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)

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> x <- c(1149822
+ ,1086979
+ ,1276674
+ ,1522522
+ ,1742117
+ ,1737275
+ ,1979900
+ ,2061036
+ ,1867943
+ ,1707752
+ ,1298756
+ ,1281814
+ ,1281151
+ ,1164976
+ ,1454329
+ ,1645288
+ ,1817743
+ ,1895785
+ ,2236311
+ ,2295951
+ ,2087315
+ ,1980891
+ ,1465446
+ ,1445026
+ ,1488120
+ ,1338333
+ ,1715789
+ ,1806090
+ ,2083316
+ ,2092278
+ ,2430800
+ ,2424894
+ ,2299016
+ ,2130688
+ ,1652221
+ ,1608162
+ ,1647074
+ ,1479691
+ ,1884978
+ ,2007898
+ ,2208954
+ ,2217164
+ ,2534291
+ ,2560312
+ ,2429069
+ ,2315077
+ ,1799608
+ ,1772590
+ ,1744799
+ ,1659093
+ ,2099821
+ ,2135736
+ ,2427894
+ ,2468882
+ ,2703217
+ ,2766841
+ ,2655236
+ ,2550373
+ ,2052097
+ ,1998055
+ ,1920748
+ ,1876694
+ ,2380930
+ ,2467402
+ ,2770771
+ ,2781340
+ ,3143926
+ ,3172235
+ ,2952540
+ ,2920877
+ ,2384552
+ ,2248987
+ ,2208616
+ ,2178756
+ ,2632870
+ ,2706905
+ ,3029745
+ ,3015402
+ ,3391414
+ ,3507805
+ ,3177852
+ ,3142961
+ ,2545815
+ ,2414007
+ ,2372578
+ ,2332664
+ ,2825328
+ ,2901478
+ ,3263955
+ ,3226738
+ ,3610786
+ ,3709274
+ ,3467185
+ ,3449646
+ ,2802951
+ ,2462530
+ ,2490645
+ ,2561520
+ ,3067554
+ ,3226951
+ ,3546493
+ ,3492787
+ ,3952263
+ ,3932072
+ ,3720284
+ ,3651555
+ ,2914972
+ ,2713514
+ ,2703997
+ ,2591373
+ ,3163748
+ ,3355137
+ ,3613702
+ ,3686773
+ ,4098716
+ ,4063517
+ ,3551489
+ ,3226663
+ ,2656842
+ ,2597484
+ ,2572399
+ ,2596631
+ ,3165225
+ ,3303145
+ ,3698247
+ ,3668631
+ ,4130433
+ ,4131400
+ ,3864358
+ ,3721110
+ ,2892532
+ ,2843451
+ ,2747502
+ ,2668775
+ ,3018602
+ ,3013392
+ ,3393657
+ ,3544233
+ ,4075832
+ ,4032923
+ ,3734509
+ ,3761285
+ ,2970090
+ ,2847849
+ ,2741680
+ ,2830639
+ ,3257673
+ ,3480085
+ ,3843271
+ ,3796961
+ ,4337767
+ ,4243630
+ ,3927202
+ ,3915296
+ ,3087396
+ ,2963792
+ ,2955792
+ ,2829925
+ ,3281195
+ ,3548011
+ ,4059648
+ ,3941175
+ ,4528594
+ ,4433151
+ ,4145737
+ ,4077132
+ ,3198519
+ ,3078660
+ ,3028202
+ ,2858642
+ ,3398954
+ ,3808883
+ ,4175961
+ ,4227542
+ ,4744616
+ ,4608012
+ ,4295049
+ ,4201144
+ ,3353276
+ ,3286851
+ ,3169889
+ ,3051720
+ ,3695426
+ ,3905501
+ ,4296458
+ ,4246247
+ ,4921849
+ ,4821446
+ ,4425064
+ ,4379099
+ ,3472889
+ ,3359160
+ ,3200944
+ ,3153170
+ ,3741498
+ ,3918719
+ ,4403449
+ ,4400407
+ ,4847473
+ ,4716136
+ ,4297440
+ ,4272253
+ ,3271834
+ ,3168388
+ ,2911748
+ ,2720999
+ ,3199918
+ ,3672623
+ ,3892013
+ ,3850845
+ ,4532467
+ ,4484739
+ ,4014972
+ ,3983758
+ ,3158459
+ ,3100569
+ ,2935404
+ ,2855719
+ ,3465611
+ ,3006985
+ ,4095110
+ ,4104793
+ ,4730788
+ ,4642726
+ ,4246919
+ ,4308117)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> 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:  0.4486477 
 beta :  0 
 gamma:  0.9174003 

Coefficients:
          [,1]
a   3958169.81
b     14927.79
s1  -606169.87
s2  -704531.19
s3  -898047.03
s4  -998244.23
s5  -413328.51
s6  -463001.32
s7   423883.34
s8   352705.97
s9   929669.30
s10  804168.28
s11  355424.81
s12  344316.10
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1py4p1322581489.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2wzez1322581489.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/369m51322581489.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/437fq1322581489.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/5k4991322581489.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/66d9h1322581489.tab") 
> 
> try(system("convert tmp/1py4p1322581489.ps tmp/1py4p1322581489.png",intern=TRUE))
character(0)
> try(system("convert tmp/2wzez1322581489.ps tmp/2wzez1322581489.png",intern=TRUE))
character(0)
> try(system("convert tmp/369m51322581489.ps tmp/369m51322581489.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.688   0.217   1.908