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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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(15136
+ ,16733
+ ,20016
+ ,17708
+ ,18019
+ ,19227
+ ,22893
+ ,23739
+ ,21133
+ ,22591
+ ,26786
+ ,29740
+ ,15028
+ ,17977
+ ,20008
+ ,21354
+ ,19498
+ ,22125
+ ,25817
+ ,28779
+ ,20960
+ ,22254
+ ,27392
+ ,29945
+ ,16933
+ ,17892
+ ,20533
+ ,23569
+ ,22417
+ ,22084
+ ,26580
+ ,27454
+ ,24081
+ ,23451
+ ,28991
+ ,31386
+ ,16896
+ ,20045
+ ,23471
+ ,21747
+ ,25621
+ ,23859
+ ,25500
+ ,30998
+ ,24475
+ ,23145
+ ,29701
+ ,34365
+ ,17556
+ ,22077
+ ,25702
+ ,22214
+ ,26886
+ ,23191
+ ,27831
+ ,35406
+ ,23195
+ ,25110
+ ,30009
+ ,36242
+ ,18450
+ ,21845
+ ,26488
+ ,22394
+ ,28057
+ ,25451
+ ,24872
+ ,33424
+ ,24052
+ ,28449
+ ,33533
+ ,37351
+ ,19969
+ ,21701
+ ,26249
+ ,24493
+ ,24603
+ ,26485
+ ,30723
+ ,34569
+ ,26689
+ ,26157
+ ,32064
+ ,38870
+ ,21337
+ ,19419
+ ,23166
+ ,28286
+ ,24570
+ ,24001
+ ,33151
+ ,24878
+ ,26804
+ ,28967
+ ,33311
+ ,40226
+ ,20504
+ ,23060
+ ,23562
+ ,27562
+ ,23940
+ ,24584
+ ,34303
+ ,25517
+ ,23494
+ ,29095
+ ,32903
+ ,34379
+ ,16991
+ ,21109
+ ,23740
+ ,25552
+ ,21752
+ ,20294
+ ,29009
+ ,25500
+ ,24166
+ ,26960
+ ,31222
+ ,38641
+ ,14672
+ ,17543
+ ,25453
+ ,32683
+ ,22449
+ ,22316
+ ,27595
+ ,25451
+ ,25421
+ ,25288
+ ,32568
+ ,35110
+ ,16052
+ ,22146
+ ,21198
+ ,19543
+ ,22084
+ ,23816
+ ,29961
+ ,26773
+ ,26635
+ ,26972
+ ,30207
+ ,38687
+ ,16974
+ ,21697
+ ,24179
+ ,23757
+ ,25013
+ ,24019
+ ,30345
+ ,24488
+ ,25156
+ ,25650
+ ,30923
+ ,37240
+ ,17466
+ ,19463
+ ,24352
+ ,26805
+ ,25236
+ ,24735
+ ,29356
+ ,31234
+ ,22724
+ ,28496
+ ,32857
+ ,37198
+ ,13652
+ ,22784
+ ,23565
+ ,26323
+ ,23779
+ ,27549
+ ,29660
+ ,23356)
> 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: 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 multiplicative seasonal component.

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

Smoothing parameters:
 alpha:  0.06944185 
 beta :  0.09554514 
 gamma:  0.2749976 

Coefficients:
            [,1]
a   2.687238e+04
b   9.909594e+00
s1  9.313958e-01
s2  1.020542e+00
s3  1.199493e+00
s4  1.400773e+00
s5  6.152247e-01
s6  8.008116e-01
s7  8.998473e-01
s8  9.671089e-01
s9  9.041869e-01
s10 9.334512e-01
s11 1.113385e+00
s12 9.992109e-01
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/rcomp/tmp/1dinp1244297254.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/20flm1244297254.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3v99p1244297254.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4t8j81244297254.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/5l72t1244297254.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/675h31244297254.tab") 
> 
> system("convert tmp/1dinp1244297254.ps tmp/1dinp1244297254.png")
> system("convert tmp/20flm1244297254.ps tmp/20flm1244297254.png")
> system("convert tmp/3v99p1244297254.ps tmp/3v99p1244297254.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.220   0.604   1.389