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(1.5469,1.5501,1.5494,1.5475,1.5449,1.5391,1.5578,1.5528,1.5496,1.549,1.5449,1.5479,1.5494,1.558,1.5691,1.5748,1.5564,1.5601,1.5687,1.5775,1.5841,1.5898,1.5922,1.5969,1.6155,1.6212,1.6124,1.6375,1.6506,1.6543,1.6567,1.6383,1.6475,1.6706,1.6485,1.6592,1.6203,1.608,1.572,1.5964,1.6247,1.6139,1.6193,1.6212,1.5942,1.5194,1.5162,1.5393,1.4935,1.4904,1.5083,1.5147,1.5118,1.5148,1.5202,1.5236,1.5148,1.5138,1.5105,1.502,1.4765,1.4671,1.4482,1.4337,1.4181,1.3767,1.346,1.3413,1.3089,1.3452,1.3442,1.2811,1.2779,1.2974,1.2867,1.2977,1.2537,1.2092,1.1766,1.1203,1.2005,1.2295,1.2307,1.2276,1.2108,1.2071,1.2061,1.2023,1.2012,1.2011,1.2011,1.2011,1.2089,1.2098,1.2052,1.2091,1.2288,1.2298,1.2266,1.2199,1.2418,1.2322,1.2366,1.2338,1.2338,1.2316,1.2316,1.2245)
> 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: 0.916699
 beta : 0.04257896
 gamma: 1

Coefficients:
             [,1]
a    1.2325140255
b   -0.0019991907
s1  -0.0099247717
s2  -0.0024614791
s3   0.0025603774
s4   0.0123611945
s5   0.0026569715
s6  -0.0112230944
s7  -0.0016766701
s8   0.0008143264
s9   0.0066223356
s10  0.0038199538
s11 -0.0039860224
s12 -0.0080140255
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/17j371432672982.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2rs531432672982.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3a3ib1432672983.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/4gjxe1432672983.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/5cjdr1432672983.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/6wa9q1432672983.tab") 
> 
> try(system("convert tmp/17j371432672982.ps tmp/17j371432672982.png",intern=TRUE))
character(0)
> try(system("convert tmp/2rs531432672982.ps tmp/2rs531432672982.png",intern=TRUE))
character(0)
> try(system("convert tmp/3a3ib1432672983.ps tmp/3a3ib1432672983.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.606   0.262   1.867