*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: Sun, 19 Dec 2010 16:45:16 +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/19/t1292777052zan2eb9ph1eodiz.htm/, Retrieved Sun, 19 Dec 2010 17:46:15 +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/19/t1292777052zan2eb9ph1eodiz.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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562325 560854 555332 543599 536662 542722 593530 610763 612613 611324 594167 595454 590865 589379 584428 573100 567456 569028 620735 628884 628232 612117 595404 597141 593408 590072 579799 574205 572775 572942 619567 625809 619916 587625 565742 557274 560576 548854 531673 525919 511038 498662 555362 564591 541657 527070 509846 514258 516922 507561 492622 490243 469357 477580 528379 533590 517945 506174 501866 516141 528222 532638 536322 536535 523597 536214 586570 596594 580523 564478 557560 575093 580112 574761 563250 551531 537034 544686 600991 604378 586111 563668 548604

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 'George Udny Yule' @ 72.249.76.132 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[65]) 53 469357 - - - - - - - 54 477580 - - - - - - - 55 528379 - - - - - - - 56 533590 - - - - - - - 57 517945 - - - - - - - 58 506174 - - - - - - - 59 501866 - - - - - - - 60 516141 - - - - - - - 61 528222 - - - - - - - 62 532638 - - - - - - - 63 536322 - - - - - - - 64 536535 - - - - - - - 65 523597 - - - - - - - 66 536214 532877.5129 517610.5327 548144.4931 0.3342 0.8833 1 0.8833 67 586570 590278.8524 566768.2994 613789.4055 0.3786 1 1 1 68 596594 601767.9847 570697.3535 632838.6158 0.3721 0.8312 1 1 69 580523 590494.0868 552084.0459 628904.1276 0.3054 0.3778 0.9999 0.9997 70 564478 581381.2046 535716.9407 627045.4685 0.2341 0.5147 0.9994 0.9934 71 557560 577168.1126 524288.0188 630048.2064 0.2337 0.681 0.9974 0.9765 72 575093 591562.2152 531490.049 651634.3814 0.2955 0.8664 0.9931 0.9867 73 580112 604373.1896 537131.2564 671615.1227 0.2397 0.8033 0.9868 0.9907 74 574761 608126.7986 533741.5017 682512.0954 0.1897 0.7698 0.9767 0.987 75 563250 609465.9831 527970.0301 690961.9362 0.1332 0.798 0.9607 0.9805 76 551531 611535.7165 522968.6887 700102.7442 0.0921 0.8574 0.9515 0.9742 77 537034 599852.4847 504260.6517 695444.3176 0.0989 0.8391 0.941 0.941 78 544686 609917.8447 503005.6058 716830.0836 0.1159 0.9093 0.9117 0.9432 79 600991 668050.5806 549669.2597 786431.9014 0.1334 0.9794 0.9113 0.9916 80 604378 680221.2985 550277.5571 810165.04 0.1263 0.884 0.8964 0.9909 81 586111 669582.568 528026.8993 811138.2367 0.1239 0.8167 0.8912 0.9784 82 563668 661061.5962 507879.6588 814243.5336 0.1064 0.8312 0.8917 0.9607 83 548604 657400.1033 492606.0267 822194.1799 0.0978 0.8675 0.8825 0.9442 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 66 0.0146 0.0063 0 11132146.2376 0 0 67 0.0203 -0.0063 0.0063 13755586.347 12443866.2923 3527.5865 68 0.0263 -0.0086 0.007 26770117.2213 17219283.2686 4149.6124 69 0.0332 -0.0169 0.0095 99422571.0209 37770105.2067 6145.7388 70 0.0401 -0.0291 0.0134 285718326.5806 87359749.4815 9346.6438 71 0.0467 -0.034 0.0168 384478080.0151 136879471.2371 11699.55 72 0.0518 -0.0278 0.0184 271235049.0289 156073125.2073 12492.923 73 0.0568 -0.0401 0.0211 588605318.6757 210139649.3909 14496.1943 74 0.0624 -0.0549 0.0249 1113276515.0044 310488190.0146 17620.6751 75 0.0682 -0.0758 0.03 2135917097.3709 493031080.7502 22204.3032 76 0.0739 -0.0981 0.0362 3600566000.3892 775534255.2629 27848.4157 77 0.0813 -0.1047 0.0419 3946162018.4797 1039753235.5309 32245.2048 78 0.0894 -0.107 0.0469 4255193562.5072 1287094799.1445 35876.1035 79 0.0904 -0.1004 0.0507 4496987345.608 1516372838.1776 38940.6322 80 0.0975 -0.1115 0.0548 5752205929.2727 1798761710.9173 42411.811 81 0.1079 -0.1247 0.0591 6967502663.7311 2121808020.4681 46063.0874 82 0.1182 -0.1473 0.0643 9485512574.9958 2554967111.9109 50546.6825 83 0.1279 -0.1655 0.0699 11836592098.8873 3070612944.5207 55413.1117

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292777052zan2eb9ph1eodiz/1w59k1292777112.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292777052zan2eb9ph1eodiz/1w59k1292777112.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292777052zan2eb9ph1eodiz/2l66e1292777112.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292777052zan2eb9ph1eodiz/2l66e1292777112.ps (open in new window)

Parameters (Session):

par1 = Niet-werkende werkzoekenden in Belgie ; par2 = http://www.nbb.be/belgostat/ ; par3 = Niet-werkende werkzoekenden in Belgie ; par4 = 12 ;

Parameters (R input):

par1 = 18 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; 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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