R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(7263.63
+ ,7135.88
+ ,7008.00
+ ,6752.38
+ ,9339.00
+ ,9211.13
+ ,7263.63
+ ,5970.38
+ ,6098.13
+ ,6098.13
+ ,6226.00
+ ,6495.50
+ ,5714.75
+ ,4932.75
+ ,4292.38
+ ,4292.38
+ ,6752.38
+ ,7008.00
+ ,5060.50
+ ,2857.38
+ ,4022.88
+ ,4022.88
+ ,4932.75
+ ,5457.88
+ ,5330.00
+ ,4022.88
+ ,4677.13
+ ,4420.25
+ ,6623.38
+ ,6098.13
+ ,4022.88
+ ,2472.75
+ ,3895.00
+ ,4292.38
+ ,4677.13
+ ,5188.38
+ ,4150.63
+ ,3254.75
+ ,3639.50
+ ,3767.25
+ ,7135.88
+ ,7135.88
+ ,5188.38
+ ,4932.75
+ ,5714.75
+ ,5330.00
+ ,6367.75
+ ,7661.00
+ ,7917.88
+ ,6098.13
+ ,5585.63
+ ,5060.50
+ ,8570.88
+ ,8827.75
+ ,8173.50
+ ,8827.75
+ ,8698.63
+ ,7661.00
+ ,8827.75
+ ,10121.00
+ ,10646.13
+ ,9083.38
+ ,8045.63
+ ,8827.75
+ ,12196.25
+ ,13234.00
+ ,12978.38
+ ,13489.50
+ ,13361.75
+ ,12068.50
+ ,14271.63
+ ,14796.75
+ ,15564.88
+ ,13234.00
+ ,12324.13
+ ,13361.75
+ ,15834.38
+ ,18037.50
+ ,17512.38
+ ,17512.38
+ ,17769.25
+ ,16872.00
+ ,19204.25
+ ,19204.25
+ ,18806.88
+ ,16602.50
+ ,16999.88
+ ,17256.75
+ ,18947.38
+ ,21150.50
+ ,19587.63
+ ,20369.75
+ ,19715.50
+ ,19332.00
+ ,22317.25
+ ,21663.00
+ ,20753.13
+ ,19459.88
+ ,20753.13
+ ,21407.38
+ ,22188.13
+ ,23225.75
+ ,22188.13
+ ,22828.50
+ ,22047.63
+ ,21919.88
+ ,25160.63
+ ,25430.13
+ ,24392.50
+ ,22572.88
+ ,24123.00
+ ,24776.00
+ ,25558.00
+ ,26723.50
+ ,25558.00
+ ,26467.88
+ ,26070.50
+ ,24648.13
+ ,27633.25
+ ,27633.25)
> 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: 0.1476142
 beta : 0.09925795
 gamma: 1

Coefficients:
            [,1]
a   19703.044969
b     180.343573
s1      1.392754
s2      1.275252
s3      1.345374
s4      1.361840
s5      1.384745
s6      1.428925
s7      1.349156
s8      1.379125
s9      1.338345
s10     1.257048
s11     1.405335
s12     1.402486
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1hb7k1470820204.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/21eoa1470820204.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3m6pz1470820204.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/43m7l1470820204.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/5ikyn1470820204.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/6e9rd1470820204.tab") 
> 
> try(system("convert tmp/1hb7k1470820204.ps tmp/1hb7k1470820204.png",intern=TRUE))
character(0)
> try(system("convert tmp/21eoa1470820204.ps tmp/21eoa1470820204.png",intern=TRUE))
character(0)
> try(system("convert tmp/3m6pz1470820204.ps tmp/3m6pz1470820204.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.642   0.149   1.811