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(420.677
+ ,417.428
+ ,423.245
+ ,423.113
+ ,418.873
+ ,405.733
+ ,397.812
+ ,389.918
+ ,391.116
+ ,443.814
+ ,460.373
+ ,455.422
+ ,456.288
+ ,452.233
+ ,459.256
+ ,461.146
+ ,451.391
+ ,443.101
+ ,438.81
+ ,430.457
+ ,435.721
+ ,488.28
+ ,505.814
+ ,502.338
+ ,500.91
+ ,501.434
+ ,515.476
+ ,520.862
+ ,519.517
+ ,511.805
+ ,508.607
+ ,505.327
+ ,511.435
+ ,570.158
+ ,591.665
+ ,593.572
+ ,586.346
+ ,586.063
+ ,591.504
+ ,594.033
+ ,585.597
+ ,572.45
+ ,562.917
+ ,554.675
+ ,553.997
+ ,601.31
+ ,622.255
+ ,616.735
+ ,606.48
+ ,595.079
+ ,598.588
+ ,599.917
+ ,591.573
+ ,575.489
+ ,567.223
+ ,555.338
+ ,555.252
+ ,608.249
+ ,630.859
+ ,628.632
+ ,624.435
+ ,609.67
+ ,615.83
+ ,621.17
+ ,604.212
+ ,584.348
+ ,573.717
+ ,555.234
+ ,544.897
+ ,598.866
+ ,620.081
+ ,607.699
+ ,589.96
+ ,578.665
+ ,580.166
+ ,579.457
+ ,571.56
+ ,560.46
+ ,551.397
+ ,536.763
+ ,540.562
+ ,588.184
+ ,607.049
+ ,598.968
+ ,577.644
+ ,562.64
+ ,565.867
+ ,561.274
+ ,554.144
+ ,539.9
+ ,526.271
+ ,511.841
+ ,505.282
+ ,554.083
+ ,584.225
+ ,568.858
+ ,539.516
+ ,521.612
+ ,525.562
+ ,526.519
+ ,515.713
+ ,503.454
+ ,489.301
+ ,479.02
+ ,475.102
+ ,523.682
+ ,551.528
+ ,531.626
+ ,511.037
+ ,492.417
+ ,492.188
+ ,492.865
+ ,480.961
+ ,461.935
+ ,456.608
+ ,441.977
+ ,439.148
+ ,488.18
+ ,520.564
+ ,501.492
+ ,485.025
+ ,464.196
+ ,460.17
+ ,467.037
+ ,460.07
+ ,447.988
+ ,442.867
+ ,436.087
+ ,431.328
+ ,484.015
+ ,509.673
+ ,512.927
+ ,502.831
+ ,470.984
+ ,471.067
+ ,476.049
+ ,474.605
+ ,470.439
+ ,461.251
+ ,454.724
+ ,455.626
+ ,516.847
+ ,525.192
+ ,522.975
+ ,518.585
+ ,509.239
+ ,512.238
+ ,519.164
+ ,517.009
+ ,509.933
+ ,509.127
+ ,500.857
+ ,506.971
+ ,569.323
+ ,579.714
+ ,577.992
+ ,565.464
+ ,547.344
+ ,554.788
+ ,562.325
+ ,560.854
+ ,555.332
+ ,543.599
+ ,536.662
+ ,542.722
+ ,593.53
+ ,610.763
+ ,612.613
+ ,611.324
+ ,594.167
+ ,595.454
+ ,590.865
+ ,589.379
+ ,584.428
+ ,573.1
+ ,567.456
+ ,569.028
+ ,620.735
+ ,628.884
+ ,628.232
+ ,612.117
+ ,595.404
+ ,597.141
+ ,593.408
+ ,590.072
+ ,579.799
+ ,574.205
+ ,572.775
+ ,572.942
+ ,619.567
+ ,625.809
+ ,619.916
+ ,587.625
+ ,565.742
+ ,557.274
+ ,560.576
+ ,548.854
+ ,531.673
+ ,525.919
+ ,511.038
+ ,498.662
+ ,555.362
+ ,564.591
+ ,541.657
+ ,527.07
+ ,509.846
+ ,514.258
+ ,516.922
+ ,507.561
+ ,492.622
+ ,490.243
+ ,469.357
+ ,477.58
+ ,528.379
+ ,533.59
+ ,517.945
+ ,506.174
+ ,501.866
+ ,516.141
+ ,528.222
+ ,532.638
+ ,536.322
+ ,536.535
+ ,523.597
+ ,536.214
+ ,586.57
+ ,596.594
+ ,580.523
+ ,564.478
+ ,557.56
+ ,575.093
+ ,580.112
+ ,574.761
+ ,563.25
+ ,551.531
+ ,537.034
+ ,544.686
+ ,600.991
+ ,604.378
+ ,586.111
+ ,563.668
+ ,548.604
+ ,551.174
+ ,555.654
+ ,547.97
+ ,540.324
+ ,530.577
+ ,520.579
+ ,518.654
+ ,572.273
+ ,581.302
+ ,563.28
+ ,547.612)
> 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:  0.8992035 
 beta :  0.07267612 
 gamma:  1 

Coefficients:
           [,1]
a   541.3110517
b    -0.8934555
s1   -3.2878335
s2    5.5191098
s3   11.6765513
s4    5.7810771
s5   -7.0394193
s6  -19.0808231
s7  -33.6122816
s8  -33.6175269
s9   16.3239176
s10  26.7538404
s11  17.8456910
s12   6.3009483
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1z4ni1322557044.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/27cn31322557044.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3lrbw1322557044.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4ygk21322557044.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/5m2o91322557044.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/67pa81322557044.tab") 
> 
> try(system("convert tmp/1z4ni1322557044.ps tmp/1z4ni1322557044.png",intern=TRUE))
character(0)
> try(system("convert tmp/27cn31322557044.ps tmp/27cn31322557044.png",intern=TRUE))
character(0)
> try(system("convert tmp/3lrbw1322557044.ps tmp/3lrbw1322557044.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.808   0.175   1.986