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*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: Mon, 27 Dec 2010 16:34:15 +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/27/t1293467547fbmeff8s802ofye.htm/, Retrieved Mon, 27 Dec 2010 17:32:28 +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/27/t1293467547fbmeff8s802ofye.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:

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Dataseries X:

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5.2 7.9 8.7 8.9 15.3 15.4 18.1 19.7 13 12.6 6.2 3.5 3.4 0 9.5 8.9 10.4 13.2 18.9 19 16.3 10.6 5.8 3.6 2.6 5 7.3 9.2 15.7 16.8 18.4 18.1 14.6 7.8 7.6 3.8 5.6 2.2 6.8 11.8 14.9 16.7 16.7 15.9 13.6 9.2 2.8 2.5 4.8 2.8 7.8 9 12.9 16.4 21.8 17.8 13.5 10 10.4 5.5 4 6.8 5.7 9.1 13.6 15 20.9 20.4 14 13.7 7.1 0.8 2.1 1.3 3.9 10.7 11.1 16.4 17.1 17.3 12.9 10.9 5.3 0.7 -0.2 6.5 8.6 8.5 13.3 16.2 17.5 21.2 14.8 10.3 7.3 5.1 4.4 6.2 7.7 9.3 15.6 16.3 16.6 17.4 15.3 9.7 3.7 4.6 5.4 3.1 7.9 10.1 15 15.6 19.7 18.1 17.7 10.7 6.2 4.2 4 5.9 7.1 10.5 15.1 16.8 15.3 18.4 16.1 11.3 7.9 5.6 3.4 4.8 6.5 8.5 15.1 15.7 18.7 19.2 12.9 14.4 6.2 3.3 4.6 7.2 7.8 9.9 13.6 17.1 17.8 18.6 14.7 10.5 8.6 4.4 2.3 2.8 8.8 10.7 13.9 19.3 19.5 20.4 15.3 7.9 8.3 4.5 3.2 5 6.6 11.1 12.8 16.3 17.4 18.9 15.8 11.7 6.4 2.9 4.7 2.4 7.2 10.7 13.4 18.5 18.3 16.8 16.6 14. 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 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[216]) 204 5.9 - - - - - - - 205 7.2 - - - - - - - 206 6.8 - - - - - - - 207 8 - - - - - - - 208 14.3 - - - - - - - 209 14.6 - - - - - - - 210 17.5 - - - - - - - 211 17.2 - - - - - - - 212 17.2 - - - - - - - 213 14.1 - - - - - - - 214 10.5 - - - - - - - 215 6.8 - - - - - - - 216 4.1 - - - - - - - 217 6.5 6.2279 1.5989 10.8569 0.4541 0.8162 0.3403 0.8162 218 6.1 6.1904 1.5257 10.855 0.4849 0.4482 0.3989 0.8101 219 6.3 7.5695 2.8904 12.2487 0.2974 0.7309 0.4285 0.9269 220 9.3 14.0495 9.2965 18.8025 0.0251 0.9993 0.4589 1 221 16.4 14.4423 9.6841 19.2004 0.21 0.9829 0.4741 1 222 16.1 17.3944 12.6342 22.1546 0.297 0.6589 0.4827 1 223 18 17.1361 12.3729 21.8992 0.3611 0.6651 0.4895 1 224 17.6 17.1597 12.3961 21.9233 0.4281 0.3648 0.4934 1 225 14 14.0737 9.31 18.8375 0.4879 0.0734 0.4957 1 226 10.5 10.4838 5.7199 15.2477 0.4973 0.074 0.4973 0.9957 227 6.9 6.7898 2.0258 11.5537 0.4819 0.0634 0.4983 0.8658 228 2.8 4.0934 -0.6705 8.8574 0.2973 0.1241 0.4989 0.4989 229 0.7 6.2238 -0.4247 12.8722 0.0517 0.8436 0.4675 0.7344 230 3.6 6.1878 -0.486 12.8615 0.2236 0.9465 0.5103 0.7301 231 6.7 7.5679 0.8839 14.2519 0.3996 0.8777 0.645 0.8454 232 12.5 14.0485 7.3123 20.7847 0.3262 0.9837 0.9165 0.9981 233 14.4 14.4416 7.7018 21.1815 0.4952 0.7138 0.2845 0.9987 234 16.5 17.394 10.6527 24.1353 0.3975 0.808 0.6466 0.9999 235 18.7 17.1358 10.3924 23.8792 0.3247 0.5733 0.4008 0.9999 236 19.4 17.1595 10.4158 23.9032 0.2575 0.3272 0.4491 0.9999 237 15.8 14.0736 7.3298 20.8175 0.3079 0.0608 0.5085 0.9981 238 11.3 10.4837 3.7397 17.2277 0.4062 0.0612 0.4981 0.9682 239 9.7 6.7897 0.0457 13.5337 0.1988 0.095 0.4872 0.7828 240 2.9 4.0934 -2.6506 10.8374 0.3644 0.0516 0.6465 0.4992 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 217 0.3792 0.0437 0 0.074 0 0 218 0.3845 -0.0146 0.0291 0.0082 0.0411 0.2027 219 0.3154 -0.1677 0.0753 1.6117 0.5647 0.7514 220 0.1726 -0.3381 0.141 22.5581 6.063 2.4623 221 0.1681 0.1356 0.1399 3.8327 5.6169 2.37 222 0.1396 -0.0744 0.129 1.6755 4.96 2.2271 223 0.1418 0.0504 0.1178 0.7463 4.3581 2.0876 224 0.1416 0.0257 0.1063 0.1939 3.8376 1.959 225 0.1727 -0.0052 0.095 0.0054 3.4118 1.8471 226 0.2318 0.0015 0.0857 3e-04 3.0706 1.7523 227 0.358 0.0162 0.0794 0.0122 2.7926 1.6711 228 0.5938 -0.316 0.0991 1.6729 2.6993 1.6429 229 0.545 -0.8875 0.1597 30.5121 4.8387 2.1997 230 0.5503 -0.4182 0.1782 6.6965 4.9714 2.2297 231 0.4506 -0.1147 0.174 0.7532 4.6902 2.1657 232 0.2446 -0.1102 0.17 2.3978 4.5469 2.1324 233 0.2381 -0.0029 0.1602 0.0017 4.2796 2.0687 234 0.1977 -0.0514 0.1541 0.7993 4.0862 2.0214 235 0.2008 0.0913 0.1508 2.4466 3.9999 2 236 0.2005 0.1306 0.1498 5.0198 4.0509 2.0127 237 0.2445 0.1227 0.1485 2.9803 3.9999 2 238 0.3282 0.0779 0.1453 0.6663 3.8484 1.9617 239 0.5068 0.4286 0.1576 8.4698 4.0493 2.0123 240 0.8406 -0.2915 0.1632 1.4242 3.94 1.9849

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293467547fbmeff8s802ofye/1blr71293467651.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293467547fbmeff8s802ofye/1blr71293467651.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293467547fbmeff8s802ofye/27dpg1293467651.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293467547fbmeff8s802ofye/27dpg1293467651.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; 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 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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