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

Title produced by software: ARIMA Forecasting

Date of computation: Mon, 07 Jan 2008 13:37:09 -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/07/t11997381492h5ew5yhkct50d0.htm/, Retrieved Mon, 07 Jan 2008 21:35:49 +0100

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Dataseries X:

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106.8 114.3 105.7 90.1 91.6 97.7 100.8 104.6 95.9 102.7 104 107.9 113.8 113.8 123.1 125.1 137.6 134 140.3 152.1 150.6 167.3 153.2 142 154.4 158.5 180.9 181.3 172.4 192 199.3 215.4 214.3 201.5 190.5 196 215.7 209.4 214.1 237.8 239 237.8 251.5 248.8 215.4 201.2 203.1 214.2

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 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[28]) 16 125.1 - - - - - - - 17 137.6 - - - - - - - 18 134 - - - - - - - 19 140.3 - - - - - - - 20 152.1 - - - - - - - 21 150.6 - - - - - - - 22 167.3 - - - - - - - 23 153.2 - - - - - - - 24 142 - - - - - - - 25 154.4 - - - - - - - 26 158.5 - - - - - - - 27 180.9 - - - - - - - 28 181.3 - - - - - - - 29 172.4 183.7448 166.3686 201.1209 0.1003 0.6086 1 0.6086 30 192 181.8884 156.525 207.2517 0.2173 0.7683 0.9999 0.5181 31 199.3 183.8524 153.2071 214.4978 0.1616 0.3011 0.9973 0.5648 32 215.4 187.7608 152.9276 222.594 0.0599 0.2581 0.9776 0.6419 33 214.3 187.2862 148.7767 225.7957 0.0846 0.0762 0.9691 0.6197 34 201.5 192.7948 150.9282 234.6614 0.3418 0.157 0.8837 0.7048 35 190.5 188.1496 143.1698 233.1294 0.4592 0.2804 0.9361 0.6173 36 196 184.4589 136.5658 232.3521 0.3184 0.4024 0.9589 0.5514 37 215.7 188.5444 137.9049 239.1839 0.1466 0.3865 0.9068 0.6104 38 209.4 189.8953 136.6509 243.1396 0.2364 0.1711 0.8761 0.6242 39 214.1 197.2759 141.5484 253.0033 0.277 0.3349 0.7177 0.7129 40 237.8 197.4077 139.3031 255.5122 0.0865 0.2867 0.7066 0.7066 41 239 198.2132 136.021 260.4054 0.0993 0.1061 0.792 0.703 42 237.8 197.6015 131.4517 263.7513 0.1168 0.11 0.5659 0.6855 43 251.5 198.2487 128.4994 267.9979 0.0673 0.1332 0.4882 0.6831 44 248.8 199.5364 126.4282 272.6447 0.0933 0.0818 0.3353 0.6875 45 215.4 199.3801 123.0736 275.6865 0.3404 0.1021 0.3508 0.6788 46 201.2 201.1951 121.8186 280.5715 0.5 0.3629 0.497 0.6884 47 203.1 199.6645 117.331 281.998 0.4674 0.4854 0.5864 0.669 48 214.2 198.4485 113.26 283.637 0.3585 0.4574 0.5225 0.6534 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 29 0.0482 -0.0617 0.0031 128.704 6.4352 2.5368 30 0.0711 0.0556 0.0028 102.2454 5.1123 2.261 31 0.085 0.084 0.0042 238.6281 11.9314 3.4542 32 0.0947 0.1472 0.0074 763.9252 38.1963 6.1803 33 0.1049 0.1442 0.0072 729.7452 36.4873 6.0405 34 0.1108 0.0452 0.0023 75.7801 3.789 1.9465 35 0.122 0.0125 6e-04 5.5244 0.2762 0.5256 36 0.1325 0.0626 0.0031 133.1961 6.6598 2.5807 37 0.137 0.144 0.0072 737.4261 36.8713 6.0722 38 0.1431 0.1027 0.0051 380.4345 19.0217 4.3614 39 0.1441 0.0853 0.0043 283.0518 14.1526 3.762 40 0.1502 0.2046 0.0102 1631.5413 81.5771 9.032 41 0.1601 0.2058 0.0103 1663.5637 83.1782 9.1202 42 0.1708 0.2034 0.0102 1615.918 80.7959 8.9887 43 0.1795 0.2686 0.0134 2835.7058 141.7853 11.9074 44 0.1869 0.2469 0.0123 2426.8989 121.3449 11.0157 45 0.1953 0.0803 0.004 256.6386 12.8319 3.5822 46 0.2013 0 0 0 0 0.0011 47 0.2104 0.0172 9e-04 11.8024 0.5901 0.7682 48 0.219 0.0794 0.004 248.1097 12.4055 3.5221

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t11997381492h5ew5yhkct50d0/19y7y1199738224.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t11997381492h5ew5yhkct50d0/19y7y1199738224.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t11997381492h5ew5yhkct50d0/28cjx1199738224.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t11997381492h5ew5yhkct50d0/28cjx1199738224.ps (open in new window)

Parameters (Session):

par1 = 20 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 20 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 1 ; par9 = 0 ; 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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