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Type 'q()' to quit R. > x <- c(15859.4,15258.9,15498.6,15106.5,15023.6,12083.0,15761.3,16942.6,15070.3,13659.6,14768.9,14725.1,15998.1,15370.6,14956.9,15469.7,15101.8,11703.7,16283.6,16726.5,14968.9,14861.0,14583.3,15305.8,17903.9,16379.4,15420.3,17870.5,15912.8,13866.5,17823.2,17872.0,17422.0,16704.5,15991.2,16583.6,19123.5,17838.7,17209.4,18586.5,16258.1,15141.6,19202.1,17746.5,19090.1,18040.3,17515.5,17751.8,21072.4,17170.0,19439.5,19795.4,17574.9,16165.4,19464.6,19932.1,19961.2,17343.4,18924.2,18574.1,21350.6) > 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: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/ > #Source of accompanying publication: Office for Research, Development, and Education > #Technical description: Write here your technical program description (don't use hard returns!) > par1 <- as.numeric(par1) > if (par2 == 'Single') K <- 1 > if (par2 == 'Double') K <- 2 > if (par2 == 'Triple') K <- par1 > nx <- length(x) > nxmK <- nx - K > x <- ts(x, frequency = par1) > if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) > if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) > if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) > fit Holt-Winters exponential smoothing with trend and multiplicative seasonal component. Call: HoltWinters(x = x, seasonal = par3) Smoothing parameters: alpha: 0.174213 beta : 0.07126213 gamma: 0.8208296 Coefficients: [,1] a 1.884675e+04 b 7.277454e+01 s1 9.707312e-01 s2 1.050597e+00 s3 1.078854e+00 s4 9.542200e-01 s5 8.706792e-01 s6 1.060656e+00 s7 1.061441e+00 s8 1.067927e+00 s9 9.494155e-01 s10 1.002565e+00 s11 9.858328e-01 s12 1.136186e+00 > myresid <- x - fit$fitted[,'xhat'] > postscript(file="/var/www/html/rcomp/tmp/1tqkm1260536768.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/27x6p1260536768.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/3e2eb1260536768.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$gamma) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/www/html/rcomp/tmp/49dwx1260536768.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Observed',header=TRUE) > a<-table.element(a,'Fitted',header=TRUE) > a<-table.element(a,'Residuals',header=TRUE) > a<-table.row.end(a) > for (i in 1:nxmK) { + a<-table.row.start(a) + a<-table.element(a,i+K,header=TRUE) + a<-table.element(a,x[i+K]) + a<-table.element(a,fit$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/5p79k1260536768.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/6bu9i1260536768.tab") > > system("convert tmp/1tqkm1260536768.ps tmp/1tqkm1260536768.png") > system("convert tmp/27x6p1260536768.ps tmp/27x6p1260536768.png") > system("convert tmp/3e2eb1260536768.ps tmp/3e2eb1260536768.png") > > > proc.time() user system elapsed 0.794 0.494 0.971