R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

  Natural language support but running in an English locale

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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(235.1
+ ,280.7
+ ,264.6
+ ,240.7
+ ,201.4
+ ,240.8
+ ,241.1
+ ,223.8
+ ,206.1
+ ,174.7
+ ,203.3
+ ,220.5
+ ,299.5
+ ,347.4
+ ,338.3
+ ,327.7
+ ,351.6
+ ,396.6
+ ,438.8
+ ,395.6
+ ,363.5
+ ,378.8
+ ,357
+ ,369
+ ,464.8
+ ,479.1
+ ,431.3
+ ,366.5
+ ,326.3
+ ,355.1
+ ,331.6
+ ,261.3
+ ,249
+ ,205.5
+ ,235.6
+ ,240.9
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+ ,253.8
+ ,232.3
+ ,193.8
+ ,177
+ ,213.2
+ ,207.2
+ ,180.6
+ ,188.6
+ ,175.4
+ ,199
+ ,179.6
+ ,225.8
+ ,234
+ ,200.2
+ ,183.6
+ ,178.2
+ ,203.2
+ ,208.5
+ ,191.8
+ ,172.8
+ ,148
+ ,159.4
+ ,154.5
+ ,213.2
+ ,196.4
+ ,182.8
+ ,176.4
+ ,153.6
+ ,173.2
+ ,171
+ ,151.2
+ ,161.9
+ ,157.2
+ ,201.7
+ ,236.4
+ ,356.1
+ ,398.3
+ ,403.7
+ ,384.6
+ ,365.8
+ ,368.1
+ ,367.9
+ ,347
+ ,343.3
+ ,292.9
+ ,311.5
+ ,300.9
+ ,366.9
+ ,356.9
+ ,329.7
+ ,316.2
+ ,269
+ ,289.3
+ ,266.2
+ ,253.6
+ ,233.8
+ ,228.4
+ ,253.6
+ ,260.1
+ ,306.6
+ ,309.2
+ ,309.5
+ ,271
+ ,279.9
+ ,317.9
+ ,298.4
+ ,246.7
+ ,227.3
+ ,209.1
+ ,259.9
+ ,266
+ ,320.6
+ ,308.5
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+ ,262.7
+ ,263.5
+ ,313.1
+ ,284.3
+ ,252.6
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+ ,246.5
+ ,312.7
+ ,333.2
+ ,446.4
+ ,511.6
+ ,515.5
+ ,506.4
+ ,483.2
+ ,522.3
+ ,509.8
+ ,460.7
+ ,405.8
+ ,375
+ ,378.5
+ ,406.8
+ ,467.8
+ ,469.8
+ ,429.8
+ ,355.8
+ ,332.7
+ ,378
+ ,360.5
+ ,334.7
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+ ,363.6
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+ ,360.7
+ ,338
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+ ,388.4
+ ,371.1
+ ,331.5
+ ,353.7
+ ,396.7
+ ,447
+ ,533.5
+ ,565.4
+ ,542.3
+ ,488.7
+ ,467.1
+ ,531.3
+ ,496.1
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+ ,386.3
+ ,394.1
+ ,404.1
+ ,462.1
+ ,448.1
+ ,432.3
+ ,386.3
+ ,395.2
+ ,421.9
+ ,382.9
+ ,384.2
+ ,345.5
+ ,323.4
+ ,372.6
+ ,376
+ ,462.7
+ ,487
+ ,444.2
+ ,399.3
+ ,394.9
+ ,455.4
+ ,414
+ ,375.5
+ ,347
+ ,339.4
+ ,385.8
+ ,378.8
+ ,451.8
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+ ,422.5
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+ ,352.8
+ ,445.3
+ ,367.5
+ ,355.1
+ ,326.2
+ ,319.8
+ ,331.8
+ ,340.9
+ ,394.1
+ ,417.2
+ ,369.9
+ ,349.2
+ ,321.4
+ ,405.7
+ ,342.9
+ ,316.5
+ ,284.2
+ ,270.9
+ ,288.8
+ ,278.8
+ ,324.4
+ ,310.9
+ ,299
+ ,273
+ ,279.3
+ ,359.2
+ ,305
+ ,282.1
+ ,250.3
+ ,246.5
+ ,257.9
+ ,266.5
+ ,315.9
+ ,318.4
+ ,295.4
+ ,266.4
+ ,245.8
+ ,362.8
+ ,324.9
+ ,294.2
+ ,289.5
+ ,295.2
+ ,290.3
+ ,272
+ ,307.4
+ ,328.7
+ ,292.9
+ ,249.1
+ ,230.4
+ ,361.5
+ ,321.7
+ ,277.2
+ ,260.7
+ ,251
+ ,257.6
+ ,241.8
+ ,287.5
+ ,292.3
+ ,274.7
+ ,254.2
+ ,230
+ ,339
+ ,318.2
+ ,287
+ ,295.8
+ ,284
+ ,271
+ ,262.7
+ ,340.6
+ ,379.4
+ ,373.3
+ ,355.2
+ ,338.4
+ ,466.9
+ ,451
+ ,422
+ ,429.2
+ ,425.9
+ ,460.7
+ ,463.6
+ ,541.4
+ ,544.2
+ ,517.5
+ ,469.4
+ ,439.4
+ ,549
+ ,533
+ ,506.1
+ ,484
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+ ,469.5
+ ,544.7
+ ,541.2
+ ,521.5
+ ,469.7
+ ,434.4
+ ,542.6
+ ,517.3
+ ,485.7
+ ,465.8
+ ,447
+ ,426.6
+ ,411.6
+ ,467.5
+ ,484.5
+ ,451.2
+ ,417.4
+ ,379.9
+ ,484.7
+ ,455
+ ,420.8
+ ,416.5
+ ,376.3
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+ ,500.8
+ ,514
+ ,475.5
+ ,430.1
+ ,414.4
+ ,538
+ ,526
+ ,488.5
+ ,520.2
+ ,504.4
+ ,568.5
+ ,610.6
+ ,818
+ ,830.9
+ ,835.9
+ ,782
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+ ,856.9
+ ,820.9
+ ,769.6
+ ,752.2
+ ,724.4
+ ,723.1
+ ,719.5
+ ,817.4
+ ,803.3
+ ,752.5
+ ,689
+ ,630.4
+ ,765.5
+ ,757.7
+ ,732.2
+ ,702.6
+ ,683.3
+ ,709.5
+ ,702.2
+ ,784.8
+ ,810.9
+ ,755.6
+ ,656.8
+ ,615.1
+ ,745.3
+ ,694.1
+ ,675.7
+ ,643.7
+ ,622.1
+ ,634.6
+ ,588
+ ,689.7
+ ,673.9
+ ,647.9
+ ,568.8
+ ,545.7
+ ,632.6
+ ,643.8
+ ,593.1
+ ,579.7
+ ,546
+ ,562.9
+ ,572.5)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2010), Exponential Smoothing (v1.0.4) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> 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 additive seasonal component.

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

Smoothing parameters:
 alpha:  0.8590898 
 beta :  0.07395515 
 gamma:  1 

Coefficients:
          [,1]
a   605.764538
b    -2.668540
s1   59.633075
s2   49.172865
s3   11.798973
s4  -42.657479
s5  -54.164262
s6   66.348080
s7   38.628450
s8  -11.116655
s9  -31.866070
s10 -53.967531
s11 -31.386357
s12 -33.264538
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/freestat/rcomp/tmp/1rtss1291068890.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/2jksv1291068890.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/3jksv1291068890.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/www/html/freestat/rcomp/tmp/4xu7m1291068890.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/www/html/freestat/rcomp/tmp/5jvos1291068890.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/www/html/freestat/rcomp/tmp/6um5v1291068890.tab") 
> 
> try(system("convert tmp/1rtss1291068890.ps tmp/1rtss1291068890.png",intern=TRUE))
character(0)
> try(system("convert tmp/2jksv1291068890.ps tmp/2jksv1291068890.png",intern=TRUE))
character(0)
> try(system("convert tmp/3jksv1291068890.ps tmp/3jksv1291068890.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.913   0.865   3.059