R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

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(-45.6
+ ,16.1
+ ,23.9
+ ,39.3
+ ,-39.4
+ ,-0.3
+ ,17.3
+ ,17.7
+ ,31.4
+ ,-28.6
+ ,-17.2
+ ,-79
+ ,-47.9
+ ,9.1
+ ,10.6
+ ,-23.9
+ ,-45
+ ,-42.2
+ ,43.2
+ ,32.1
+ ,-15.3
+ ,21.8
+ ,-12
+ ,-95.8
+ ,-14.3
+ ,47.8
+ ,64.8
+ ,40.2
+ ,-28.8
+ ,23.5
+ ,70.3
+ ,12.3
+ ,43.5
+ ,-30.1
+ ,-5.3
+ ,-24
+ ,11.1
+ ,21.5
+ ,38.5
+ ,16.8
+ ,-36.2
+ ,6
+ ,26.6
+ ,-8
+ ,13.2
+ ,-23.6
+ ,19.4
+ ,-46.2
+ ,-8.2
+ ,33.8
+ ,16.6
+ ,5.4
+ ,-25
+ ,-5.3
+ ,16.7
+ ,19
+ ,24.8
+ ,-11.4
+ ,4.9
+ ,-58.7
+ ,16.8
+ ,13.6
+ ,6.4
+ ,22.8
+ ,-19.6
+ ,2.2
+ ,19.8
+ ,-10.7
+ ,4.7
+ ,-44.5
+ ,-34.7
+ ,-119.7
+ ,-42.2
+ ,-5.4
+ ,19.1
+ ,18.8
+ ,-2.3
+ ,0.2
+ ,20.9
+ ,3.7
+ ,50.4
+ ,-18.6
+ ,10.6
+ ,-66
+ ,10
+ ,27.2
+ ,13.5
+ ,47.2
+ ,-20.3
+ ,23.1
+ ,12.6
+ ,19.8
+ ,5.4
+ ,-25.2
+ ,-6.5
+ ,-46.5
+ ,-2.6
+ ,-0.3
+ ,38.5
+ ,-8.9
+ ,-38
+ ,19.5
+ ,51.7
+ ,19.4
+ ,18.2
+ ,-50.8
+ ,-6.1
+ ,-54.6
+ ,12.1
+ ,26.3
+ ,19.5
+ ,-0.8
+ ,-49.6
+ ,28.8
+ ,31.7
+ ,2.3
+ ,3.8
+ ,-66.2
+ ,-20.5
+ ,-113.2
+ ,-65.2
+ ,-3.9
+ ,9.1
+ ,23.2
+ ,-39.1
+ ,12.5
+ ,49.1
+ ,54.9
+ ,30.8
+ ,-3.5
+ ,-28.3
+ ,-61
+ ,-2
+ ,40
+ ,74
+ ,23.1
+ ,-45.3
+ ,17.5
+ ,25.8
+ ,15.2
+ ,-3.6
+ ,-40.5
+ ,11.5
+ ,-59.8
+ ,23.3
+ ,-27.8
+ ,55.7
+ ,22.7
+ ,-79.2
+ ,28.8
+ ,17.3
+ ,39.6
+ ,-22.2
+ ,-43
+ ,-50.3
+ ,-86.5
+ ,-31.9
+ ,23.1
+ ,53.6
+ ,21.6
+ ,-64.2
+ ,35.2
+ ,52.1
+ ,40.6
+ ,17.1
+ ,-7.8
+ ,-10
+ ,-58
+ ,14
+ ,15.8
+ ,46
+ ,-8.9
+ ,-26.7
+ ,39
+ ,-1.3
+ ,38.7
+ ,22.1
+ ,-49.2
+ ,-3.4
+ ,-86.7
+ ,-24.3
+ ,42.8
+ ,44.9
+ ,4.4
+ ,-60.5
+ ,41.4
+ ,38.5
+ ,28.5
+ ,7.6
+ ,-46.4
+ ,7
+ ,-73
+ ,5.7
+ ,23.6
+ ,39.4
+ ,30.3
+ ,-92.5
+ ,77.8
+ ,12.4
+ ,28.9
+ ,6.4
+ ,-12
+ ,-9.1
+ ,-53.2
+ ,-23.1
+ ,47.3
+ ,20.7
+ ,27.8
+ ,-84.3
+ ,62.8
+ ,26.4
+ ,32.3
+ ,13.3
+ ,-17.9
+ ,10
+ ,-45.6
+ ,13.5
+ ,11.9
+ ,26
+ ,-6.3
+ ,-79.9
+ ,54.2
+ ,22.9
+ ,31.8
+ ,3.8
+ ,-11.4
+ ,-8.6
+ ,-49.4
+ ,-2.5
+ ,23
+ ,29
+ ,20.6
+ ,-117
+ ,37.9
+ ,30.7
+ ,4.7
+ ,-5.7
+ ,4.9
+ ,18.3
+ ,-35.4
+ ,-21.3
+ ,35.8
+ ,43.8
+ ,18.7
+ ,-131.1
+ ,39.8
+ ,44.5
+ ,16.5
+ ,9.7
+ ,-6.6
+ ,15.8
+ ,-45.7
+ ,-4.8
+ ,17.6
+ ,20.5
+ ,24.2
+ ,-109
+ ,20.8
+ ,31.2
+ ,-8.8
+ ,11.8
+ ,13
+ ,8.3
+ ,-77.9
+ ,-38.8
+ ,6.1
+ ,18.1
+ ,16.8
+ ,-128.5
+ ,15.9
+ ,29
+ ,-7.2
+ ,3.3
+ ,-34.8
+ ,-2.9
+ ,-77.8
+ ,-2.8
+ ,26.7
+ ,48.1
+ ,30
+ ,-109.6
+ ,16
+ ,26.9
+ ,22.1
+ ,27
+ ,-24.5
+ ,12
+ ,-75.2
+ ,3.5
+ ,19.7
+ ,51.8
+ ,35.3
+ ,-108.2
+ ,25.3
+ ,31.6
+ ,19.9
+ ,18.8
+ ,20.4
+ ,15
+ ,-55.9
+ ,-17
+ ,33.3
+ ,33.8
+ ,37.5
+ ,-104.8
+ ,29.7
+ ,34.2
+ ,4.3
+ ,40.2
+ ,-29.3
+ ,-0.2
+ ,-95
+ ,-13.2
+ ,38.5
+ ,45.4
+ ,15.7
+ ,-123.6
+ ,12
+ ,37.5
+ ,-31.7
+ ,15.8
+ ,-64.1
+ ,-42.1
+ ,-207.4
+ ,-12.9
+ ,-5
+ ,53.9
+ ,19.7
+ ,-94.6
+ ,36
+ ,51.3
+ ,17.4
+ ,27.8
+ ,1.3
+ ,3.6
+ ,-97.9
+ ,14.1
+ ,50.8
+ ,63.5
+ ,58.6
+ ,-135.1
+ ,7.8
+ ,25.5
+ ,29.6
+ ,19.3
+ ,-26.2
+ ,7.3
+ ,-82.6
+ ,-26.1
+ ,55.3
+ ,98.8
+ ,41.7
+ ,-130.2
+ ,51.2
+ ,18.4
+ ,32
+ ,21.6
+ ,-12.5
+ ,46.6
+ ,-101.7
+ ,15.8
+ ,26
+ ,79.1
+ ,23.1
+ ,-86.9
+ ,-11.2
+ ,50.7
+ ,13.4
+ ,33.7
+ ,-16.9
+ ,-9.6)
> par3 = 'multiplicative'
> 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 multiplicative seasonal component.

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

Smoothing parameters:
 alpha:  0.3 
 beta :  0.1 
 gamma:  0.1 

Coefficients:
           [,1]
a     1.8666854
b    -0.6753179
s1  -23.1186801
s2   -2.6925621
s3   13.2605715
s4    3.1049587
s5    1.6219834
s6   -5.7872074
s7    2.8492221
s8    3.7805787
s9    2.6237833
s10 -10.5447577
s11  -6.4670652
s12   5.4026213
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1a7sb1322155774.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2s3041322155774.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3lt1t1322155774.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4iuof1322155774.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/57u9y1322155774.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/67eq41322155774.tab") 
> 
> try(system("convert tmp/1a7sb1322155774.ps tmp/1a7sb1322155774.png",intern=TRUE))
character(0)
> try(system("convert tmp/2s3041322155774.ps tmp/2s3041322155774.png",intern=TRUE))
character(0)
> try(system("convert tmp/3lt1t1322155774.ps tmp/3lt1t1322155774.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.046   0.169   3.259