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(0.0314796223103059
+ ,-3.00870920563557
+ ,-2.07677512619799
+ ,-1.25010391965540
+ ,0.817975239137125
+ ,0.0252076485413113
+ ,0.554937772830776
+ ,0.230027371950115
+ ,2.35672227418686
+ ,1.41350455171120
+ ,2.73311719024401
+ ,1.31551925971717
+ ,-2.70076272244080
+ ,-0.721411049152714
+ ,-0.149388576811997
+ ,-0.118199629770334
+ ,-0.676562489695275
+ ,1.79699928690761
+ ,1.79845572032988
+ ,0.245100010770855
+ ,1.80710848932636
+ ,-1.75934771184948
+ ,-0.0186697168761931
+ ,0.189651523600062
+ ,-1.84149562719087
+ ,-1.07019530156943
+ ,-0.507291477584104
+ ,0.866365633831705
+ ,-1.76077926699189
+ ,-0.580719393339347
+ ,-0.435702079860853
+ ,-0.994868534845203
+ ,1.63136048315789
+ ,-1.1949403709466
+ ,-1.00525975426991
+ ,1.32302234837564
+ ,-0.628357549594746
+ ,0.632048410440518
+ ,-2.16903155809288
+ ,2.53779364144266
+ ,-0.632933703679292
+ ,-1.41749196342200
+ ,-0.455343045381255
+ ,0.812255211942954
+ ,0.627897309219833
+ ,0.650904313655623
+ ,-1.29800419154382
+ ,0.74391671726854
+ ,-1.50461634127457
+ ,-1.42734677658523
+ ,0.263353807408564
+ ,-0.430830854870631
+ ,0.379576092518008
+ ,1.70309353400146
+ ,-3.12314448117342
+ ,-1.32526207118689
+ ,-0.60032490743804
+ ,1.23607137604666
+ ,0.738007075905376
+ ,0.899100896289585)
> 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:  0.005113117 
 beta :  0.2601144 
 gamma:  0.5250511 

Coefficients:
            [,1]
a    0.111113290
b   -0.007689367
s1  -1.728734596
s2  -1.066510725
s3  -0.744849489
s4   0.244779606
s5  -0.477378000
s6   0.437180064
s7  -1.895949547
s8  -0.795779494
s9   0.050324447
s10  0.434600826
s11 -0.117659575
s12  0.697713460
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/rcomp/tmp/1ij1j1259789205.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2hzqm1259789205.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3c39o1259789205.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4hhqm1259789205.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/58pd61259789205.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/6g6x91259789205.tab") 
> system("convert tmp/1ij1j1259789205.ps tmp/1ij1j1259789205.png")
> system("convert tmp/2hzqm1259789205.ps tmp/2hzqm1259789205.png")
> system("convert tmp/3c39o1259789205.ps tmp/3c39o1259789205.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.825   0.505   0.993