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(221102
+ ,220892
+ ,225537
+ ,219334
+ ,216126
+ ,224573
+ ,213991
+ ,221865
+ ,215382
+ ,213962
+ ,217009
+ ,318110
+ ,219662
+ ,212650
+ ,209307
+ ,210541
+ ,210609
+ ,208910
+ ,207541
+ ,207699
+ ,205005
+ ,205747
+ ,203644
+ ,229937
+ ,214446
+ ,210194
+ ,206535
+ ,216524
+ ,198243
+ ,208274
+ ,207493
+ ,215525
+ ,207562
+ ,213355
+ ,209048
+ ,220497
+ ,214563
+ ,211571
+ ,216385
+ ,211496
+ ,209683
+ ,206304
+ ,213925
+ ,204829
+ ,205729
+ ,200296
+ ,207960
+ ,207729
+ ,208327
+ ,207794
+ ,213700
+ ,213136
+ ,210354
+ ,202205
+ ,220425
+ ,210038
+ ,205201
+ ,197441
+ ,200021
+ ,203165
+ ,201699
+ ,201003
+ ,232308
+ ,211412
+ ,209661
+ ,213587
+ ,193611
+ ,192543
+ ,196040
+ ,191407
+ ,189726
+ ,191272
+ ,187924
+ ,198213
+ ,199352
+ ,199289
+ ,195475
+ ,198045
+ ,197615
+ ,189015
+ ,189668
+ ,189120
+ ,194168
+ ,192304
+ ,185913
+ ,197599
+ ,186085
+ ,190566
+ ,187054
+ ,193222
+ ,189856
+ ,190608
+ ,190588
+ ,186773
+ ,183510
+ ,180106
+ ,180150
+ ,178412
+ ,182353
+ ,203805
+ ,186054
+ ,184290
+ ,187483
+ ,187111
+ ,189561
+ ,184439
+ ,182985
+ ,183828
+ ,184036
+ ,183214
+ ,183464
+ ,173718
+ ,180210
+ ,171252
+ ,172705
+ ,174006
+ ,172043
+ ,169445
+ ,169449
+ ,177073
+ ,170799
+ ,171648
+ ,172220
+ ,165795
+ ,167466
+ ,165528
+ ,162851
+ ,165864
+ ,162094
+ ,162385
+ ,164293
+ ,165983
+ ,159680
+ ,161739
+ ,159302
+ ,167795
+ ,164242
+ ,159743
+ ,160887
+ ,163844
+ ,161172
+ ,159330
+ ,155570
+ ,156749
+ ,155012
+ ,163419
+ ,153630
+ ,154535
+ ,151543
+ ,152955
+ ,150166
+ ,151416
+ ,150332
+ ,152196
+ ,153422
+ ,147435)
> par3 = 'multiplicative'
> par2 = 'Double'
> par1 = '12'
> par3 <- 'multiplicative'
> par2 <- 'Double'
> 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 without seasonal component.

Call:
HoltWinters(x = x, gamma = F)

Smoothing parameters:
 alpha: 1
 beta : 1
 gamma: FALSE

Coefficients:
    [,1]
a 147435
b  -5987
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/10crn1389527983.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2im661389527983.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3ljdp1389527983.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4q7131389527983.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/5eby31389527983.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/6kqe21389527983.tab") 
> 
> try(system("convert tmp/10crn1389527983.ps tmp/10crn1389527983.png",intern=TRUE))
character(0)
> try(system("convert tmp/2im661389527983.ps tmp/2im661389527983.png",intern=TRUE))
character(0)
> try(system("convert tmp/3ljdp1389527983.ps tmp/3ljdp1389527983.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  5.264   1.011   6.227