1.3162
+ ,1.2789
+ ,1.2526
+ ,1.2288
+ ,1.2400
+ ,1.2856
+ ,1.2974
+ ,1.2828)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> 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:  0.8549788 
 beta :  0.007152189 
 gamma:  1 

Coefficients:
             [,1]
a    1.3088682129
b    0.0002372431
s1  -0.0224693402
s2  -0.0021868753
s3   0.0182681883
s4   0.0392807197
s5   0.0422064244
s6   0.0166423417
s7   0.0012780881
s8   0.0044626706
s9   0.0048540522
s10 -0.0021515317
s11 -0.0071946970
s12 -0.0260682129
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1m4ac1354722220.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2y8031354722220.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/39yy31354722220.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4nte21354722220.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/585g51354722221.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/6mpvj1354722221.tab") 
> 
> try(system("convert tmp/1m4ac1354722220.ps tmp/1m4ac1354722220.png",intern=TRUE))
character(0)
> try(system("convert tmp/2y8031354722220.ps tmp/2y8031354722220.png",intern=TRUE))
character(0)
> try(system("convert tmp/39yy31354722220.ps tmp/39yy31354722220.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.209   0.426   2.615