R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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(23100
+ ,22650
+ ,22440
+ ,22910
+ ,22980
+ ,22535
+ ,22300
+ ,22780
+ ,22780
+ ,23300
+ ,23800
+ ,24510
+ ,24660
+ ,24730
+ ,25070
+ ,24690
+ ,24880
+ ,23920
+ ,23880
+ ,23990
+ ,24590
+ ,23610
+ ,23580
+ ,23360
+ ,23910
+ ,23940
+ ,23060
+ ,22800
+ ,23020
+ ,22890
+ ,22780
+ ,22530
+ ,22290
+ ,22820
+ ,22480
+ ,22110
+ ,22000
+ ,22230
+ ,22260
+ ,22590
+ ,22820
+ ,22420
+ ,22230
+ ,21600
+ ,21000
+ ,21360
+ ,21640
+ ,21450
+ ,21710
+ ,21620
+ ,21800
+ ,21490
+ ,21670
+ ,22130
+ ,22050
+ ,22050
+ ,22140
+ ,22390
+ ,22220
+ ,21790
+ ,21510
+ ,21670
+ ,21745
+ ,21850
+ ,22105
+ ,22050
+ ,21670
+ ,21680
+ ,21800
+ ,21920
+ ,21980
+ ,22270
+ ,21740
+ ,21950
+ ,22010
+ ,21890
+ ,21920
+ ,22110
+ ,22340
+ ,22210
+ ,22240
+ ,21960
+ ,22220
+ ,22060
+ ,22090
+ ,21960
+ ,21940
+ ,21790
+ ,21710
+ ,21690
+ ,21710
+ ,21670
+ ,21640
+ ,21500
+ ,21290
+ ,21250
+ ,21580
+ ,21670
+ ,21620
+ ,21510
+ ,21360
+ ,21420
+ ,21470
+ ,21370
+ ,21370
+ ,21340
+ ,21130
+ ,21130
+ ,20990
+ ,21240
+ ,21320
+ ,21430
+ ,21390
+ ,21530
+ ,21510
+ ,21630
+ ,21560
+ ,21610
+ ,21560
+ ,21310
+ ,21340
+ ,21410
+ ,21550
+ ,21380
+ ,21600
+ ,21530
+ ,21560
+ ,21670
+ ,21540
+ ,21540
+ ,21550
+ ,21590
+ ,21420
+ ,21420
+ ,21370
+ ,21380
+ ,21210
+ ,21505
+ ,21365
+ ,21385
+ ,21350
+ ,21360
+ ,21530
+ ,21380
+ ,21630
+ ,22145
+ ,22315
+ ,22340
+ ,22440
+ ,22135
+ ,21955
+ ,22060
+ ,22050
+ ,22035
+ ,22280
+ ,22315
+ ,22205
+ ,21970
+ ,22075
+ ,22115
+ ,22105
+ ,21885
+ ,21805
+ ,21910
+ ,21995
+ ,22245
+ ,22100
+ ,22130
+ ,22300
+ ,22915
+ ,23040
+ ,22880
+ ,23000
+ ,23160
+ ,23020
+ ,22770
+ ,22660
+ ,22740
+ ,22905
+ ,22720
+ ,22705
+ ,22735
+ ,22600
+ ,22510
+ ,22560
+ ,22575
+ ,22685
+ ,22980
+ ,23275
+ ,23845
+ ,23640
+ ,23640
+ ,23835
+ ,23625
+ ,24055
+ ,24005
+ ,24325
+ ,24445
+ ,24670
+ ,24615
+ ,24700
+ ,25065
+ ,25185
+ ,25220
+ ,25235
+ ,24975
+ ,25055
+ ,25520
+ ,25880
+ ,25960
+ ,25740
+ ,24965
+ ,25235
+ ,24895
+ ,24635
+ ,24835
+ ,24635
+ ,24695
+ ,25090
+ ,25220
+ ,24740
+ ,25005
+ ,24650
+ ,24460
+ ,24680
+ ,24840
+ ,24630
+ ,24490
+ ,24695)
> par3 = 'multiplicative'
> par2 = 'Double'
> par1 = '5'
> #'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 without seasonal component.

Call:
 HoltWinters(x = x, gamma = F) 

Smoothing parameters:
 alpha:  1 
 beta :  0.1092631 
 gamma:  FALSE 

Coefficients:
         [,1]
a 24695.00000
b    -8.73478
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/rcomp/tmp/1jike1275664923.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2jike1275664923.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3u92h1275664923.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4fs051275664923.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/5jtya1275664923.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/6mbfy1275664923.tab") 
> 
> try(system("convert tmp/1jike1275664923.ps tmp/1jike1275664923.png",intern=TRUE))
character(0)
> try(system("convert tmp/2jike1275664923.ps tmp/2jike1275664923.png",intern=TRUE))
character(0)
> try(system("convert tmp/3u92h1275664923.ps tmp/3u92h1275664923.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.428   0.576   2.927