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Type 'q()' to quit R. > x <- c(0.3415,0.3554,0.4035,0.435,0.4105,0.4559,0.4755,0.4918,0.5175,0.5191,0.4754,0.4531,0.469,0.4716,0.4824,0.527,0.5172,0.515,0.5245,0.53,0.4836,0.4663,0.4592,0.4553,0.4217,0.4366,0.4532,0.4743,0.4776,0.4949,0.5069,0.498,0.5213,0.5394,0.6075,0.5919,0.5758,0.5916,0.6474,0.6704,0.7553,0.7891,0.784,0.7007,0.668,0.6102,0.5238,0.4237,0.3983,0.3879,0.3733,0.394,0.3945,0.4324,0.4233,0.455,0.4344,0.4388,0.4561,0.4512) > par10 = 'FALSE' > par9 = '0' > par8 = '0' > par7 = '0' > par6 = '1' > par5 = '12' > par4 = '0' > par3 = '1' > par2 = '0.0' > par1 = '12' > #'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: ar1 0.5132 s.e. 0.1414 sigma^2 estimated as 0.003698: log likelihood = 64.76, aic = -125.52 > (forecast <- predict(arima.out,par1)) $pred Time Series: Start = 49 End = 60 Frequency = 1 [1] -0.9675778 -1.0234421 -1.0521133 -1.0668283 -1.0743805 -1.0782565 [7] -1.0802458 -1.0812667 -1.0817907 -1.0820597 -1.0821977 -1.0822685 $se Time Series: Start = 49 End = 60 Frequency = 1 [1] 0.06080902 0.11029535 0.15439152 0.19326728 0.22774226 0.25866438 [7] 0.28674347 0.31253458 0.33646216 0.35884979 0.37994579 0.39994289 > (lb <- forecast$pred - 1.96 * forecast$se) Time Series: Start = 49 End = 60 Frequency = 1 [1] -1.086763 -1.239621 -1.354721 -1.445632 -1.520755 -1.585239 -1.642263 [8] -1.693835 -1.741257 -1.785405 -1.826891 -1.866157 > (ub <- forecast$pred + 1.96 * forecast$se) Time Series: Start = 49 End = 60 Frequency = 1 [1] -0.8483921 -0.8072632 -0.7495059 -0.6880244 -0.6280057 -0.5712743 [7] -0.5182286 -0.4686990 -0.4223249 -0.3787141 -0.3375039 -0.2983805 > if (par2 == 0) { + x <- exp(x) + forecast$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] 0.3415000 0.3554000 0.4035000 0.4350000 0.4105000 0.4559000 0.4755000 [8] 0.4918000 0.5175000 0.5191000 0.4754000 0.4531000 0.4690000 0.4716000 [15] 0.4824000 0.5270000 0.5172000 0.5150000 0.5245000 0.5300000 0.4836000 [22] 0.4663000 0.4592000 0.4553000 0.4217000 0.4366000 0.4532000 0.4743000 [29] 0.4776000 0.4949000 0.5069000 0.4980000 0.5213000 0.5394000 0.6075000 [36] 0.5919000 0.5758000 0.5916000 0.6474000 0.6704000 0.7553000 0.7891000 [43] 0.7840000 0.7007000 0.6680000 0.6102000 0.5238000 0.4237000 0.3800024 [50] 0.3593559 0.3491990 0.3440982 0.3415093 0.3401881 0.3395121 0.3391656 [57] 0.3389879 0.3388968 0.3388500 0.3388260 > (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) Time Series: Start = 49 End = 60 Frequency = 1 [1] 0.06458116 0.12312470 0.18029744 0.23496763 0.28705973 0.33687410 [7] 0.38479975 0.43120576 0.47640770 0.52066386 0.56418185 0.60712780 > postscript(file="/var/www/rcomp/tmp/199ra1292955968.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$pred[i]) / locSD) + } > perf.mape[1] = abs(perf.pe[1]) > perf.mse[1] = abs(perf.se[1]) > for (i in 2:fx) { + perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) + perf.mape1[i] = perf.mape[i] / i + perf.mse[i] = perf.mse[i-1] + perf.se[i] + perf.mse1[i] = perf.mse[i] / i + } > perf.rmse = sqrt(perf.mse1) > postscript(file="/var/www/rcomp/tmp/2ys641292955968.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) > dum <- forecast$pred > dum[1:par1] <- x[(nx+1):lx] > lines(dum, lty=1) > lines(ub,lty=3) > lines(lb,lty=3) > dev.off() null device 1 > > #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'time',1,header=TRUE) > a<-table.element(a,'Y[t]',1,header=TRUE) > a<-table.element(a,'F[t]',1,header=TRUE) > a<-table.element(a,'95% LB',1,header=TRUE) > a<-table.element(a,'95% UB',1,header=TRUE) > a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) > mylab <- paste('P(F[t]>Y[',nx,sep='') > mylab <- paste(mylab,'])',sep='') > a<-table.element(a,mylab,1,header=TRUE) > a<-table.row.end(a) > for (i in (nx-par5):nx) { + a<-table.row.start(a) + a<-table.element(a,i,header=TRUE) + a<-table.element(a,x[i]) + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.row.end(a) + } > for (i in 1:fx) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,round(x[nx+i],4)) + a<-table.element(a,round(forecast$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/rcomp/tmp/3nb4g1292955968.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/rcomp/tmp/48u241292955968.tab") > > try(system("convert tmp/199ra1292955968.ps tmp/199ra1292955968.png",intern=TRUE)) character(0) > try(system("convert tmp/2ys641292955968.ps tmp/2ys641292955968.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 0.680 0.400 1.069