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Type 'q()' to quit R. > x <- c(5789,6333,6901,5813,6504,5619,5867,6084,5258,5601,5081,4678,5463,5546,6810,6407,5985,5119,5904,5034,4922,6083,4365,4464,4557,5885,5286,6017,5376,5935,6276,5510,5998,5193,4602,5326,5307,5014,6153,6441,5584,6427,6062,5589,6216,5809,4989,6706,7174,6122,8075,6292,6337,8576,6077,5931,6288,7167,6054,6468,6403,6927,7914,7728,8701,8522,6481,7502,7778,7424,6941,8574,9171,7718,9083,7164,8213,8124,7075,7026,7390,7778,6203,6905,7087,6495,7664,6516,6322,7828,6708,6717,5707,8063,6315,5893,6914,7319,6615,7341,6210,7408,6168,5878,6834,6211,5982,6973) > 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$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ > #Source of accompanying publication: > #Technical description: > par1 <- as.numeric(par1) > if (par2 == 'Single') K <- 1 > if (par2 == 'Double') K <- 2 > if (par2 == 'Triple') K <- par1 > nx <- length(x) > nxmK <- nx - K > x <- ts(x, frequency = par1) > if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) > if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) > if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) > fit Holt-Winters exponential smoothing with trend and multiplicative seasonal component. Call: HoltWinters(x = x, seasonal = par3) Smoothing parameters: alpha: 0.2272263 beta : 0.004007195 gamma: 0.4682686 Coefficients: [,1] a 6442.5482277 b -13.6834571 s1 1.0570934 s2 1.0277361 s3 1.0916501 s4 1.0559057 s5 1.0102575 s6 1.1666898 s7 0.9853803 s8 0.9777636 s9 1.0198207 s10 1.0755497 s11 0.9375713 s12 1.0220097 > myresid <- x - fit$fitted[,'xhat'] > postscript(file="/var/www/html/rcomp/tmp/18p2b1264450506.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/rcomp/tmp/2nee71264450506.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/rcomp/tmp/3jqyl1264450506.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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/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$gamma) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/www/html/rcomp/tmp/4ehph1264450506.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Observed',header=TRUE) > a<-table.element(a,'Fitted',header=TRUE) > a<-table.element(a,'Residuals',header=TRUE) > a<-table.row.end(a) > for (i in 1:nxmK) { + a<-table.row.start(a) + a<-table.element(a,i+K,header=TRUE) + a<-table.element(a,x[i+K]) + a<-table.element(a,fit$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/rcomp/tmp/5did11264450506.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/rcomp/tmp/6wt0w1264450506.tab") > > try(system("convert tmp/18p2b1264450506.ps tmp/18p2b1264450506.png",intern=TRUE)) character(0) > try(system("convert tmp/2nee71264450506.ps tmp/2nee71264450506.png",intern=TRUE)) character(0) > try(system("convert tmp/3jqyl1264450506.ps tmp/3jqyl1264450506.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 0.925 0.510 1.161