Arima Forecasting (Paper)

*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: Sun, 19 Dec 2010 13:15:37 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/19/t1292764433faiw9jraogmxblq.htm/, Retrieved Sun, 19 Dec 2010 14:13:53 +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/2010/Dec/19/t1292764433faiw9jraogmxblq.htm/}, year = {2010}, } @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 = {2010}, 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 «

14.458 13.594 17.814 20.235 21.811 21.439 21.393 19.831 20.468 21.080 21.600 17.390 17.848 19.592 21.092 20.899 25.890 24.965 22.225 20.977 22.897 22.785 22.769 19.637 20.203 20.450 23.083 21.738 26.766 25.280 22.574 22.729 21.378 22.902 24.989 21.116 15.169 15.846 20.927 18.273 22.538 15.596 14.034 11.366 14.861 15.149 13.577 13.026 13.190 13.196 15.826 14.733 16.307 15.703 14.589 12.043 15.057 14.053 12.698 10.888 10.045 11.549 13.767 12.434 13.116 14.211 12.266 12.602 15.714 13.742 12.745 10.491 10.057 10.900 11.771 11.992 11.933 14.504 11.727 11.477 13.578 11.555 11.846 11.397 10.066 10.269 14.279 13.870 13.695 14.420 11.424 9.704 12.464 14.301 13.464 9.893 11.572 12.380 16.692 16.052 16.459 14.761 13.654 13.480 18.068 16.560 14.530 10.650 11.651 13.735 13.360 17.818 20.613 16.231 13.862 12.004 17.734 15.034 12.609 12.320 10.833 11.350 13.648 14.890 16.325 18.045 15.616 11.926 16 etc...

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 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk 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[108]) 96 9.893 - - - - - - - 97 11.572 - - - - - - - 98 12.38 - - - - - - - 99 16.692 - - - - - - - 100 16.052 - - - - - - - 101 16.459 - - - - - - - 102 14.761 - - - - - - - 103 13.654 - - - - - - - 104 13.48 - - - - - - - 105 18.068 - - - - - - - 106 16.56 - - - - - - - 107 14.53 - - - - - - - 108 10.65 - - - - - - - 109 11.651 11.3113 8.0834 14.5392 0.4183 0.656 0.4371 0.656 110 13.735 12.111 8.2202 16.0018 0.2067 0.5916 0.4461 0.7691 111 13.36 15.6091 11.2966 19.9216 0.1533 0.8028 0.3113 0.9879 112 17.818 15.1242 10.4641 19.7842 0.1286 0.771 0.3482 0.9701 113 20.613 16.6913 11.7178 21.6648 0.0611 0.3285 0.5365 0.9914 114 16.231 15.6174 10.3518 20.8829 0.4097 0.0315 0.6251 0.9678 115 13.862 13.9987 8.4572 19.5401 0.4807 0.2149 0.5485 0.8819 116 12.004 13.1649 7.3609 18.9689 0.3475 0.4069 0.4576 0.8021 117 17.734 16.0337 9.9785 22.0889 0.291 0.9039 0.2551 0.9593 118 15.034 15.4432 9.1468 21.7396 0.4493 0.2379 0.364 0.9322 119 12.609 14.5833 8.0544 21.1123 0.2767 0.4462 0.5064 0.8812 120 12.32 11.5522 4.7979 18.3065 0.4118 0.3795 0.6033 0.6033 121 10.833 11.3568 4.0076 18.7061 0.4444 0.3986 0.4687 0.5748 122 11.35 11.9754 4.2189 19.7319 0.4372 0.6136 0.3283 0.6312 123 13.648 15.2116 7.1011 23.3221 0.3528 0.8246 0.6727 0.8648 124 14.89 14.7502 6.3097 23.1906 0.487 0.601 0.2381 0.8295 125 16.325 16.609 7.8537 25.3643 0.4747 0.6498 0.185 0.9089 126 18.045 15.6932 6.6347 24.7517 0.3054 0.4456 0.4537 0.8624 127 15.616 13.9433 4.5916 23.2949 0.3629 0.195 0.5068 0.755 128 11.926 12.9407 3.3049 22.5765 0.4182 0.2932 0.5756 0.6794 129 16.855 15.37 5.4581 25.2818 0.3845 0.7521 0.3201 0.8247 130 15.083 15.014 4.8334 25.1945 0.4947 0.3615 0.4985 0.7996 131 12.52 14.4532 4.0105 24.896 0.3584 0.453 0.6354 0.7623 132 12.355 11.6391 0.9392 22.339 0.4478 0.4359 0.4504 0.5719 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 109 0.1456 0.03 0 0.1154 0 0 110 0.1639 0.1341 0.0821 2.6372 1.3763 1.1732 111 0.141 -0.1441 0.1027 5.0584 2.6037 1.6136 112 0.1572 0.1781 0.1216 7.2567 3.7669 1.9409 113 0.152 0.235 0.1443 15.3801 6.0896 2.4677 114 0.172 0.0393 0.1268 0.3765 5.1374 2.2666 115 0.202 -0.0098 0.11 0.0187 4.4061 2.0991 116 0.2249 -0.0882 0.1073 1.3477 4.0238 2.006 117 0.1927 0.106 0.1072 2.891 3.898 1.9743 118 0.208 -0.0265 0.0991 0.1674 3.5249 1.8775 119 0.2284 -0.1354 0.1024 3.8979 3.5588 1.8865 120 0.2983 0.0665 0.0994 0.5896 3.3114 1.8197 121 0.3302 -0.0461 0.0953 0.2744 3.0778 1.7544 122 0.3305 -0.0522 0.0922 0.3912 2.8859 1.6988 123 0.272 -0.1028 0.0929 2.4449 2.8565 1.6901 124 0.292 0.0095 0.0877 0.0195 2.6792 1.6368 125 0.269 -0.0171 0.0836 0.0807 2.5263 1.5894 126 0.2945 0.1499 0.0872 5.5308 2.6932 1.6411 127 0.3422 0.12 0.089 2.7981 2.6987 1.6428 128 0.3799 -0.0784 0.0884 1.0296 2.6153 1.6172 129 0.329 0.0966 0.0888 2.2053 2.5958 1.6111 130 0.346 0.0046 0.085 0.0048 2.478 1.5742 131 0.3686 -0.1338 0.0871 3.7374 2.5328 1.5915 132 0.469 0.0615 0.0861 0.5125 2.4486 1.5648

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292764433faiw9jraogmxblq/1uosl1292764533.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292764433faiw9jraogmxblq/1uosl1292764533.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292764433faiw9jraogmxblq/2177e1292764533.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292764433faiw9jraogmxblq/2177e1292764533.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods 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 par7 <- as.numeric(par7) #q 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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by