*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 09:54:38 -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/t1260550519ehek24kdwti5d67.htm/, Retrieved Fri, 11 Dec 2009 17:55:22 +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/t1260550519ehek24kdwti5d67.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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20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971

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 27165 - - - - - - - 21 26736 - - - - - - - 22 23691 - - - - - - - 23 18157 - - - - - - - 24 17328 - - - - - - - 25 18205 - - - - - - - 26 20995 - - - - - - - 27 17382 - - - - - - - 28 9367 - - - - - - - 29 31124 - - - - - - - 30 26551 - - - - - - - 31 30651 - - - - - - - 32 25859 - - - - - - - 33 25100 24211.6232 20506.6416 27916.6047 0.3192 0.1917 0.0909 0.1917 34 25778 23612.0852 19774.3932 27449.7771 0.1343 0.2237 0.4839 0.1256 35 20418 18123.3289 12761.4706 23485.1871 0.2008 0.0026 0.4951 0.0023 36 18688 17363.9365 11768.4431 22959.43 0.3214 0.1424 0.505 0.0015 37 20424 17591.5685 11939.5559 23243.581 0.163 0.3519 0.4158 0.0021 38 24776 19990.4484 14338.42 25642.4768 0.0485 0.4402 0.3638 0.0209 39 19814 16213.9142 10564.6744 21863.1541 0.1058 0.0015 0.3426 4e-04 40 12738 8334.6937 2672.4722 13996.9152 0.0637 0 0.3604 0 41 31566 30298.2313 24565.1549 36031.3076 0.3324 1 0.3889 0.9355 42 30111 25872.157 20036.4241 31707.8899 0.0773 0.0279 0.4098 0.5018 43 30019 29992.8661 24068.987 35916.7453 0.4966 0.4844 0.4138 0.9143 44 31934 25137.1087 19157.5059 31116.7116 0.0129 0.0548 0.4065 0.4065 45 25826 23409.8205 16008.3483 30811.2927 0.2611 0.012 0.3272 0.2583 46 26835 22766.6945 15192.7505 30340.6384 0.1462 0.2143 0.2179 0.2118 47 20205 17280.618 8515.87 26045.3659 0.2566 0.0163 0.2415 0.0275 48 17789 16550.378 7478.3248 25622.4311 0.3945 0.2149 0.3221 0.0222 49 20520 16806.48 7597.0221 26015.9379 0.2147 0.4172 0.2207 0.027 50 22518 19217.2967 9989.512 28445.0813 0.2416 0.391 0.1189 0.0792 51 15572 15435.9614 6181.0241 24690.8986 0.4885 0.0668 0.1769 0.0136 52 11509 7544.5988 -1778.9867 16868.1844 0.2023 0.0458 0.1375 1e-04 53 25447 29498.4636 20034.8836 38962.0436 0.2007 0.9999 0.3343 0.7745 54 24090 25069.6928 15433.5108 34705.8748 0.421 0.4694 0.1526 0.4362 55 27786 29193.4329 19398.7414 38988.1244 0.3891 0.8464 0.4344 0.7477 56 26195 24342.4335 14424.1267 34260.7403 0.3571 0.2481 0.0668 0.3822 57 20516 22618.2425 11458.7336 33777.7513 0.356 0.2649 0.2866 0.2846 58 22759 21975.4568 10569.9909 33380.9227 0.4464 0.599 0.2018 0.2523 59 19028 16487.8685 3968.94 29006.7969 0.3454 0.1631 0.2803 0.0712 60 16971 15755.86 2862.4608 28649.2592 0.4267 0.3094 0.3786 0.0623 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0781 0.0367 0 789213.397 0 0 34 0.0829 0.0917 0.0642 4691187.0691 2740200.2331 1655.355 35 0.1509 0.1266 0.085 5265515.6545 3581972.0402 1892.6098 36 0.1644 0.0763 0.0828 1753144.0473 3124765.042 1767.7005 37 0.1639 0.161 0.0985 8022668.4578 4104345.7252 2025.9185 38 0.1443 0.2394 0.1219 22901503.9081 7237205.4223 2690.2055 39 0.1778 0.222 0.1362 12960617.4668 8054835.7144 2838.1042 40 0.3466 0.5283 0.1853 19389106.3721 9471619.5466 3077.5996 41 0.0965 0.0418 0.1693 1607237.5134 8597799.3207 2932.2004 42 0.1151 0.1638 0.1688 17967789.6187 9534798.3505 3087.8469 43 0.1008 9e-04 0.1535 682.9796 8668060.5895 2944.157 44 0.1214 0.2704 0.1632 46197730.9211 11795533.1171 3434.4626 45 0.1613 0.1032 0.1586 5837923.4726 11337255.4522 3367.0841 46 0.1697 0.1787 0.1601 16551109.8479 11709673.6233 3421.94 47 0.2588 0.1692 0.1607 8552010.3274 11499162.7369 3391.0415 48 0.2797 0.0748 0.1553 1534184.5493 10876351.6002 3297.9314 49 0.2796 0.221 0.1592 13790230.8044 11047756.2592 3323.8165 50 0.245 0.1718 0.1599 10894642.3479 11039249.9308 3322.5367 51 0.3059 0.0088 0.1519 18506.5097 10459210.8034 3234.0703 52 0.6305 0.5255 0.1706 15716476.8274 10722074.1046 3274.4578 53 0.1637 -0.1373 0.169 16414357.3685 10993135.2124 3315.5897 54 0.1961 -0.0391 0.1631 959798.0372 10537074.4317 3246.086 55 0.1712 -0.0482 0.1581 1980867.3576 10165065.4285 3188.27 56 0.2079 0.0761 0.1547 3432002.5429 9884521.1416 3143.9658 57 0.2517 -0.0929 0.1522 4419423.4068 9665917.2322 3109.0058 58 0.2648 0.0357 0.1477 613939.9499 9317764.2598 3052.5013 59 0.3874 0.1541 0.148 6452268.2034 9211634.7762 3035.0675 60 0.4175 0.0771 0.1454 1476565.2377 8935382.2927 2989.211

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260550519ehek24kdwti5d67/1817i1260550476.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260550519ehek24kdwti5d67/1817i1260550476.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260550519ehek24kdwti5d67/2i79q1260550477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260550519ehek24kdwti5d67/2i79q1260550477.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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