*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 12:39:13 -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/t126056044556cx3vo7ycd727m.htm/, Retrieved Fri, 11 Dec 2009 20:40:47 +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/t126056044556cx3vo7ycd727m.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:

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285 574 865 1147 1516 1789 2087 2372 2669 2966 3270 3652 329 658 988 1303 1603 1929 2235 2544 2872 3198 3544 3903 332 665 1001 1329 1639 1975 2304 2640 2992 3330 3690 4063 368 738 1103 1474 1846 2224 2608 2984 3351 3736 4122 4558 378 749 1113 1500 1867 2244 2621 2988 3349 3723 4108 4514

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 1 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 2544 - - - - - - - 21 2872 - - - - - - - 22 3198 - - - - - - - 23 3544 - - - - - - - 24 3903 - - - - - - - 25 332 - - - - - - - 26 665 - - - - - - - 27 1001 - - - - - - - 28 1329 - - - - - - - 29 1639 - - - - - - - 30 1975 - - - - - - - 31 2304 - - - - - - - 32 2640 - - - - - - - 33 2992 2521.234 1026.1265 4016.3415 0.2686 0.4381 0.3228 0.4381 34 3330 2562.8547 768.9432 4356.7662 0.201 0.3196 0.2439 0.4664 35 3690 2131.727 272.4345 3991.0195 0.0502 0.1033 0.0683 0.296 36 4063 2016.0797 161.493 3870.6664 0.0153 0.0384 0.0231 0.2548 37 368 1589.7745 -267.2242 3446.7733 0.0986 0.0045 0.9078 0.1338 38 738 1607.0333 -270.5722 3484.6388 0.1822 0.9021 0.8373 0.1405 39 1103 1384.8905 -495.4935 3265.2745 0.3844 0.7499 0.6555 0.0954 40 1474 1614.1585 -265.7376 3494.0547 0.4419 0.703 0.6169 0.1424 41 1846 1560.1986 -347.017 3467.4141 0.3845 0.5353 0.4677 0.1336 42 2224 1881.9914 -95.3324 3859.3152 0.3673 0.5142 0.4633 0.2262 43 2608 1838.4122 -261.6632 3938.4876 0.2363 0.3595 0.332 0.2272 44 2984 2101.91 -119.2688 4323.0888 0.2182 0.3276 0.3175 0.3175 45 3351 1959.4565 -374.0103 4292.9233 0.1212 0.1947 0.1929 0.2838 46 3736 2114.727 -288.5509 4518.0049 0.093 0.1567 0.1608 0.3342 47 4122 1882.8472 -566.3065 4332.0009 0.0366 0.069 0.0741 0.2723 48 4558 1984.6008 -485.0062 4454.2078 0.0206 0.0449 0.0495 0.3015 49 378 1741.1723 -741.6125 4223.9572 0.1409 0.0131 0.8608 0.239 50 749 1867.2474 -623.2283 4357.7231 0.1894 0.8794 0.8129 0.2715 51 1113 1671.5088 -830.361 4173.3785 0.3309 0.7651 0.672 0.224 52 1500 1852.1296 -663.7591 4368.0182 0.3919 0.7176 0.6158 0.2697 53 1867 1703.8777 -838.0291 4245.7845 0.45 0.5625 0.4564 0.2352 54 2244 1914.5422 -658.0919 4487.1762 0.4009 0.5144 0.4068 0.2902 55 2621 1775.6758 -840.3123 4391.6638 0.2633 0.3628 0.2664 0.2586 56 2988 1976.49 -680.2816 4633.2616 0.2278 0.3172 0.2287 0.3122 57 3349 1815.197 -886.66 4517.054 0.1329 0.1974 0.1326 0.2748 58 3723 1988.405 -748.5723 4725.3823 0.1071 0.1649 0.1054 0.3204 59 4108 1802.4122 -968.8611 4573.6854 0.0515 0.0872 0.0504 0.2768 60 4514 1958.6728 -837.3455 4754.691 0.0366 0.0659 0.0342 0.3165 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.3026 0.1867 0 221620.5998 0 0 34 0.3571 0.2993 0.243 588511.8985 405066.2491 636.4482 35 0.445 0.731 0.4057 2428214.6887 1079449.0623 1038.9654 36 0.4693 1.0153 0.5581 4189882.7067 1857057.4734 1362.739 37 0.596 -0.7685 0.6002 1492733.0036 1784192.5795 1335.7367 38 0.5961 -0.5408 0.5903 755218.8743 1612696.9619 1269.9201 39 0.6927 -0.2035 0.535 79462.2485 1393663.4314 1180.5352 40 0.5942 -0.0868 0.479 19644.4171 1221911.0546 1105.4009 41 0.6237 0.1832 0.4461 81682.4441 1095218.9868 1046.5271 42 0.536 0.1817 0.4197 116969.8846 997394.0766 998.6962 43 0.5828 0.4186 0.4196 592265.4007 960564.197 980.0838 44 0.5392 0.4197 0.4196 778082.7535 945357.41 972.2949 45 0.6076 0.7102 0.442 1936393.3684 1021590.9453 1010.7378 46 0.5798 0.7667 0.4651 2628526.2611 1136372.0392 1066.0075 47 0.6637 1.1892 0.5134 5013805.1696 1394867.5813 1181.0451 48 0.6349 1.2967 0.5624 6622383.5495 1721587.3293 1312.0927 49 0.7275 -0.7829 0.5753 1858238.7736 1729625.6495 1315.1523 50 0.6805 -0.5989 0.5767 1250477.2196 1703006.2923 1304.9928 51 0.7637 -0.3341 0.5639 311932.0622 1629791.8592 1276.633 52 0.693 -0.1901 0.5452 123995.2436 1554502.0284 1246.7967 53 0.7611 0.0957 0.5238 26608.885 1481745.212 1217.2696 54 0.6856 0.1721 0.5078 108542.4464 1419326.9045 1191.3551 55 0.7517 0.4761 0.5064 714573.0746 1388685.4336 1178.425 56 0.6858 0.5118 0.5067 1023152.3892 1373454.8901 1171.9449 57 0.7594 0.845 0.5202 2352551.7625 1412618.765 1188.5364 58 0.7023 0.8724 0.5337 3008819.6981 1474011.1086 1214.0886 59 0.7845 1.2792 0.5613 5315735.2945 1616297.1895 1271.3368 60 0.7283 1.3046 0.5879 6529697.2905 1791775.7646 1338.5723

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t126056044556cx3vo7ycd727m/1ms3h1260560351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t126056044556cx3vo7ycd727m/1ms3h1260560351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t126056044556cx3vo7ycd727m/2pfn71260560351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t126056044556cx3vo7ycd727m/2pfn71260560351.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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