Olieprijs ARIMA forecast

*The author of this computation has been verified*

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

Title produced by software: ARIMA Forecasting

Date of computation: Sat, 25 Dec 2010 20:49:28 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/25/t1293310060wq118da23ez2m81.htm/, Retrieved Sat, 25 Dec 2010 21:47:42 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/25/t1293310060wq118da23ez2m81.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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25.22 27.63 27.47 22.54 27.4 29.68 28.51 29.89 32.62 30.93 32.52 25.28 25.64 27.41 24.4 25.55 28.45 27.72 24.54 25.67 25.54 20.48 18.94 18.6 19.49 20.29 23.69 25.65 25.43 24.13 25.77 26.63 28.34 27.55 24.5 28.52 31.29 32.65 30.34 25.02 25.81 27.55 28.4 29.83 27.1 29.59 28.77 29.88 31.18 30.87 33.8 33.36 37.92 35.19 38.37 43.03 43.38 49.77 43.05 39.65 44.28 45.56 53.08 51.86 48.67 54.31 57.58 64.09 62.98 58.52 55.54 56.75 63.57 59.92 62.25 70.44 70.19 68.86 73.9 73.61 62.77 58.38 58.48 62.31 54.3 57.76 62.14 67.4 67.48 71.32 77.2 70.8 77.13 83.04 92.53 91.45 91.92 94.82 103.28 110.44 123.94 133.05 133.9 113.85 99.06 72.84 53.24 41.58 44.86 43.24 46.84 50.85 57.94 68.59 64.92 72.5 67.69 73.19 77.04 74.67

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 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[96]) 84 62.31 - - - - - - - 85 54.3 - - - - - - - 86 57.76 - - - - - - - 87 62.14 - - - - - - - 88 67.4 - - - - - - - 89 67.48 - - - - - - - 90 71.32 - - - - - - - 91 77.2 - - - - - - - 92 70.8 - - - - - - - 93 77.13 - - - - - - - 94 83.04 - - - - - - - 95 92.53 - - - - - - - 96 91.45 - - - - - - - 97 91.92 88.7957 68.2363 120.2673 0.4229 0.4344 0.9842 0.4344 98 94.82 90.001 63.3935 137.692 0.4215 0.4686 0.9074 0.4763 99 103.28 86.6975 58.0161 143.3983 0.2833 0.3894 0.802 0.4348 100 110.44 84.8779 54.5402 149.8913 0.2205 0.2895 0.7009 0.4215 101 123.94 82.4904 51.3715 153.6086 0.1267 0.2206 0.6604 0.4025 102 133.05 85.7605 51.2521 171.8467 0.1408 0.1924 0.6288 0.4485 103 133.9 84.2072 49.0632 176.9083 0.1467 0.1509 0.5589 0.4391 104 113.85 83.3896 47.4021 183.7557 0.276 0.162 0.5971 0.4375 105 99.06 83.1584 46.1319 192.4288 0.3877 0.291 0.5431 0.4409 106 72.84 82.0518 44.6174 197.9032 0.4381 0.3868 0.4933 0.4368 107 53.24 83.7035 44.2808 214.1972 0.3236 0.5648 0.4473 0.4537 108 41.58 84.5179 43.6588 228.151 0.279 0.6652 0.4623 0.4623 109 44.86 85.5802 42.8894 248.01 0.3116 0.7023 0.4695 0.4718 110 43.24 84.0818 41.3261 255.5466 0.3203 0.673 0.4512 0.4664 111 46.84 86.3233 41.1274 284.091 0.3478 0.6653 0.4333 0.4797 112 50.85 87.6435 40.6534 310.0051 0.3728 0.6404 0.4204 0.4866 113 57.94 89.664 40.4244 343.807 0.4034 0.6177 0.3958 0.4945 114 68.59 86.6748 38.7305 341.1643 0.4446 0.5876 0.3605 0.4853 115 64.92 87.9662 38.3685 372.6678 0.437 0.5531 0.3759 0.4904 116 72.5 88.669 37.8604 402.0139 0.4597 0.559 0.4374 0.4931 117 67.69 88.8615 37.2401 428.7144 0.4514 0.5376 0.4765 0.494 118 73.19 89.8819 36.8691 467.1636 0.4654 0.5459 0.5353 0.4968 119 77.04 88.3493 35.8591 477.039 0.4773 0.5305 0.5703 0.4938 120 74.67 87.6234 35.0981 496.8281 0.4753 0.5202 0.5873 0.4927 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 97 0.1808 0.0352 0 9.7611 0 0 98 0.2704 0.0535 0.0444 23.223 16.4921 4.061 99 0.3337 0.1913 0.0933 274.9778 102.654 10.1318 100 0.3908 0.3012 0.1453 653.4192 240.3453 15.5031 101 0.4399 0.5025 0.2167 1718.0721 535.8906 23.1493 102 0.5121 0.5514 0.2725 2236.2968 819.2917 28.6233 103 0.5617 0.5901 0.3179 2469.3745 1055.0178 32.481 104 0.6141 0.3653 0.3238 927.8335 1039.1198 32.2354 105 0.6704 0.1912 0.3091 252.8617 951.7578 30.8506 106 0.7204 -0.1123 0.2894 84.8578 865.0678 29.412 107 0.7954 -0.3639 0.2962 928.0238 870.791 29.5092 108 0.8671 -0.508 0.3138 1843.6592 951.8634 30.8523 109 0.9684 -0.4758 0.3263 1658.1363 1006.1921 31.7205 110 1.0404 -0.4857 0.3377 1668.0495 1053.4676 32.4572 111 1.1689 -0.4574 0.3457 1558.9345 1087.1654 32.9722 112 1.2944 -0.4198 0.3503 1353.7611 1103.8276 33.2239 113 1.4461 -0.3538 0.3505 1006.4129 1098.0973 33.1376 114 1.498 -0.2087 0.3426 327.0595 1055.2619 32.4848 115 1.6513 -0.262 0.3384 531.1295 1027.676 32.0574 116 1.803 -0.1824 0.3306 261.4363 989.364 31.4542 117 1.9513 -0.2383 0.3262 448.2308 963.5958 31.0418 118 2.1416 -0.1857 0.3198 278.6207 932.4605 30.5362 119 2.2446 -0.128 0.3115 127.9009 897.4797 29.958 120 2.3827 -0.1478 0.3046 167.7906 867.076 29.4462

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293310060wq118da23ez2m81/1t6q71293310165.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t1293310060wq118da23ez2m81/1t6q71293310165.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t1293310060wq118da23ez2m81/2pxog1293310165.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t1293310060wq118da23ez2m81/2pxog1293310165.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = -0.5 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = -0.5 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; 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,par1)) (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.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) 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:par1] <- 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.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='mytable1.tab')

Copyright

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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