R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-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(6.34
+ ,6.42
+ ,6.55
+ ,6.46
+ ,6.25
+ ,6.62
+ ,6.77
+ ,7.08
+ ,7.31
+ ,7.3
+ ,7.19
+ ,7.51
+ ,7.66
+ ,7.5
+ ,8.02
+ ,7.63
+ ,7.25
+ ,7.24
+ ,7.16
+ ,6.83
+ ,6.59
+ ,6.76
+ ,6.43
+ ,6.21
+ ,5.69
+ ,5.56
+ ,5.55
+ ,5.32
+ ,5.07
+ ,5.19
+ ,5.18
+ ,5.16
+ ,4.96
+ ,4.67
+ ,4.54
+ ,4.39
+ ,4.25
+ ,4.32
+ ,4.55
+ ,4.47
+ ,4.36
+ ,4.33
+ ,4.32
+ ,4.49
+ ,4.42
+ ,4.55
+ ,4.56
+ ,4.41
+ ,4.22
+ ,4.17
+ ,4.05
+ ,4.12
+ ,4.13
+ ,4.08
+ ,4.01
+ ,3.93
+ ,3.75
+ ,3.59
+ ,3.55
+ ,3.27
+ ,3.0617
+ ,3.0297
+ ,3.0462
+ ,2.7564
+ ,2.6827
+ ,2.8363
+ ,3.03
+ ,3.2373
+ ,3.3011
+ ,3.6837
+ ,3.6892
+ ,3.8263
+ ,3.9495
+ ,4.1114
+ ,4.2675
+ ,4.3645
+ ,4.8485
+ ,4.9649
+ ,5.105
+ ,5.2484
+ ,5.2192
+ ,5.2184
+ ,5.1933
+ ,4.8809
+ ,4.5736
+ ,4.5913
+ ,4.4711
+ ,4.4811
+ ,4.5205
+ ,4.3125
+ ,4.3109
+ ,4.1075
+ ,3.77
+ ,3.3694
+ ,3.1979
+ ,3.2981
+ ,3.4832
+ ,3.5936
+ ,3.8156
+ ,3.8602
+ ,3.9627
+ ,3.8688
+ ,3.6448
+ ,3.4404
+ ,3.2364
+ ,3.1259
+ ,3.0174
+ ,2.8716
+ ,2.7045
+ ,2.5036
+ ,2.4112
+ ,2.447
+ ,2.2521
+ ,2.0137
+ ,2.0761
+ ,2.2786
+ ,2.2576
+ ,2.3025
+ ,2.4103
+ ,2.3808
+ ,2.2163
+ ,2.163
+ ,2.055
+ ,2.1626
+ ,2.2974
+ ,2.4044
+ ,2.361
+ ,2.302
+ ,2.377
+ ,2.3161
+ ,2.3283
+ ,2.301
+ ,2.3121
+ ,2.31
+ ,2.3348
+ ,2.2651
+ ,2.1933
+ ,2.1028
+ ,2.168
+ ,2.2229
+ ,2.2195
+ ,2.4136
+ ,2.6844
+ ,2.7833
+ ,2.8335
+ ,2.9142
+ ,3.1053
+ ,3.2214
+ ,3.3078
+ ,3.4005
+ ,3.5386
+ ,3.6151
+ ,3.7153
+ ,3.7992
+ ,3.8637
+ ,3.9209
+ ,4.0644
+ ,4.0936
+ ,4.1055
+ ,4.2527
+ ,4.3731
+ ,4.5055
+ ,4.5638
+ ,4.6663
+ ,4.7245
+ ,4.6467
+ ,4.6072
+ ,4.7929
+ ,4.498
+ ,4.3489
+ ,4.5901
+ ,4.8199
+ ,4.9938
+ ,5.3608
+ ,5.3932
+ ,5.323
+ ,5.3839
+ ,5.2478
+ ,4.3504
+ ,3.452
+ ,2.6216
+ ,2.1354
+ ,1.9089
+ ,1.771
+ ,1.6444
+ ,1.6105
+ ,1.412
+ ,1.3343
+ ,1.261
+ ,1.2426
+ ,1.2306
+ ,1.2424
+ ,1.2322
+ ,1.2252
+ ,1.2151
+ ,1.2252
+ ,1.2493
+ ,1.2813
+ ,1.3734
+ ,1.421
+ ,1.4205
+ ,1.4954
+ ,1.5405
+ ,1.5261
+ ,1.55
+ ,1.714
+ ,1.9241
+ ,2.0856
+ ,2.1471
+ ,2.1441
+ ,2.1827
+ ,2.0969
+ ,2.0669
+ ,2.1101
+ ,2.0439
+ ,2.0035
+ ,1.8366
+ ,1.6783
+ ,1.4985
+ ,1.3678
+ ,1.266
+ ,1.219
+ ,1.0608
+ ,0.8766
+ ,0.7398
+ ,0.6501
+ ,0.5879
+ ,0.5493
+ ,0.5753
+ ,0.5942
+ ,0.545
+ ,0.5284
+ ,0.4838
+ ,0.5071
+ ,0.5254
+ ,0.5423
+ ,0.5434
+ ,0.541)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> par3 <- 'additive'
> par2 <- 'Triple'
> par1 <- '12'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), Exponential Smoothing (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/
> #Source of accompanying publication: 
> #
> 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 additive seasonal component.

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

Smoothing parameters:
 alpha: 0.8557739
 beta : 0.1100044
 gamma: 1

Coefficients:
           [,1]
a    0.61328674
b   -0.01254753
s1  -0.17374251
s2  -0.22685527
s3  -0.27510958
s4  -0.22661480
s5  -0.06886037
s6   0.14040761
s7   0.26322866
s8   0.30668678
s9   0.21356996
s10  0.07687865
s11 -0.02169301
s12 -0.07228674
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/fisher/rcomp/tmp/1ehlp1385124656.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/fisher/rcomp/tmp/217uw1385124656.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/fisher/rcomp/tmp/3xrs01385124656.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/fisher/rcomp/tmp/4pafk1385124656.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/fisher/rcomp/tmp/50h141385124656.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/fisher/rcomp/tmp/6r4ct1385124656.tab") 
> 
> try(system("convert tmp/1ehlp1385124656.ps tmp/1ehlp1385124656.png",intern=TRUE))
character(0)
> try(system("convert tmp/217uw1385124656.ps tmp/217uw1385124656.png",intern=TRUE))
character(0)
> try(system("convert tmp/3xrs01385124656.ps tmp/3xrs01385124656.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.714   0.484   3.182