workshop 10

*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 07:50:25 -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/t1260543090s4ncy1x3vkhi28s.htm/, Retrieved Fri, 11 Dec 2009 15:51:32 +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/t1260543090s4ncy1x3vkhi28s.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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Dataseries X:

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6.9 6.8 6.7 6.6 6.5 6.5 7.0 7.5 7.6 7.6 7.6 7.8 8.0 8.0 8.0 7.9 7.9 8.0 8.5 9.2 9.4 9.5 9.5 9.6 9.7 9.7 9.6 9.5 9.4 9.3 9.6 10.2 10.2 10.1 9.9 9.8 9.8 9.7 9.5 9.3 9.1 9.0 9.5 10.0 10.2 10.1 10.0 9.9 10.0 9.9 9.7 9.5 9.2 9.0 9.3 9.8 9.8 9.6 9.4 9.3 9.2 9.2 9.0 8.8 8.7 8.7 9.1 9.7 9.8 9.6 9.4 9.4 9.5 9.4 9.3 9.2 9.0 8.9 9.2 9.8 9.9 9.6 9.2 9.1 9.1 9.0 8.9 8.7 8.5 8.3 8.5 8.7 8.4 8.1 7.8 7.7 7.5 7.2 6.8 6.7 6.4 6.3 6.8 7.3 7.1 7.0 6.8 6.6 6.3 6.1 6.1 6.3 6.3 6.0 6.2 6.4 6.8 7.5 7.5 7.6 7.6 7.4 7.3 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

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 6 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[152]) 140 8.4 - - - - - - - 141 8.4 - - - - - - - 142 8.4 - - - - - - - 143 8.4 - - - - - - - 144 8.6 - - - - - - - 145 8.9 - - - - - - - 146 8.8 - - - - - - - 147 8.3 - - - - - - - 148 7.5 - - - - - - - 149 7.2 - - - - - - - 150 7.4 - - - - - - - 151 8.8 - - - - - - - 152 9.3 - - - - - - - 153 9.3 9.3562 9.043 9.6693 0.3626 0.6374 1 0.6374 154 8.7 9.1871 8.6133 9.7609 0.0481 0.3499 0.9964 0.3499 155 8.2 9.0239 8.2277 9.8201 0.0213 0.7874 0.9377 0.2483 156 8.3 9.1868 8.2554 10.1182 0.031 0.9811 0.8915 0.4058 157 8.5 9.5071 8.4931 10.521 0.0258 0.9902 0.8797 0.6555 158 8.6 9.4619 8.3818 10.542 0.0589 0.9596 0.8852 0.6156 159 8.5 9.0746 7.9191 10.2301 0.1649 0.7896 0.9056 0.3511 160 8.2 8.4822 7.2419 9.7226 0.3278 0.4888 0.9397 0.0981 161 8.1 8.1755 6.8521 9.4989 0.4555 0.4855 0.9257 0.0479 162 7.9 8.2834 6.8886 9.6782 0.295 0.6017 0.8928 0.0766 163 8.6 9.4087 7.9517 10.8656 0.1383 0.9788 0.7936 0.5581 164 8.7 9.7853 8.2696 11.3009 0.0802 0.9373 0.7348 0.7348 165 8.7 9.8416 8.2041 11.4791 0.0859 0.9141 0.7416 0.7416 166 8.5 9.7658 7.9724 11.5591 0.0833 0.8779 0.8779 0.6946 167 8.4 9.66 7.7062 11.6139 0.1031 0.8777 0.9285 0.641 168 8.5 9.8143 7.7293 11.8993 0.1083 0.9082 0.9227 0.6856 169 8.7 10.081 7.8901 12.2719 0.1083 0.9214 0.9214 0.7576 170 8.7 10.008 7.721 12.2949 0.1312 0.8688 0.8862 0.728 171 8.6 9.6365 7.25 12.0231 0.1973 0.7791 0.8247 0.6089 172 8.5 9.0895 6.6 11.5791 0.3213 0.65 0.7581 0.4342 173 8.3 8.7968 6.2066 11.3869 0.3535 0.5888 0.701 0.3517 174 8 8.8919 6.2087 11.5752 0.2574 0.6673 0.7656 0.3828 175 8.2 9.9802 7.2102 12.7502 0.1039 0.9194 0.8356 0.6849 176 8.1 10.3403 7.4866 13.194 0.0619 0.9292 0.87 0.7625 177 8.1 10.4 7.4154 13.3847 0.0655 0.9345 0.8679 0.765 178 8 10.339 7.1984 13.4796 0.0722 0.9188 0.8744 0.7416 179 7.9 10.2407 6.939 13.5424 0.0823 0.9083 0.8627 0.7117 180 7.9 10.3922 6.9495 13.8349 0.078 0.922 0.8593 0.733 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 153 0.0171 -0.006 0 0.0032 0 0 154 0.0319 -0.053 0.0295 0.2373 0.1202 0.3467 155 0.045 -0.0913 0.0501 0.6788 0.3064 0.5535 156 0.0517 -0.0965 0.0617 0.7864 0.4264 0.653 157 0.0544 -0.1059 0.0706 1.0142 0.544 0.7375 158 0.0582 -0.0911 0.074 0.7429 0.5771 0.7597 159 0.065 -0.0633 0.0725 0.3302 0.5418 0.7361 160 0.0746 -0.0333 0.0676 0.0796 0.4841 0.6957 161 0.0826 -0.0092 0.0611 0.0057 0.4309 0.6564 162 0.0859 -0.0463 0.0596 0.147 0.4025 0.6344 163 0.079 -0.0859 0.062 0.6539 0.4254 0.6522 164 0.079 -0.1109 0.0661 1.1778 0.4881 0.6986 165 0.0849 -0.116 0.0699 1.3033 0.5508 0.7422 166 0.0937 -0.1296 0.0742 1.6021 0.6259 0.7911 167 0.1032 -0.1304 0.0779 1.5877 0.69 0.8307 168 0.1084 -0.1339 0.0814 1.7273 0.7548 0.8688 169 0.1109 -0.137 0.0847 1.9071 0.8226 0.907 170 0.1166 -0.1307 0.0872 1.7108 0.872 0.9338 171 0.1264 -0.1076 0.0883 1.0744 0.8826 0.9395 172 0.1397 -0.0649 0.0871 0.3475 0.8559 0.9251 173 0.1502 -0.0565 0.0857 0.2468 0.8269 0.9093 174 0.154 -0.1003 0.0863 0.7956 0.8254 0.9085 175 0.1416 -0.1784 0.0904 3.1692 0.9273 0.963 176 0.1408 -0.2167 0.0956 5.0189 1.0978 1.0478 177 0.1464 -0.2212 0.1006 5.2902 1.2655 1.125 178 0.155 -0.2262 0.1055 5.4709 1.4273 1.1947 179 0.1645 -0.2286 0.11 5.479 1.5773 1.2559 180 0.169 -0.2398 0.1147 6.2109 1.7428 1.3202

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260543090s4ncy1x3vkhi28s/1qvzu1260543018.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260543090s4ncy1x3vkhi28s/1qvzu1260543018.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260543090s4ncy1x3vkhi28s/2g0pt1260543019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260543090s4ncy1x3vkhi28s/2g0pt1260543019.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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