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Forecast olie

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

Title produced by software: ARIMA Forecasting

Date of computation: Thu, 13 Dec 2007 03:48:05 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/13/t1197541983wsvb5l13v9ogt7s.htm/, Retrieved Thu, 13 Dec 2007 11:33:06 +0100

User-defined keywords:

Paper G 29

Dataseries X:

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145,3 143,6 142,8 155,9 156,2 149,8 152,7 155,5 159,3 143 141,4 142,8 146,4 152,3 164,3 168 171,3 162,7 150,2 142,5 138,2 138 145,1 138,4 131,8 130,8 126,3 123 124 120,8 122,1 106,5 104,3 108,7 113,8 112,5 106,1 98,4 96 99,3 97,5 95,3 88 94,7 99,4 98,9 96,4 95,3 99,5 101,6 103,9 106,6 108,3 102 93,8 91,6 97,7 94,8 98 103,8 97,8 91,2 89,3 87,5 90,4 94,2 102,2 101,3 96 90,8 93,2 90,9 91,1 90,2 94,3 96 99 103,3 113,1 112,8 112,1 107,4 111 110,5 110,8 112,4 111,5 116,2 122,5 121,3 113,9 110,7 120,8 141,1 147,4 148 158,1 165 187 190,3 182,4 168,8 151,2 120,1 112,5 106,2 107,1 108,5 106,5 108,3 125,6 124 127,2 136,9 135,8 124,3 115,4 113,6 114,4 118,4 117 116,5 115,4 113,6 117,4 116,9 116,4 111,1 110,2 118,9 131,8 130,6 138,3 148,4 148,7 144,3 152,5 162,9 167,2 166,5 185,6

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 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[129]) 117 115.4 - - - - - - - 118 113.6 - - - - - - - 119 114.4 - - - - - - - 120 118.4 - - - - - - - 121 117 - - - - - - - 122 116.5 - - - - - - - 123 115.4 - - - - - - - 124 113.6 - - - - - - - 125 117.4 - - - - - - - 126 116.9 - - - - - - - 127 116.4 - - - - - - - 128 111.1 - - - - - - - 129 110.2 - - - - - - - 130 118.9 111.278 101.1473 122.4234 0.0901 0.5752 0.3415 0.5752 131 131.8 114.6228 97.4781 134.783 0.0475 0.3388 0.5086 0.6664 132 130.6 115.0585 93.9195 140.9554 0.1197 0.1026 0.4002 0.6435 133 138.3 116.0204 91.8171 146.6037 0.0767 0.1751 0.475 0.6454 134 148.4 116.2503 89.7466 150.581 0.0332 0.104 0.4943 0.6351 135 148.7 120.008 90.7674 158.6684 0.0729 0.075 0.5924 0.6905 136 144.3 122.2778 90.898 164.4905 0.1533 0.1099 0.6565 0.7125 137 152.5 123.86 90.7219 169.1026 0.1074 0.1879 0.6102 0.723 138 162.9 121.4644 87.8375 167.9648 0.0404 0.0954 0.5763 0.6825 139 167.2 118.127 84.4794 165.1761 0.0205 0.0311 0.5287 0.6294 140 166.5 110.6554 78.3699 156.2414 0.0082 0.0075 0.4924 0.5078 141 185.6 110.8932 77.8696 157.9217 9e-04 0.0102 0.5115 0.5115 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 130 0.0511 0.0685 0.0057 58.0948 4.8412 2.2003 131 0.0897 0.1499 0.0125 295.0546 24.5879 4.9586 132 0.1148 0.1351 0.0113 241.5391 20.1283 4.4865 133 0.1345 0.192 0.016 496.3827 41.3652 6.4316 134 0.1507 0.2766 0.023 1033.6018 86.1335 9.2808 135 0.1644 0.2391 0.0199 823.2321 68.6027 8.2827 136 0.1761 0.1801 0.015 484.9786 40.4149 6.3573 137 0.1864 0.2312 0.0193 820.2486 68.354 8.2677 138 0.1953 0.3411 0.0284 1716.9067 143.0756 11.9614 139 0.2032 0.4154 0.0346 2408.1608 200.6801 14.1662 140 0.2102 0.5047 0.0421 3118.6169 259.8847 16.1209 141 0.2164 0.6737 0.0561 5581.1098 465.0925 21.566

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197541983wsvb5l13v9ogt7s/1ek9y1197542879.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197541983wsvb5l13v9ogt7s/1ek9y1197542879.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197541983wsvb5l13v9ogt7s/2ikp11197542879.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197541983wsvb5l13v9ogt7s/2ikp11197542879.ps (open in new window)

Parameters:

par1 = 12 ; par2 = 0.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; 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) } (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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