Forcasting Roebel

*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 16:40:42 +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/t1293295223snv4r8zea876wpm.htm/, Retrieved Sat, 25 Dec 2010 17:40:25 +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/t1293295223snv4r8zea876wpm.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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40,7819 39,5915 38,8859 39,9068 41,47 41,5613 41,6005 41,4113 41,84 42,2892 43,1521 43,5998 43,116 42,4185 42,3687 42,2975 42,8528 43,535 44,7265 45,7293 45,7585 46,1685 46,5075 46,527 46,601 46,4607 46,7135 46,4113 45,55 44,6081 44,4395 44,9847 45,7558 45,3942 45,697 45,5664 46,0205 45,9195 45,8005 45,535 45,4977 45,5782 45,7697 45,2445 45,0615 45,2865 44,791 44,7625 44,7644 44,9973 44,7265 45,1465 44,7465 45,1795 45,6515 45,492 45,2775 45,2115 45,411 45,4005 44,7692 44,8913 45,032 44,879 44,833 44,8257 44,7815 44,479 44,6317 44,5043 44,3217 44,1005 44,047 43,6835 43,7864 44,1807 43,9595 43,937 43,991 43,865 43,671 43,93 43,863 43,7095 43,9435 43,736 43,6295 43,598 43,8726 43,8935 43,5957 43,7155 43,528 43,3415 43,3374 43,332 43,3869 43,5016 43,4875 43,6023 43,3886 43,3105 43,4455 43,5185 43,5755 43,6217 43,644 43,5789 43,5215 43,5033 43,632 43,263 43,3717 43,2745 43,2647 43,324 43,4455 43,409 etc...

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 3 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[476]) 471 43.1555 - - - - - - - 472 43.1885 - - - - - - - 473 43.43 - - - - - - - 474 43.31 - - - - - - - 475 42.815 - - - - - - - 476 42.7017 - - - - - - - 477 42.28 42.7791 42.2636 43.2946 0.0289 0.6157 0.0598 0.6157 478 41.922 42.8329 41.9955 43.6703 0.0165 0.9022 0.0811 0.6206 479 42.17 42.8338 41.7921 43.8754 0.1058 0.9569 0.1851 0.5981 480 42.1962 42.8212 41.6451 43.9972 0.1488 0.8611 0.5041 0.5789 481 42.3215 42.8167 41.5182 44.1151 0.2274 0.8255 0.5689 0.5689 482 42.3173 42.8179 41.4069 44.229 0.2434 0.7548 0.7725 0.5641 483 42.391 42.8196 41.2993 44.3398 0.2903 0.7414 0.8764 0.5604 484 42.463 42.8197 41.2001 44.4394 0.333 0.6981 0.7841 0.5568 485 42.4125 42.8195 41.105 44.534 0.3209 0.6582 0.7619 0.5536 486 42.304 42.8193 41.0164 44.6222 0.2877 0.6708 0.7058 0.5509 487 41.813 42.8193 40.931 44.7077 0.1481 0.7036 0.6989 0.5486 488 41.651 42.8194 40.8501 44.7886 0.1224 0.8417 0.6651 0.5466 489 41.539 42.8194 40.7717 44.8671 0.1102 0.8683 0.6335 0.5448 490 41.1575 42.8194 40.6968 44.942 0.0624 0.8815 0.6464 0.5433 491 40.9545 42.8194 40.624 45.0148 0.048 0.9311 0.6773 0.5418 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 477 0.0061 -0.0117 0 0.2491 0 0 478 0.01 -0.0213 0.0165 0.8297 0.5394 0.7344 479 0.0124 -0.0155 0.0161 0.4406 0.5065 0.7117 480 0.014 -0.0146 0.0158 0.3906 0.4775 0.691 481 0.0155 -0.0116 0.0149 0.2452 0.431 0.6565 482 0.0168 -0.0117 0.0144 0.2506 0.401 0.6332 483 0.0181 -0.01 0.0138 0.1837 0.3699 0.6082 484 0.0193 -0.0083 0.0131 0.1273 0.3396 0.5827 485 0.0204 -0.0095 0.0127 0.1656 0.3203 0.5659 486 0.0215 -0.012 0.0126 0.2655 0.3148 0.5611 487 0.0225 -0.0235 0.0136 1.0127 0.3782 0.615 488 0.0235 -0.0273 0.0147 1.3651 0.4605 0.6786 489 0.0244 -0.0299 0.0159 1.6394 0.5512 0.7424 490 0.0253 -0.0388 0.0175 2.7618 0.7091 0.8421 491 0.0262 -0.0436 0.0193 3.4778 0.8937 0.9453

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293295223snv4r8zea876wpm/1hac01293295238.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t1293295223snv4r8zea876wpm/1hac01293295238.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t1293295223snv4r8zea876wpm/25b9t1293295238.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t1293295223snv4r8zea876wpm/25b9t1293295238.ps (open in new window)

Parameters (Session):

par1 = 15 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 15 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; 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 <- 5 #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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