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)

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> x <- c(221.102
+ ,220.892
+ ,225.537
+ ,219.334
+ ,216.126
+ ,224.573
+ ,213.991
+ ,221.865
+ ,215.382
+ ,213.962
+ ,217.009
+ ,318.110
+ ,219.662
+ ,212.650
+ ,209.307
+ ,210.541
+ ,210.609
+ ,208.910
+ ,207.541
+ ,207.699
+ ,205.005
+ ,205.747
+ ,203.644
+ ,229.937
+ ,214.446
+ ,210.194
+ ,206.535
+ ,216.524
+ ,198.243
+ ,208.274
+ ,207.493
+ ,215.525
+ ,207.562
+ ,213.355
+ ,209.048
+ ,220.497
+ ,214.563
+ ,211.571
+ ,216.385
+ ,211.496
+ ,209.683
+ ,206.304
+ ,213.925
+ ,204.829
+ ,205.729
+ ,200.296
+ ,207.960
+ ,207.729
+ ,208.327
+ ,207.794
+ ,213.700
+ ,213.136
+ ,210.354
+ ,202.205
+ ,220.425
+ ,210.038
+ ,205.201
+ ,197.441
+ ,200.021
+ ,203.165
+ ,201.699
+ ,201.003
+ ,232.308
+ ,211.412
+ ,209.661
+ ,213.587
+ ,193.611
+ ,192.543
+ ,196.040
+ ,191.407
+ ,189.726
+ ,191.272
+ ,187.924
+ ,198.213
+ ,199.352
+ ,199.289
+ ,195.475
+ ,198.045
+ ,197.615
+ ,189.015
+ ,189.668
+ ,189.120
+ ,194.168
+ ,192.304
+ ,185.913
+ ,197.599
+ ,186.085
+ ,190.566
+ ,187.054
+ ,193.222
+ ,189.856
+ ,190.608
+ ,190.588
+ ,186.773
+ ,183.510
+ ,180.106
+ ,180.150
+ ,178.412
+ ,182.353
+ ,203.805
+ ,186.054
+ ,184.290
+ ,187.483
+ ,187.111
+ ,189.561
+ ,184.439
+ ,182.985
+ ,183.828
+ ,184.036
+ ,183.214
+ ,183.464
+ ,173.718
+ ,180.210
+ ,171.252
+ ,172.705
+ ,174.006
+ ,172.043
+ ,169.445
+ ,169.449
+ ,177.073
+ ,170.799
+ ,171.648
+ ,172.220
+ ,165.795
+ ,167.466
+ ,165.528
+ ,162.851
+ ,165.864
+ ,162.094
+ ,162.385
+ ,164.293
+ ,165.983
+ ,159.680
+ ,161.739
+ ,159.302
+ ,167.795
+ ,164.242
+ ,159.743
+ ,160.887
+ ,163.844
+ ,161.172
+ ,159.330
+ ,155.570
+ ,156.749
+ ,155.012
+ ,163.419
+ ,153.630
+ ,154.535
+ ,151.543
+ ,152.955
+ ,150.166
+ ,151.416
+ ,150.332
+ ,152.196
+ ,153.422
+ ,147.435)
> par3 = 'multiplicative'
> par2 = 'Triple'
> par1 = '12'
> par3 <- 'multiplicative'
> 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 multiplicative seasonal component.

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

Smoothing parameters:
 alpha: 0.160528
 beta : 0.02018023
 gamma: 0.98245

Coefficients:
           [,1]
a   146.0328280
b    -0.5958819
s1    1.0120399
s2    1.0640098
s3    1.0079419
s4    1.0260758
s5    1.0156934
s6    1.0272045
s7    1.0149512
s8    1.0303519
s9    1.0270571
s10   1.0395900
s11   1.0437126
s12   1.0097752
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/134rf1387054098.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2w6bx1387054098.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3k3rf1387054098.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/409bq1387054098.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/5p5fb1387054098.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/63kh71387054098.tab") 
> 
> try(system("convert tmp/134rf1387054098.ps tmp/134rf1387054098.png",intern=TRUE))
character(0)
> try(system("convert tmp/2w6bx1387054098.ps tmp/2w6bx1387054098.png",intern=TRUE))
character(0)
> try(system("convert tmp/3k3rf1387054098.ps tmp/3k3rf1387054098.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.942   0.532   3.458