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

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> x <- c(464,675,703,887,1139,1077,1318,1260,1120,963,996,960,530,883,894,1045,1199,1287,1565,1577,1076,918,1008,1063,544,635,804,980,1018,1064,1404,1286,1104,999,996,1015,615,722,832,977,1270,1437,1520,1708,1151,934,1159,1209,699,830,996,1124,1458,1270,1753,2258,1208,1241,1265,1828,809,997,1164,1205,1538,1513,1378,2083,1357,1536,1526,1376,779,1005,1193,1522,1539,1546,2116,2326,1596,1356,1553,1613,814,1150,1225,1691,1759,1754,2100,2062,2012,1897,1964,2186,966,1549,1538,1612,2078,2137,2907,2249,1883,1739,1828,1868,1138,1430,1809,1763,2200,2067,2503,2141,2103,1972,2181,2344,970,1199,1718,1683,2025,2051,2439,2353,2230,1852,2147,2286,1007,1665,1642,1518,1831,2207,2822,2393,2306,1785,2047,2171,1212,1335,2011,1860,1954,2152,2835,2224,2182,1992,2389,2724,891,1247,2017,2257,2255,2255,3057,3330,1896,2096,2374,2535,1041,1728,2201,2455,2204,2660,3670,2665,2639,2226,2586,2684,1185,1749,2459,2618,2585,3310,3923)
> par3 = 'multiplicative'
> 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 multiplicative seasonal component.

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

Smoothing parameters:
 alpha:  0.1290741 
 beta :  0.0005009341 
 gamma:  0.3224623 

Coefficients:
            [,1]
a   2785.5036509
b     11.5524071
s1     1.1655214
s2     0.9890790
s3     0.8938193
s4     1.0177694
s5     1.0797497
s6     0.4690901
s7     0.6752417
s8     0.8993748
s9     0.9397249
s10    0.9511130
s11    1.0847383
s12    1.3648732
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/www/html/freestat/rcomp/tmp/1idjo1275508476.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/2bnir1275508476.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/3bnir1275508476.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$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/47wgi1275508476.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/505xl1275508476.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/6lov81275508476.tab") 
> 
> try(system("convert tmp/1idjo1275508476.ps tmp/1idjo1275508476.png",intern=TRUE))
character(0)
> try(system("convert tmp/2bnir1275508476.ps tmp/2bnir1275508476.png",intern=TRUE))
character(0)
> try(system("convert tmp/3bnir1275508476.ps tmp/3bnir1275508476.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.603   0.775   1.746