R version 2.9.0 (2009-04-17) Copyright (C) 2009 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. 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(100.01,103.84,104.48,95.43,104.80,108.64,105.65,108.42,115.35,113.64,115.24,100.33,101.29,104.48,99.26,100.11,103.52,101.18,96.39,97.56,96.39,85.10,79.77,79.13,80.84,82.75,92.55,96.60,96.92,95.32,98.52,100.22,104.91,103.10,97.13,103.42,111.72,118.11,111.62,100.22,102.03,105.76,107.68,110.77,105.44,112.26,114.07,117.90,124.72,126.42,134.73,135.79,143.36,140.37,144.74,151.98,150.92,163.38,154.43,146.66,157.95,162.10,180.42,179.57,171.58,185.43,190.64,203.00,202.36,193.41,186.17,192.24,209.60,206.41,209.82,230.37,235.80,232.07,244.64,242.19,217.48,209.39,211.73,221.00,203.11,214.71,224.19,238.04,238.36,246.24,259.87,249.97,266.48,282.98,306.31,301.73,314.62,332.62,355.51,370.32,408.13,433.58,440.51,386.29,342.84,254.97,203.42,170.09,174.03,167.85,177.01,188.19,211.20,240.91,230.26,251.25,241.66) > par10 = 'FALSE' > par9 = '0' > par8 = '0' > par7 = '0' > par6 = '0' > par5 = '12' > par4 = '0' > par3 = '2' > par2 = '1' > 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) #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") sigma^2 estimated as 170.3: log likelihood = -410.75, aic = 823.5 > (forecast <- predict(arima.out,fx)) $pred Time Series: Start = 106 End = 117 Frequency = 1 [1] 299.39 255.94 212.49 169.04 125.59 82.14 38.69 -4.76 -48.21 [10] -91.66 -135.11 -178.56 $se Time Series: Start = 106 End = 117 Frequency = 1 [1] 13.05165 29.18439 48.83482 71.48685 96.79365 124.50484 154.42925 [8] 186.41490 220.33728 256.09194 293.58969 332.75319 > (lb <- forecast$pred - 1.96 * forecast$se) Time Series: Start = 106 End = 117 Frequency = 1 [1] 273.80876 198.73861 116.77376 28.92577 -64.12556 -161.88949 [7] -263.99133 -370.13321 -480.07106 -593.60020 -710.54580 -830.75624 > (ub <- forecast$pred + 1.96 * forecast$se) Time Series: Start = 106 End = 117 Frequency = 1 [1] 324.9712 313.1414 308.2062 309.1542 315.3056 326.1695 341.3713 360.6132 [9] 383.6511 410.2802 440.3258 473.6362 > if (par2 == 0) { + x <- exp(x) + forecast$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] 100.01 103.84 104.48 95.43 104.80 108.64 105.65 108.42 115.35 [10] 113.64 115.24 100.33 101.29 104.48 99.26 100.11 103.52 101.18 [19] 96.39 97.56 96.39 85.10 79.77 79.13 80.84 82.75 92.55 [28] 96.60 96.92 95.32 98.52 100.22 104.91 103.10 97.13 103.42 [37] 111.72 118.11 111.62 100.22 102.03 105.76 107.68 110.77 105.44 [46] 112.26 114.07 117.90 124.72 126.42 134.73 135.79 143.36 140.37 [55] 144.74 151.98 150.92 163.38 154.43 146.66 157.95 162.10 180.42 [64] 179.57 171.58 185.43 190.64 203.00 202.36 193.41 186.17 192.24 [73] 209.60 206.41 209.82 230.37 235.80 232.07 244.64 242.19 217.48 [82] 209.39 211.73 221.00 203.11 214.71 224.19 238.04 238.36 246.24 [91] 259.87 249.97 266.48 282.98 306.31 301.73 314.62 332.62 355.51 [100] 370.32 408.13 433.58 440.51 386.29 342.84 299.39 255.94 212.49 [109] 169.04 125.59 82.14 38.69 -4.76 -48.21 -91.66 -135.11 -178.56 > (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) Time Series: Start = 106 End = 117 Frequency = 1 [1] 0.04359415 0.11402823 0.22982172 0.42289903 0.77071148 [6] 1.51576384 3.99145128 -39.16279464 -4.57036455 -2.79393344 [11] -2.17296789 -1.86353711 > postscript(file="/var/www/html/rcomp/tmp/1fyx51260611100.ps",horizontal=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$pred , lwd=2 , col ='white') > box() > par(opar) > dev.off() null device 1 > prob.dec <- array(NA, dim=fx) > prob.sdec <- array(NA, dim=fx) > prob.ldec <- array(NA, dim=fx) > prob.pval <- array(NA, dim=fx) > perf.pe <- array(0, dim=fx) > perf.mape <- array(0, dim=fx) > perf.se <- array(0, dim=fx) > perf.mse <- array(0, dim=fx) > perf.rmse <- array(0, dim=fx) > for (i in 1:fx) { + locSD <- (ub[i] - forecast$pred[i]) / 1.96 + perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i] + perf.mape[i] = perf.mape[i] + abs(perf.pe[i]) + perf.se[i] = (x[nx+i] - forecast$pred[i])^2 + perf.mse[i] = perf.mse[i] + perf.se[i] + prob.dec[i] = pnorm((x[nx+i-1] - forecast$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$pred[i]) / locSD) + } > perf.mape = perf.mape / fx > perf.mse = perf.mse / fx > perf.rmse = sqrt(perf.mse) > postscript(file="/var/www/html/rcomp/tmp/2b23b1260611100.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) > dum <- forecast$pred > dum[1:12] <- x[(nx+1):lx] > lines(dum, lty=1) > lines(ub,lty=3) > lines(lb,lty=3) > dev.off() null device 1 > > #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'time',1,header=TRUE) > a<-table.element(a,'Y[t]',1,header=TRUE) > a<-table.element(a,'F[t]',1,header=TRUE) > a<-table.element(a,'95% LB',1,header=TRUE) > a<-table.element(a,'95% UB',1,header=TRUE) > a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) > mylab <- paste('P(F[t]>Y[',nx,sep='') > mylab <- paste(mylab,'])',sep='') > a<-table.element(a,mylab,1,header=TRUE) > a<-table.row.end(a) > for (i in (nx-par5):nx) { + a<-table.row.start(a) + a<-table.element(a,i,header=TRUE) + a<-table.element(a,x[i]) + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.row.end(a) + } > for (i in 1:fx) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,round(x[nx+i],4)) + a<-table.element(a,round(forecast$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/rcomp/tmp/36eqr1260611101.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.mape[i],4)) + a<-table.element(a,round(perf.se[i],4)) + a<-table.element(a,round(perf.mse[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/rcomp/tmp/4pvcd1260611101.tab") > > system("convert tmp/1fyx51260611100.ps tmp/1fyx51260611100.png") > system("convert tmp/2b23b1260611100.ps tmp/2b23b1260611100.png") > > > proc.time() user system elapsed 0.558 0.352 0.815