R version 3.2.2 (2015-08-14) -- "Fire Safety" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) 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. R is a collaborative project with many contributors. 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(86.48,86.48,86.7,87.86,88.24,88.23,88.73,88.82,87.16,86.29,86.37,86.59,85.46,85.85,86.93,87.66,87.84,88.09,88.58,88.06,88.26,89,90.78,90,89.84,89.82,91.12,91.5,93.03,94.23,94.76,92.83,92.49,90.85,88.19,86.31,85.74,86.62,86.66,87.39,87.59,88.8,88.64,89.55,89.04,88.49,89.5,89.46,90.33,90.27,91.5,92.53,93.14,93.01,92.84,92.88,93.05,93.17,93.67,94.9,95.72,96.08,97.52,98.26,98.48,98.09,98.03,98.14,98.71,98.69,98.72,98.47,99.49,99.84,100.9,101.31,100.09,99.28,99.57,101.04,101.87,101.39,100.3,99.95,99.87,100.51,100.27,100.04,99.23,99.32,99.95,100.23,101.02,99.83,99.61,100.12,99.83,100.03,100.07,100.46,100.43,100.68,101.8,101.21,100.63,100.55,99.76,98.8) > par3 = 'multiplicative' > par2 = 'Double' > par1 = '12' > par3 <- 'multiplicative' > par2 <- 'Double' > par1 <- '12' > #'GNU S' R Code compiled by R2WASP v. 1.2.327 () > #Author: root > #To cite this work: Wessa P., (2013), Exponential Smoothing (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ > #Source of accompanying publication: > # > par1 <- as.numeric(par1) > if (par2 == 'Single') K <- 1 > if (par2 == 'Double') K <- 2 > if (par2 == 'Triple') K <- par1 > nx <- length(x) > nxmK <- nx - K > x <- ts(x, frequency = par1) > if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) > if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) > if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) > fit Holt-Winters exponential smoothing with trend and without seasonal component. Call: HoltWinters(x = x, gamma = F) Smoothing parameters: alpha: 1 beta : 0.007323236 gamma: FALSE Coefficients: [,1] a 98.80000000 b 0.05588051 > myresid <- x - fit$fitted[,'xhat'] > postscript(file="/var/wessaorg/rcomp/tmp/1ix7w1448901097.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/2lnt71448901097.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/3k39s1448901097.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$gamma) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/4e4ek1448901097.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'t',header=TRUE) > a<-table.element(a,'Observed',header=TRUE) > a<-table.element(a,'Fitted',header=TRUE) > a<-table.element(a,'Residuals',header=TRUE) > a<-table.row.end(a) > for (i in 1:nxmK) { + a<-table.row.start(a) + a<-table.element(a,i+K,header=TRUE) + a<-table.element(a,x[i+K]) + a<-table.element(a,fit$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/5b7mj1448901097.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/690lk1448901097.tab") > > try(system("convert tmp/1ix7w1448901097.ps tmp/1ix7w1448901097.png",intern=TRUE)) character(0) > try(system("convert tmp/2lnt71448901097.ps tmp/2lnt71448901097.png",intern=TRUE)) character(0) > try(system("convert tmp/3k39s1448901097.ps tmp/3k39s1448901097.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.612 0.286 1.902