R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(133448.00
+ ,132951.00
+ ,132447.00
+ ,131404.00
+ ,141722.00
+ ,141176.00
+ ,133448.00
+ ,128310.00
+ ,128807.00
+ ,128807.00
+ ,129360.00
+ ,130354.00
+ ,131901.00
+ ,131901.00
+ ,130907.00
+ ,128310.00
+ ,141722.00
+ ,143766.00
+ ,140679.00
+ ,133448.00
+ ,136542.00
+ ,131901.00
+ ,133994.00
+ ,134995.00
+ ,136038.00
+ ,133448.00
+ ,133994.00
+ ,130354.00
+ ,141722.00
+ ,145313.00
+ ,142226.00
+ ,136542.00
+ ,142723.00
+ ,136038.00
+ ,142226.00
+ ,141722.00
+ ,143269.00
+ ,137585.00
+ ,143766.00
+ ,143269.00
+ ,152544.00
+ ,150451.00
+ ,142226.00
+ ,138082.00
+ ,143766.00
+ ,136038.00
+ ,141722.00
+ ,142723.00
+ ,144816.00
+ ,140182.00
+ ,142723.00
+ ,144270.00
+ ,149954.00
+ ,145313.00
+ ,139132.00
+ ,132447.00
+ ,138635.00
+ ,121625.00
+ ,129857.00
+ ,134491.00
+ ,139132.00
+ ,132447.00
+ ,132447.00
+ ,132447.00
+ ,136038.00
+ ,130907.00
+ ,124173.00
+ ,118538.00
+ ,122626.00
+ ,106666.00
+ ,116445.00
+ ,122129.00
+ ,123172.00
+ ,117488.00
+ ,117985.00
+ ,116445.00
+ ,121625.00
+ ,117985.00
+ ,110810.00
+ ,105623.00
+ ,114394.00
+ ,95347.00
+ ,107716.00
+ ,113351.00
+ ,113351.00
+ ,106666.00
+ ,100485.00
+ ,99988.00
+ ,105623.00
+ ,100485.00
+ ,90713.00
+ ,83979.00
+ ,91210.00
+ ,74207.00
+ ,89663.00
+ ,97888.00
+ ,100485.00
+ ,94801.00
+ ,87619.00
+ ,92757.00
+ ,94801.00
+ ,93254.00
+ ,77791.00
+ ,70616.00
+ ,75747.00
+ ,60291.00
+ ,76251.00
+ ,81935.00
+ ,86569.00
+ ,78841.00
+ ,71610.00
+ ,75747.00
+ ,77791.00
+ ,73703.00
+ ,58247.00
+ ,51513.00
+ ,57694.00
+ ,40691.00
+ ,59241.00
+ ,70616.00)
> 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)
Warning message:
In HoltWinters(x, seasonal = par3) :
  optimization difficulties: ERROR: ABNORMAL_TERMINATION_IN_LNSRCH
> fit
Holt-Winters exponential smoothing with trend and additive seasonal component.

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

Smoothing parameters:
 alpha: 0.405343
 beta : 0.06451955
 gamma: 1

Coefficients:
           [,1]
a    61417.0286
b    -1339.6264
s1   10128.0011
s2    2690.6343
s3   -3876.5857
s4     734.2721
s5    3598.9137
s6    1007.1298
s7  -12231.6366
s8  -16449.9831
s9   -7600.9171
s10 -21378.1448
s11  -1361.1484
s12   9198.9714
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1hh2t1439721740.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/25h3g1439721740.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3xmk71439721740.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4uvst1439721740.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/5z2y51439721740.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/6d9gj1439721740.tab") 
> 
> try(system("convert tmp/1hh2t1439721740.ps tmp/1hh2t1439721740.png",intern=TRUE))
character(0)
> try(system("convert tmp/25h3g1439721740.ps tmp/25h3g1439721740.png",intern=TRUE))
character(0)
> try(system("convert tmp/3xmk71439721740.ps tmp/3xmk71439721740.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.395   0.226   1.618