forecast biefstuk

*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: Fri, 24 Dec 2010 10:50:44 +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/24/t1293187746q43w8uaz6dm64ra.htm/, Retrieved Fri, 24 Dec 2010 11:49:06 +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/24/t1293187746q43w8uaz6dm64ra.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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10,92 10,98 11,15 11,19 11,33 11,38 11,4 11,45 11,56 11,61 11,82 11,77 11,85 11,82 11,92 11,86 11,87 11,94 11,86 11,92 11,83 11,91 11,93 11,99 11,96 12,12 11,85 12,01 12,1 12,21 12,31 12,31 12,39 12,35 12,41 12,51 12,27 12,51 12,44 12,47 12,51 12,58 12,5 12,52 12,59 12,51 12,67 12,64 12,54 12,66 12,67 12,62 12,72 12,85 12,85 12,82

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 'RServer@AstonUniversity' @ vre.aston.ac.uk 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 11.86 - - - - - - - 17 11.87 - - - - - - - 18 11.94 - - - - - - - 19 11.86 - - - - - - - 20 11.92 - - - - - - - 21 11.83 - - - - - - - 22 11.91 - - - - - - - 23 11.93 - - - - - - - 24 11.99 - - - - - - - 25 11.96 - - - - - - - 26 12.12 - - - - - - - 27 11.85 - - - - - - - 28 12.01 - - - - - - - 29 12.1 11.8388 11.7056 11.972 1e-04 0.0059 0.3231 0.0059 30 12.21 11.9852 11.83 12.1403 0.0023 0.0734 0.7158 0.3768 31 12.31 11.8963 11.6561 12.1366 4e-04 0.0052 0.6166 0.1769 32 12.31 12.0025 11.7211 12.2838 0.0161 0.0161 0.7172 0.479 33 12.39 11.9118 11.5567 12.2669 0.0042 0.014 0.6742 0.2939 34 12.35 11.9485 11.5444 12.3525 0.0257 0.0161 0.574 0.3827 35 12.41 11.8663 11.3896 12.3431 0.0127 0.0234 0.3968 0.2774 36 12.51 11.9065 11.3666 12.4464 0.0142 0.0338 0.3809 0.3536 37 12.27 11.8832 11.2599 12.5066 0.112 0.0244 0.4046 0.3451 38 12.51 11.9374 11.2368 12.638 0.0546 0.1761 0.3048 0.4196 39 12.44 11.9171 11.1291 12.7051 0.0967 0.0701 0.5663 0.4086 40 12.47 11.9239 11.0557 12.7921 0.1088 0.122 0.4229 0.4229 41 12.51 11.8751 10.9204 12.8297 0.0962 0.111 0.3221 0.3909 42 12.58 11.8685 10.8287 12.9084 0.0899 0.1133 0.2599 0.3949 43 12.5 11.8538 10.7198 12.9877 0.132 0.1047 0.2152 0.3936 44 12.52 11.8827 10.6525 13.113 0.155 0.1627 0.248 0.4197 45 12.59 11.8922 10.5599 13.2245 0.1523 0.1779 0.232 0.4312 46 12.51 11.9021 10.4689 13.3354 0.2029 0.1734 0.2701 0.4414 47 12.67 11.8758 10.3402 13.4114 0.1554 0.2091 0.2477 0.432 48 12.64 11.8526 10.215 13.4903 0.173 0.164 0.2157 0.4253 49 12.54 11.8297 10.086 13.5734 0.2123 0.1812 0.3103 0.4197 50 12.66 11.8369 9.9836 13.6903 0.192 0.2286 0.2383 0.4274 51 12.67 11.8522 9.8843 13.8202 0.2077 0.2106 0.2791 0.4376 52 12.62 11.8707 9.7864 13.955 0.2405 0.2261 0.2865 0.4479 53 12.72 11.8655 9.6638 14.0672 0.2234 0.2509 0.2831 0.4488 54 12.85 11.8452 9.5265 14.1638 0.1978 0.2298 0.2673 0.4446 55 12.85 11.8165 9.3794 14.2536 0.2029 0.2029 0.2913 0.4382 56 12.82 11.8042 9.246 14.3625 0.2182 0.2115 0.2917 0.4374 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 29 0.0057 0.0221 0 0.0682 0 0 30 0.0066 0.0188 0.0204 0.0506 0.0594 0.2437 31 0.0103 0.0348 0.0252 0.1711 0.0966 0.3109 32 0.012 0.0256 0.0253 0.0946 0.0961 0.31 33 0.0152 0.0401 0.0283 0.2287 0.1226 0.3502 34 0.0173 0.0336 0.0292 0.1612 0.1291 0.3593 35 0.0205 0.0458 0.0315 0.2956 0.1528 0.391 36 0.0231 0.0507 0.0339 0.3642 0.1793 0.4234 37 0.0268 0.0325 0.0338 0.1496 0.176 0.4195 38 0.0299 0.048 0.0352 0.3278 0.1912 0.4372 39 0.0337 0.0439 0.036 0.2734 0.1986 0.4457 40 0.0371 0.0458 0.0368 0.2983 0.2069 0.4549 41 0.041 0.0535 0.0381 0.4032 0.222 0.4712 42 0.0447 0.0599 0.0396 0.5062 0.2423 0.4923 43 0.0488 0.0545 0.0406 0.4176 0.254 0.504 44 0.0528 0.0536 0.0415 0.4061 0.2635 0.5133 45 0.0572 0.0587 0.0425 0.4869 0.2767 0.526 46 0.0614 0.0511 0.0429 0.3695 0.2818 0.5309 47 0.066 0.0669 0.0442 0.6308 0.3002 0.5479 48 0.0705 0.0664 0.0453 0.6199 0.3162 0.5623 49 0.0752 0.06 0.046 0.5045 0.3251 0.5702 50 0.0799 0.0695 0.0471 0.6775 0.3412 0.5841 51 0.0847 0.069 0.048 0.6687 0.3554 0.5962 52 0.0896 0.0631 0.0487 0.5614 0.364 0.6033 53 0.0947 0.072 0.0496 0.7301 0.3786 0.6153 54 0.0999 0.0848 0.051 1.0096 0.4029 0.6347 55 0.1052 0.0875 0.0523 1.0681 0.4275 0.6539 56 0.1106 0.0861 0.0535 1.0318 0.4491 0.6702

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187746q43w8uaz6dm64ra/1j1cq1293187840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187746q43w8uaz6dm64ra/1j1cq1293187840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187746q43w8uaz6dm64ra/2q2911293187840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187746q43w8uaz6dm64ra/2q2911293187840.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods par1 <- 28 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 par6 <- 3 par7 <- as.numeric(par7) #q par7 <- 3 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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