R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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Type 'contributors()' for more information and
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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(227.86
+ ,198.24
+ ,194.97
+ ,184.88
+ ,196.79
+ ,205.36
+ ,226.72
+ ,226.05
+ ,202.50
+ ,194.79
+ ,192.43
+ ,219.25
+ ,217.47
+ ,192.34
+ ,196.83
+ ,186.07
+ ,197.31
+ ,215.02
+ ,242.67
+ ,225.17
+ ,206.69
+ ,197.75
+ ,196.43
+ ,213.55
+ ,222.75
+ ,194.03
+ ,201.85
+ ,189.50
+ ,206.07
+ ,225.59
+ ,247.91
+ ,247.64
+ ,213.01
+ ,203.01
+ ,200.26
+ ,220.50
+ ,237.90
+ ,216.94
+ ,214.01
+ ,196.00
+ ,208.37
+ ,232.75
+ ,257.46
+ ,267.69
+ ,220.18
+ ,210.61
+ ,209.59
+ ,232.75
+ ,232.75
+ ,219.82
+ ,226.74
+ ,208.04
+ ,220.12
+ ,235.69
+ ,257.05
+ ,258.69
+ ,227.15
+ ,219.91
+ ,219.30
+ ,259.04
+ ,237.29
+ ,212.88
+ ,226.03
+ ,211.07
+ ,222.91
+ ,249.18
+ ,266.38
+ ,268.53
+ ,238.02
+ ,224.69
+ ,213.75
+ ,237.43
+ ,248.46
+ ,210.82
+ ,221.40
+ ,209.00
+ ,234.37
+ ,248.43
+ ,271.98
+ ,268.11
+ ,233.88
+ ,223.43
+ ,221.38
+ ,233.76
+ ,243.97
+ ,217.76
+ ,224.66
+ ,210.84
+ ,220.35
+ ,236.84
+ ,266.15
+ ,255.20
+ ,234.76
+ ,221.29
+ ,221.26
+ ,244.13
+ ,245.78
+ ,224.62
+ ,234.80
+ ,211.37
+ ,222.39
+ ,249.63
+ ,282.29
+ ,279.13
+ ,236.60
+ ,223.62
+ ,225.86
+ ,246.41
+ ,261.70
+ ,225.01
+ ,231.54
+ ,214.82
+ ,227.70
+ ,263.86
+ ,278.15
+ ,274.64
+ ,237.66
+ ,227.97
+ ,224.75
+ ,242.91
+ ,253.08
+ ,228.13
+ ,233.68
+ ,217.38
+ ,236.38
+ ,256.08
+ ,292.83
+ ,304.71
+ ,245.57
+ ,234.41
+ ,234.12
+ ,258.17
+ ,268.66
+ ,245.31
+ ,247.47
+ ,226.25
+ ,251.67
+ ,268.79
+ ,288.94
+ ,290.16
+ ,250.69
+ ,240.80)
> 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:  0.1574259 
 beta :  0.001000688 
 gamma:  0.3316144 

Coefficients:
           [,1]
a   255.3535975
b     0.3168805
s1  -16.1464193
s2    5.5769025
s3   13.9156143
s4  -12.8862191
s5   -7.6828756
s6  -25.8338836
s7   -7.9830663
s8   13.2237146
s9   37.4911215
s10  37.7658094
s11  -3.9057397
s12 -14.7215481
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/freestat/rcomp/tmp/1vma91274289247.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/2vma91274289247.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/36d9u1274289247.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/freestat/rcomp/tmp/4k5731274289247.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/freestat/rcomp/tmp/5ce6n1274289247.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/freestat/rcomp/tmp/6yx5b1274289247.tab") 
> 
> try(system("convert tmp/1vma91274289247.ps tmp/1vma91274289247.png",intern=TRUE))
character(0)
> try(system("convert tmp/2vma91274289247.ps tmp/2vma91274289247.png",intern=TRUE))
character(0)
> try(system("convert tmp/36d9u1274289247.ps tmp/36d9u1274289247.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.488   0.790   1.883