WS10 ARIMA Forecasting

*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, 11 Dec 2009 06:38:44 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t1260538979cvzxr94iovnhefx.htm/, Retrieved Fri, 11 Dec 2009 14:43:01 +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/2009/Dec/11/t1260538979cvzxr94iovnhefx.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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No (this computation is public)

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Dataseries X:

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7.1 6.9 6.8 7.5 7.6 7.8 8.0 8.1 8.2 8.3 8.2 8.0 7.9 7.6 7.6 8.3 8.4 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8.0 8.2 8.1 8.1 8.0 7.9 7.9 8.0 8.0 7.9 8.0 7.7 7.2 7.5 7.3 7.0 7.0 7.0 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8.0 8.0 7.7 7.3 7.4 8.1 8.3 8.2

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 11 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[62]) 50 8.3 - - - - - - - 51 8 - - - - - - - 52 8.2 - - - - - - - 53 8.1 - - - - - - - 54 8.1 - - - - - - - 55 8 - - - - - - - 56 7.9 - - - - - - - 57 7.9 - - - - - - - 58 8 - - - - - - - 59 8 - - - - - - - 60 7.9 - - - - - - - 61 8 - - - - - - - 62 7.7 - - - - - - - 63 7.2 7.3582 7.0815 7.6349 0.1312 0.0077 0 0.0077 64 7.5 7.5195 7.0388 8.0002 0.4683 0.9037 0.0028 0.2309 65 7.3 7.3084 6.6979 7.9188 0.4893 0.2692 0.0055 0.1043 66 7 7.2008 6.5561 7.8454 0.2708 0.3815 0.0031 0.0645 67 7 7.0653 6.4206 7.7099 0.4214 0.5786 0.0022 0.0268 68 7 7.0184 6.3736 7.6632 0.4777 0.5223 0.0037 0.0191 69 7.2 7.1938 6.5505 7.8371 0.4925 0.7226 0.0157 0.0615 70 7.3 7.2863 6.6333 7.9394 0.4837 0.6022 0.0161 0.1072 71 7.1 7.1216 6.4204 7.8227 0.476 0.309 0.007 0.0529 72 6.8 6.7179 5.9457 7.4901 0.4175 0.1661 0.0013 0.0063 73 6.4 6.4251 5.5977 7.2524 0.4763 0.1872 1e-04 0.0013 74 6.1 6.1064 5.2551 6.9577 0.4941 0.2495 1e-04 1e-04 75 6.5 5.9257 5.01 6.8413 0.1095 0.3545 0.0032 1e-04 76 7.7 6.537 5.5413 7.5326 0.011 0.529 0.029 0.011 77 7.9 6.5438 5.4682 7.6195 0.0067 0.0176 0.0841 0.0176 78 7.5 6.403 5.2739 7.5321 0.0284 0.0047 0.15 0.0122 79 6.9 6.0429 4.8803 7.2055 0.0742 0.007 0.0533 0.0026 80 6.6 5.7792 4.5945 6.9639 0.0872 0.0318 0.0217 7e-04 81 6.9 5.8487 4.6391 7.0583 0.0442 0.1117 0.0143 0.0014 82 7.7 5.9454 4.6992 7.1916 0.0029 0.0666 0.0166 0.0029 83 8 5.8284 4.5291 7.1278 5e-04 0.0024 0.0276 0.0024 84 8 5.5003 4.1386 6.8619 2e-04 2e-04 0.0307 8e-04 85 7.7 5.1302 3.7091 6.5513 2e-04 0 0.0399 2e-04 86 7.3 4.8157 3.3463 6.2851 5e-04 1e-04 0.0433 1e-04 87 7.4 4.5415 3.0123 6.0707 1e-04 2e-04 0.006 0 88 8.1 5.0481 3.4565 6.6396 1e-04 0.0019 5e-04 5e-04 89 8.3 5.0156 3.3624 6.6687 0 1e-04 3e-04 7e-04 90 8.2 4.8902 3.1826 6.5978 1e-04 0 0.0014 6e-04 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 63 0.0192 -0.0215 0 0.025 0 0 64 0.0326 -0.0026 0.012 4e-04 0.0127 0.1127 65 0.0426 -0.0011 0.0084 1e-04 0.0085 0.0922 66 0.0457 -0.0279 0.0133 0.0403 0.0164 0.1283 67 0.0466 -0.0092 0.0125 0.0043 0.014 0.1184 68 0.0469 -0.0026 0.0108 3e-04 0.0117 0.1083 69 0.0456 9e-04 0.0094 0 0.0101 0.1003 70 0.0457 0.0019 0.0085 2e-04 0.0088 0.094 71 0.0502 -0.003 0.0079 5e-04 0.0079 0.0889 72 0.0586 0.0122 0.0083 0.0067 0.0078 0.0882 73 0.0657 -0.0039 0.0079 6e-04 0.0071 0.0845 74 0.0711 -0.001 0.0073 0 0.0065 0.0809 75 0.0788 0.0969 0.0142 0.3299 0.0314 0.1772 76 0.0777 0.1779 0.0259 1.3527 0.1258 0.3547 77 0.0839 0.2072 0.038 1.8391 0.24 0.4899 78 0.09 0.1713 0.0463 1.2034 0.3002 0.5479 79 0.0982 0.1418 0.052 0.7346 0.3258 0.5708 80 0.1046 0.142 0.057 0.6737 0.3451 0.5875 81 0.1055 0.1797 0.0634 1.1052 0.3851 0.6206 82 0.1069 0.2951 0.075 3.0787 0.5198 0.721 83 0.1137 0.3726 0.0892 4.7156 0.7196 0.8483 84 0.1263 0.4545 0.1058 6.2487 0.9709 0.9853 85 0.1413 0.5009 0.123 6.6039 1.2158 1.1026 86 0.1557 0.5159 0.1393 6.1718 1.4223 1.1926 87 0.1718 0.6294 0.1589 8.171 1.6923 1.3009 88 0.1609 0.6046 0.1761 9.3143 1.9854 1.4091 89 0.1682 0.6549 0.1938 10.7875 2.3114 1.5203 90 0.1782 0.6768 0.2111 10.955 2.6201 1.6187

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260538979cvzxr94iovnhefx/11os41260538713.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260538979cvzxr94iovnhefx/11os41260538713.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260538979cvzxr94iovnhefx/2ztxc1260538713.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260538979cvzxr94iovnhefx/2ztxc1260538713.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 1 ; par7 = 0 ; par8 = 3 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ; 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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