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Type 'q()' to quit R. > x <- c(608,651,691,627,634,731,475,337,803,722,590,724,627,696,825,677,656,785,412,352,839,729,696,641,695,638,762,635,721,854,418,367,824,687,601,676,740,691,683,594,729,731,386,331,706,715,657,653,642,643,718,654,632,731,392,344,792,852,649,629,685,617,715,715,629,916,531,357,917,828,708,858,775,785,1006,789,734,906,532,387,991,841,892,782) > par10 = 'FALSE' > par9 = '0' > par8 = '2' > par7 = '1' > par6 = '1' > par5 = '12' > par4 = '1' > par3 = '0' > par2 = '-0.3' > 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 ma1 sar1 sar2 0.9535 -0.7704 -0.4716 -0.4275 s.e. 0.0686 0.1048 0.1584 0.1439 sigma^2 estimated as 1.437e-05: log likelihood = 246.26, aic = -482.51 > (forecast <- predict(arima.out,par1)) $pred Time Series: Start = 73 End = 84 Frequency = 1 [1] 0.1352527 0.1390571 0.1359350 0.1388812 0.1382622 0.1299628 0.1560035 [8] 0.1700083 0.1308895 0.1328005 0.1383484 0.1345175 $se Time Series: Start = 73 End = 84 Frequency = 1 [1] 0.003790632 0.003853650 0.003910059 0.003960643 0.004006075 0.004046934 [7] 0.004083724 0.004116885 0.004146801 0.004173812 0.004198216 0.004220280 > (lb <- forecast$pred - 1.96 * forecast$se) Time Series: Start = 73 End = 84 Frequency = 1 [1] 0.1278231 0.1315039 0.1282713 0.1311184 0.1304103 0.1220308 0.1479994 [8] 0.1619392 0.1227617 0.1246198 0.1301199 0.1262458 > (ub <- forecast$pred + 1.96 * forecast$se) Time Series: Start = 73 End = 84 Frequency = 1 [1] 0.1426824 0.1466102 0.1435987 0.1466441 0.1461141 0.1378947 0.1640076 [8] 0.1780774 0.1390172 0.1409811 0.1465769 0.1427893 > if (par2 == 0) { + x <- exp(x) + forecast$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] 608.0000 651.0000 691.0000 627.0000 634.0000 731.0000 475.0000 337.0000 [9] 803.0000 722.0000 590.0000 724.0000 627.0000 696.0000 825.0000 677.0000 [17] 656.0000 785.0000 412.0000 352.0000 839.0000 729.0000 696.0000 641.0000 [25] 695.0000 638.0000 762.0000 635.0000 721.0000 854.0000 418.0000 367.0000 [33] 824.0000 687.0000 601.0000 676.0000 740.0000 691.0000 683.0000 594.0000 [41] 729.0000 731.0000 386.0000 331.0000 706.0000 715.0000 657.0000 653.0000 [49] 642.0000 643.0000 718.0000 654.0000 632.0000 731.0000 392.0000 344.0000 [57] 792.0000 852.0000 649.0000 629.0000 685.0000 617.0000 715.0000 715.0000 [65] 629.0000 916.0000 531.0000 357.0000 917.0000 828.0000 708.0000 858.0000 [73] 787.3718 717.8322 774.2753 720.8664 731.6812 899.3671 489.2744 367.3664 [81] 878.3164 836.8893 730.1629 801.8078 > (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) Time Series: Start = 73 End = 84 Frequency = 1 [1] 0.10572825 0.10439497 0.10888063 0.10782746 0.10978290 0.11917048 [7] 0.09791957 0.08977714 0.12155211 0.12044217 0.11570615 0.12019749 > postscript(file="/var/www/html/freestat/rcomp/tmp/1xlh41292937410.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$pred[i]) / locSD) + } > perf.mape[1] = abs(perf.pe[1]) > perf.mse[1] = abs(perf.se[1]) > for (i in 2:fx) { + perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) + perf.mape1[i] = perf.mape[i] / i + perf.mse[i] = perf.mse[i-1] + perf.se[i] + perf.mse1[i] = perf.mse[i] / i + } > perf.rmse = sqrt(perf.mse1) > postscript(file="/var/www/html/freestat/rcomp/tmp/2m4ef1292937410.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(forecast$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/3t5tr1292937410.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/4e5sx1292937410.tab") > > try(system("convert tmp/1xlh41292937410.ps tmp/1xlh41292937410.png",intern=TRUE)) character(0) > try(system("convert tmp/2m4ef1292937410.ps tmp/2m4ef1292937410.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.949 0.462 2.036