R version 2.8.0 (2008-10-20) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 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. Natural language support but running in an English locale 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(36845,35338,35022,34777,26887,23970,22780,17351,21382,24561,17409,11514,31514,27071,29462,26105,22397,23843,21705,18089,20764,25316,17704,15548,28029,29383,36438,32034,22679,24319,18004,17537,20366,22782,19169,13807,29743,25591,29096,26482,22405,27044,17970,18730,19684,19785,18479,10698,31956,29506,34506,27165,26736,23691,18157,17328,18205,20995,17382,9367) > par10 = 'FALSE' > par9 = '0' > par8 = '0' > par7 = '1' > par6 = '0' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '0.0' > par1 = '24' > #'GNU S' R Code compiled by R2WASP v. 1.0.44 () > #Author: Prof. Dr. P. Wessa > #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/ > #Source of accompanying publication: > #Technical description: > par1 <- as.numeric(par1) #cut off periods > par2 <- as.numeric(par2) #lambda > par3 <- as.numeric(par3) #degree of non-seasonal differencing > par4 <- as.numeric(par4) #degree of seasonal differencing > par5 <- as.numeric(par5) #seasonal period > par6 <- as.numeric(par6) #p > par7 <- as.numeric(par7) #q > par8 <- as.numeric(par8) #P > par9 <- as.numeric(par9) #Q > if (par10 == 'TRUE') par10 <- TRUE > if (par10 == 'FALSE') par10 <- FALSE > if (par2 == 0) x <- log(x) > if (par2 != 0) x <- x^par2 > lx <- length(x) > first <- lx - 2*par1 > nx <- lx - par1 > nx1 <- nx + 1 > fx <- lx - nx > if (fx < 1) { + fx <- par5 + nx1 <- lx + fx - 1 + first <- lx - 2*fx + } > first <- 1 > if (fx < 3) fx <- round(lx/10,0) > (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML')) Call: arima(x = x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8, par4, par9), period = par5), include.mean = par10, method = "ML") Coefficients: ma1 -0.5819 s.e. 0.1537 sigma^2 estimated as 0.01772: log likelihood = 13.54, aic = -23.07 > (forecast <- predict(arima.out,par1)) $pred Time Series: Start = 37 End = 60 Frequency = 1 [1] 10.189923 10.237099 10.452295 10.323481 9.978122 10.047941 9.747277 [8] 9.720996 9.870550 9.982654 9.809977 9.481859 10.138850 10.186027 [15] 10.401223 10.272408 9.927050 9.996868 9.696204 9.669923 9.819477 [22] 9.931581 9.758905 9.430786 $se Time Series: Start = 37 End = 60 Frequency = 1 [1] 0.1331197 0.1442854 0.1546470 0.1643566 0.1735238 0.1822304 0.1905395 [8] 0.1985012 0.2061556 0.2135358 0.2206693 0.2275793 0.2956823 0.3159393 [15] 0.3349736 0.3529829 0.3701169 0.3864922 0.4022012 0.4173194 0.4319087 [22] 0.4460210 0.4597003 0.4729841 > (lb <- forecast$pred - 1.96 * forecast$se) Time Series: Start = 37 End = 60 Frequency = 1 [1] 9.929008 9.954300 10.149187 10.001342 9.638016 9.690769 9.373819 [8] 9.331933 9.466485 9.564123 9.377465 9.035803 9.559313 9.566786 [15] 9.744674 9.580562 9.201621 9.239344 8.907890 8.851977 8.972936 [22] 9.057380 8.857892 8.503737 > (ub <- forecast$pred + 1.96 * forecast$se) Time Series: Start = 37 End = 60 Frequency = 1 [1] 10.450837 10.519898 10.755403 10.645620 10.318229 10.405112 10.120734 [8] 10.110058 10.274615 10.401184 10.242489 9.927914 10.718387 10.805268 [15] 11.057771 10.964255 10.652479 10.754393 10.484519 10.487869 10.666018 [22] 10.805782 10.659917 10.357835 > if (par2 == 0) { + x <- exp(x) + forecast$pred <- exp(forecast$pred) + lb <- exp(lb) + ub <- exp(ub) + } > if (par2 != 0) { + x <- x^(1/par2) + forecast$pred <- forecast$pred^(1/par2) + lb <- lb^(1/par2) + ub <- ub^(1/par2) + } > if (par2 < 0) { + olb <- lb + lb <- ub + ub <- olb + } > (actandfor <- c(x[1:nx], forecast$pred)) [1] 36845.00 35338.00 35022.00 34777.00 26887.00 23970.00 22780.00 17351.00 [9] 21382.00 24561.00 17409.00 11514.00 31514.00 27071.00 29462.00 26105.00 [17] 22397.00 23843.00 21705.00 18089.00 20764.00 25316.00 17704.00 15548.00 [25] 28029.00 29383.00 36438.00 32034.00 22679.00 24319.00 18004.00 17537.00 [33] 20366.00 22782.00 19169.00 13807.00 26633.43 27920.02 34623.75 30439.02 [41] 21549.81 23108.15 17107.58 16663.83 19351.97 21647.68 18214.57 13119.55 [49] 25307.35 26529.87 32899.83 28923.46 20476.84 21957.60 16255.79 15834.14 [57] 18388.44 20569.84 17307.67 12466.32 > (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) Time Series: Start = 37 End = 60 Frequency = 1 [1] 0.1521005 0.1667545 0.1806432 0.1939166 0.2066823 0.2190209 0.2309943 [8] 0.2426513 0.2540313 0.2651664 0.2760835 0.2868052 0.4006185 0.4375091 [15] 0.4735333 0.5088777 0.5436824 0.5780560 0.6120844 0.6458372 0.6793714 [22] 0.7127345 0.7459668 0.7791023 > postscript(file="/var/www/html/freestat/rcomp/tmp/18skw1293557528.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mar=c(4,4,2,2),las=1) > ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub)) > plot(x,ylim=ylim,type='n',xlim=c(first,lx)) > usr <- par('usr') > rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon') > rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender') > abline(h= (-3:3)*2 , col ='gray', lty =3) > polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA) > lines(nx1:lx, lb , lty=2) > lines(nx1:lx, ub , lty=2) > lines(x, lwd=2) > lines(nx1:lx, forecast$pred , lwd=2 , col ='white') > box() > par(opar) > dev.off() null device 1 > prob.dec <- array(NA, dim=fx) > prob.sdec <- array(NA, dim=fx) > prob.ldec <- array(NA, dim=fx) > prob.pval <- array(NA, dim=fx) > perf.pe <- array(0, dim=fx) > perf.mape <- array(0, dim=fx) > perf.mape1 <- array(0, dim=fx) > perf.se <- array(0, dim=fx) > perf.mse <- array(0, dim=fx) > perf.mse1 <- array(0, dim=fx) > perf.rmse <- array(0, dim=fx) > for (i in 1:fx) { + locSD <- (ub[i] - forecast$pred[i]) / 1.96 + perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i] + perf.se[i] = (x[nx+i] - forecast$pred[i])^2 + prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD) + prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD) + prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD) + prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD) + } > perf.mape[1] = abs(perf.pe[1]) > perf.mse[1] = abs(perf.se[1]) > for (i in 2:fx) { + perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) + perf.mape1[i] = perf.mape[i] / i + perf.mse[i] = perf.mse[i-1] + perf.se[i] + perf.mse1[i] = perf.mse[i] / i + } > perf.rmse = sqrt(perf.mse1) > postscript(file="/var/www/html/freestat/rcomp/tmp/24ki51293557528.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) > dum <- forecast$pred > dum[1:par1] <- x[(nx+1):lx] > lines(dum, lty=1) > lines(ub,lty=3) > lines(lb,lty=3) > dev.off() null device 1 > > #Note: the /var/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/freestat/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'time',1,header=TRUE) > a<-table.element(a,'Y[t]',1,header=TRUE) > a<-table.element(a,'F[t]',1,header=TRUE) > a<-table.element(a,'95% LB',1,header=TRUE) > a<-table.element(a,'95% UB',1,header=TRUE) > a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) > mylab <- paste('P(F[t]>Y[',nx,sep='') > mylab <- paste(mylab,'])',sep='') > a<-table.element(a,mylab,1,header=TRUE) > a<-table.row.end(a) > for (i in (nx-par5):nx) { + a<-table.row.start(a) + a<-table.element(a,i,header=TRUE) + a<-table.element(a,x[i]) + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.row.end(a) + } > for (i in 1:fx) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,round(x[nx+i],4)) + a<-table.element(a,round(forecast$pred[i],4)) + a<-table.element(a,round(lb[i],4)) + a<-table.element(a,round(ub[i],4)) + a<-table.element(a,round((1-prob.pval[i]),4)) + a<-table.element(a,round((1-prob.dec[i]),4)) + a<-table.element(a,round((1-prob.sdec[i]),4)) + a<-table.element(a,round((1-prob.ldec[i]),4)) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/www/html/freestat/rcomp/tmp/3alxz1293557528.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'time',1,header=TRUE) > a<-table.element(a,'% S.E.',1,header=TRUE) > a<-table.element(a,'PE',1,header=TRUE) > a<-table.element(a,'MAPE',1,header=TRUE) > a<-table.element(a,'Sq.E',1,header=TRUE) > a<-table.element(a,'MSE',1,header=TRUE) > a<-table.element(a,'RMSE',1,header=TRUE) > a<-table.row.end(a) > for (i in 1:fx) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,round(perc.se[i],4)) + a<-table.element(a,round(perf.pe[i],4)) + a<-table.element(a,round(perf.mape1[i],4)) + a<-table.element(a,round(perf.se[i],4)) + a<-table.element(a,round(perf.mse1[i],4)) + a<-table.element(a,round(perf.rmse[i],4)) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/www/html/freestat/rcomp/tmp/4w3e51293557528.tab") > try(system("convert tmp/18skw1293557528.ps tmp/18skw1293557528.png",intern=TRUE)) character(0) > try(system("convert tmp/24ki51293557528.ps tmp/24ki51293557528.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 0.993 0.462 1.068