*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, 21 Dec 2009 13:06:10 -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/21/t1261426269jdsyhel7dkepakc.htm/, Retrieved Mon, 21 Dec 2009 21:11:11 +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/21/t1261426269jdsyhel7dkepakc.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.9 1 1.2 1.5 1.8 2.3 2.7 3.1 3.7 4.5 5.8 7 7.9 8.5 8.7 8.7 8.5 8.3 8.3 8.7 8.5 7.6 6.5 5.6 4.5 4.2 4.1 4 4.1 4.3 4 3.5 3.2 3.2 3.2 3 3 2.4 2.3 1.7 1.5 1.1 0.8 1 1.5 1.9 1.8 1.9 1.7 1.8 1.6 2.2 2.2 2.3 2.3 2.2 2.5 2.1 2.1 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 4 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[32]) 20 8.7 - - - - - - - 21 8.5 - - - - - - - 22 7.6 - - - - - - - 23 6.5 - - - - - - - 24 5.6 - - - - - - - 25 4.5 - - - - - - - 26 4.2 - - - - - - - 27 4.1 - - - - - - - 28 4 - - - - - - - 29 4.1 - - - - - - - 30 4.3 - - - - - - - 31 4 - - - - - - - 32 3.5 - - - - - - - 33 3.2 3.4204 3.0785 3.7623 0.1032 0.324 0 0.324 34 3.2 3.566 2.7612 4.3708 0.1864 0.8136 0 0.5638 35 3.2 4.1325 2.8407 5.4243 0.0785 0.9215 2e-04 0.8314 36 3 4.6727 2.8766 6.4687 0.034 0.946 0.1558 0.8997 37 3 4.9844 2.624 7.3447 0.0497 0.9503 0.6562 0.8911 38 2.4 4.9633 2.0289 7.8977 0.0434 0.9051 0.6949 0.8358 39 2.3 4.6637 1.1395 8.1879 0.0943 0.896 0.623 0.7412 40 1.7 4.1761 0.0259 8.3263 0.1211 0.8122 0.5331 0.6252 41 1.5 3.5437 -1.2409 8.3283 0.2012 0.775 0.4099 0.5071 42 1.1 2.9048 -2.5327 8.3422 0.2577 0.6937 0.3075 0.4151 43 0.8 2.4695 -3.6475 8.5866 0.2963 0.6696 0.3119 0.3706 44 1 2.3813 -4.4256 9.1882 0.3454 0.6756 0.3737 0.3737 45 1.5 1.7929 -5.6948 9.2807 0.4694 0.5822 0.3563 0.3275 46 1.9 0.6533 -7.5093 8.8158 0.3823 0.4194 0.2704 0.2471 47 1.8 -0.6849 -9.5189 8.1491 0.2907 0.2832 0.1944 0.1766 48 1.9 -1.8862 -11.4006 7.6283 0.2177 0.2238 0.1571 0.1336 49 1.7 -3.1917 -13.3921 7.0088 0.1736 0.1639 0.1171 0.0993 50 1.8 -3.8586 -14.7519 7.0348 0.1543 0.1586 0.1301 0.0928 51 1.6 -4.3406 -15.9395 7.2582 0.1577 0.1497 0.1309 0.0926 52 2.2 -4.7895 -17.1025 7.5235 0.1329 0.1546 0.1508 0.0935 53 2.2 -5.0589 -18.0962 7.9785 0.1376 0.1376 0.1621 0.0991 54 2.3 -5.2667 -19.0412 8.5079 0.1408 0.144 0.1825 0.1061 55 2.3 -5.8617 -20.3832 8.6598 0.1353 0.1353 0.1843 0.1032 56 2.2 -6.6571 -21.9367 8.6225 0.1279 0.1253 0.163 0.0963 57 2.5 -7.0692 -23.1986 9.0603 0.1225 0.13 0.1489 0.0995 58 2.1 -7.2132 -24.2882 9.8618 0.1425 0.1324 0.1478 0.1094 59 2.1 -7.0219 -25.1095 11.0656 0.1615 0.1615 0.1695 0.1271 60 2 -6.882 -26.0352 12.2712 0.1817 0.179 0.1844 0.144 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.051 -0.0644 0 0.0486 0 0 34 0.1152 -0.1026 0.0835 0.134 0.0913 0.3021 35 0.1595 -0.2257 0.1309 0.8696 0.3507 0.5922 36 0.1961 -0.358 0.1877 2.7978 0.9625 0.9811 37 0.2416 -0.3981 0.2298 3.9376 1.5575 1.248 38 0.3016 -0.5165 0.2775 6.5705 2.393 1.5469 39 0.3855 -0.5068 0.3103 5.5869 2.8493 1.688 40 0.507 -0.5929 0.3456 6.1309 3.2595 1.8054 41 0.6889 -0.5767 0.3713 4.1767 3.3614 1.8334 42 0.9551 -0.6213 0.3963 3.2571 3.351 1.8306 43 1.2638 -0.6761 0.4217 2.7874 3.2997 1.8165 44 1.4584 -0.5801 0.4349 1.908 3.1838 1.7843 45 2.1307 -0.1634 0.414 0.0858 2.9455 1.7162 46 6.3751 1.9085 0.5208 1.5544 2.8461 1.687 47 -6.581 -3.6282 0.728 6.1746 3.068 1.7516 48 -2.5737 -2.0073 0.8079 14.335 3.7722 1.9422 49 -1.6306 -1.5326 0.8505 23.9284 4.9578 2.2266 50 -1.4404 -1.4665 0.8848 32.0192 6.4613 2.5419 51 -1.3633 -1.3686 0.9102 35.2913 7.9786 2.8246 52 -1.3117 -1.4593 0.9377 48.853 10.0223 3.1658 53 -1.3149 -1.4349 0.9614 52.6911 12.0542 3.4719 54 -1.3344 -1.4367 0.983 57.2543 14.1087 3.7562 55 -1.264 -1.3924 1.0008 66.6133 16.3915 4.0486 56 -1.171 -1.3305 1.0145 78.4488 18.9773 4.3563 57 -1.1641 -1.3536 1.0281 91.5687 21.8809 4.6777 58 -1.2078 -1.2911 1.0382 86.735 24.3753 4.9371 59 -1.3142 -1.2991 1.0479 83.2098 26.5544 5.1531 60 -1.4199 -1.2906 1.0565 78.8901 28.4235 5.3314

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261426269jdsyhel7dkepakc/1aztv1261425966.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261426269jdsyhel7dkepakc/1aztv1261425966.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261426269jdsyhel7dkepakc/2svtf1261425966.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261426269jdsyhel7dkepakc/2svtf1261425966.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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