paper2

R Software Module: rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Thu, 24 Jan 2008 06:08:17 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/24/t1201179862wm6qwo64l7a6xpw.htm/, Retrieved Thu, 24 Jan 2008 14:04:22 +0100

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Dataseries X:

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7.3 7.2 7.1 6.9 6.8 6.7 6.8 6.8 6.7 6.8 6.8 6.7 6.3 6.2 6.2 6.5 6.5 6.4 6.2 6.2 6.3 7.5 7.4 7.4 7.4 7.4 7.4 7.2 7.2 7.2 7.5 7.4 7.5 8.0 8.0 8.0 8.1 8.1 8.1 7.9 7.9 8.0 8.2 8.1 8.2 8.5 8.5 8.6 8.4 8.4 8.4 7.7 7.8 7.9 8.8 8.8 8.9 8.5 8.5 8.5 8.4 8.5 8.4 8.3 8.4 8.4 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.3 8.3 8.3 8.2 8.1 8.1 8.2 8.0 7.9 7.9 7.8 7.7 7.9 7.7 7.6

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Univariate ARIMA Extrapolation Forecast time Y[t] F[t] 95% LB 95% UB p-value (H0: Y[t] = F[t]) P(F[t]>Y[t-1]) P(F[t]>Y[t-s]) P(F[t]>Y[78]) 66 8.4 - - - - - - - 67 8.50000000000001 - - - - - - - 68 8.50000000000001 - - - - - - - 69 8.50000000000001 - - - - - - - 70 8.50000000000001 - - - - - - - 71 8.50000000000001 - - - - - - - 72 8.50000000000001 - - - - - - - 73 8.50000000000001 - - - - - - - 74 8.50000000000001 - - - - - - - 75 8.50000000000001 - - - - - - - 76 8.3 - - - - - - - 77 8.3 - - - - - - - 78 8.3 - - - - - - - 79 8.2 8.5932 8.1801 9.025 0.0371 0.9084 0.6639 0.9084 80 8.1 8.5995 8.0013 9.2376 0.0625 0.8901 0.6201 0.8212 81 8.1 8.5811 7.8462 9.3773 0.1182 0.8818 0.5791 0.7555 82 8.2 8.2836 7.4995 9.1408 0.4242 0.6627 0.3104 0.4851 83 8 8.3029 7.4557 9.2358 0.2623 0.5856 0.3394 0.5024 84 7.9 8.2629 7.3635 9.2601 0.2378 0.6973 0.3206 0.4709 85 7.9 8.2304 7.2765 9.2955 0.2716 0.7284 0.3099 0.4491 86 7.8 8.2389 7.2297 9.3731 0.2241 0.7209 0.3259 0.4579 87 7.7 8.2348 7.1748 9.4336 0.191 0.7614 0.3323 0.4575 88 7.9 8.3698 7.246 9.6479 0.2357 0.8478 0.5426 0.5426 89 7.7 8.3828 7.212 9.7219 0.1588 0.7601 0.5482 0.5482 90 7.6 8.3747 7.1616 9.7697 0.1382 0.8284 0.5418 0.5418 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 79 0.0256 -0.0458 0.0038 0.1546 0.0129 0.1135 80 0.0379 -0.0581 0.0048 0.2495 0.0208 0.1442 81 0.0473 -0.0561 0.0047 0.2314 0.0193 0.1389 82 0.0528 -0.0101 8e-04 0.007 6e-04 0.0241 83 0.0573 -0.0365 0.003 0.0917 0.0076 0.0874 84 0.0616 -0.0439 0.0037 0.1317 0.011 0.1048 85 0.066 -0.0401 0.0033 0.1092 0.0091 0.0954 86 0.0702 -0.0533 0.0044 0.1926 0.016 0.1267 87 0.0743 -0.0649 0.0054 0.286 0.0238 0.1544 88 0.0779 -0.0561 0.0047 0.2207 0.0184 0.1356 89 0.0815 -0.0815 0.0068 0.4662 0.0389 0.1971 90 0.085 -0.0925 0.0077 0.6001 0.05 0.2236

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/24/t1201179862wm6qwo64l7a6xpw/112631201180091.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/24/t1201179862wm6qwo64l7a6xpw/112631201180091.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/24/t1201179862wm6qwo64l7a6xpw/22re91201180091.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/24/t1201179862wm6qwo64l7a6xpw/22re91201180091.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 0.1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 0.1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

R code (references can be found in the software module):

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')) (forecast <- predict(arima.out,fx)) (lb <- forecast$pred - 1.96 * forecast$se) (ub <- forecast$pred + 1.96 * forecast$se) 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$pred)) (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) bitmap(file='test1.png') opar <- par(mar=c(4,4,2,2),las=1) ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub)) plot(x,ylim=ylim,type='n',xlim=c(first,lx)) usr <- par('usr') rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon') rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender') abline(h= (-3:3)*2 , col ='gray', lty =3) polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA) lines(nx1:lx, lb , lty=2) lines(nx1:lx, ub , lty=2) lines(x, lwd=2) lines(nx1:lx, forecast$pred , lwd=2 , col ='white') box() par(opar) dev.off() 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) bitmap(file='test2.png') 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() load(file='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<br />(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='mytable.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='mytable1.tab')

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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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