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Type 'q()' to quit R. > x <- c(6.81,6.8,6.8,6.85,6.85,6.85,6.85,6.85,6.85,6.86,6.86,6.88,6.88,6.88,6.91,6.91,6.91,6.91,6.99,6.99,6.99,7.02,7.02,7.05,7.05,7.05,7.05,7.1,7.1,7.1,7.1,7.12,7.13,7.18,7.24,7.24,7.24,7.27,7.27,7.27,7.27,7.3,7.3,7.57,7.76,7.94,7.94,7.96,7.96,7.98,7.99,8,8,8.04,8.04,8.04,8.04,8.04,8.07,8.07,8.07,8.07,8.11,8.11,8.12,8.11,8.13,8.15,8.16,8.2,8.2,8.2) > par3 = 'additive' > par2 = 'Triple' > par1 = '12' > 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$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ > #Source of accompanying publication: > #Technical description: > par1 <- as.numeric(par1) > if (par2 == 'Single') K <- 1 > if (par2 == 'Double') K <- 2 > if (par2 == 'Triple') K <- par1 > nx <- length(x) > nxmK <- nx - K > x <- ts(x, frequency = par1) > if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) > if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) > if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) > fit Holt-Winters exponential smoothing with trend and additive seasonal component. Call: HoltWinters(x = x, seasonal = par3) Smoothing parameters: alpha: 1 beta : 0.1364164 gamma: 0.06702261 Coefficients: [,1] a 8.187118e+00 b 1.050304e-02 s1 4.548611e-03 s2 -7.118056e-03 s3 1.121528e-02 s4 -1.284722e-03 s5 -1.461806e-02 s6 -2.836806e-02 s7 1.413194e-02 s8 7.881944e-03 s9 -3.472222e-05 s10 2.881944e-03 s11 -2.118056e-03 s12 1.288194e-02 > myresid <- x - fit$fitted[,'xhat'] > postscript(file="/var/wessaorg/rcomp/tmp/1jm6a1355739315.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/2r01f1355739315.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/3fk9i1355739315.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$gamma) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/4i4fa1355739316.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Observed',header=TRUE) > a<-table.element(a,'Fitted',header=TRUE) > a<-table.element(a,'Residuals',header=TRUE) > a<-table.row.end(a) > for (i in 1:nxmK) { + a<-table.row.start(a) + a<-table.element(a,i+K,header=TRUE) + a<-table.element(a,x[i+K]) + a<-table.element(a,fit$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/54nh41355739316.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/6qy221355739316.tab") > > try(system("convert tmp/1jm6a1355739315.ps tmp/1jm6a1355739315.png",intern=TRUE)) character(0) > try(system("convert tmp/2r01f1355739315.ps tmp/2r01f1355739315.png",intern=TRUE)) character(0) > try(system("convert tmp/3fk9i1355739315.ps tmp/3fk9i1355739315.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 2.011 0.315 2.306