*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: Thu, 17 Dec 2009 01:51:10 -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/17/t1261040025w4yde9vrz6yozij.htm/, Retrieved Thu, 17 Dec 2009 09:53:47 +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/17/t1261040025w4yde9vrz6yozij.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 «

8.3 8.2 8 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 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9

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 3 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[44]) 32 8.7 - - - - - - - 33 8.7 - - - - - - - 34 8.5 - - - - - - - 35 8.4 - - - - - - - 36 8.5 - - - - - - - 37 8.7 - - - - - - - 38 8.7 - - - - - - - 39 8.6 - - - - - - - 40 8.5 - - - - - - - 41 8.3 - - - - - - - 42 8 - - - - - - - 43 8.2 - - - - - - - 44 8.1 - - - - - - - 45 8.1 8.214 7.913 8.515 0.2289 0.7711 8e-04 0.7711 46 8 8.4364 7.9716 8.9013 0.0329 0.922 0.3943 0.922 47 7.9 8.6816 8.1526 9.2106 0.0019 0.9942 0.8516 0.9844 48 7.9 8.9577 8.4286 9.4867 0 1 0.955 0.9993 49 8 8.9749 8.4303 9.5195 2e-04 0.9999 0.8388 0.9992 50 8 8.6036 8.0386 9.1686 0.0181 0.9819 0.369 0.9597 51 7.9 8.091 7.5259 8.6561 0.2538 0.6239 0.0387 0.4876 52 8 7.7375 7.1489 8.3262 0.1911 0.2943 0.0056 0.1137 53 7.7 7.6303 6.9695 8.291 0.4181 0.1364 0.0235 0.0818 54 7.2 7.7202 6.9909 8.4495 0.081 0.5217 0.226 0.1537 55 7.5 8.4638 7.7032 9.2243 0.0065 0.9994 0.7517 0.8257 56 7.3 8.5548 7.7899 9.3196 7e-04 0.9966 0.8781 0.8781 57 7 8.4684 7.6825 9.2542 1e-04 0.9982 0.8209 0.8209 58 7 8.2424 7.4212 9.0636 0.0015 0.9985 0.7186 0.6331 59 7 8.0994 7.23 8.9689 0.0066 0.9934 0.6735 0.4995 60 7.2 8.2636 7.3514 9.1759 0.0111 0.9967 0.7827 0.6374 61 7.3 8.4649 7.5154 9.4144 0.0081 0.9955 0.8314 0.7744 62 7.1 8.4073 7.4278 9.3868 0.0045 0.9866 0.7924 0.7307 63 6.8 8.1171 7.1058 9.1285 0.0053 0.9756 0.6631 0.5133 64 6.4 7.7465 6.6965 8.7965 0.006 0.9614 0.3181 0.2547 65 6.1 7.4435 6.3424 8.5446 0.0084 0.9684 0.324 0.1213 66 6.5 7.3023 6.1401 8.4645 0.088 0.9787 0.5685 0.0893 67 7.7 7.9561 6.7287 9.1834 0.3413 0.99 0.7668 0.4091 68 7.9 8.0812 6.7922 9.3702 0.3914 0.7189 0.8826 0.4886 69 7.5 8.1223 6.7389 9.5057 0.189 0.6236 0.9441 0.5126 70 6.9 8.0154 6.5363 9.4945 0.0697 0.7527 0.9108 0.4554 71 6.6 7.9131 6.3511 9.4752 0.0497 0.8982 0.8741 0.4073 72 6.9 8.0185 6.3942 9.6429 0.0886 0.9565 0.8383 0.4609 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 45 0.0187 -0.0139 0 0.013 0 0 46 0.0281 -0.0517 0.0328 0.1905 0.1017 0.319 47 0.0311 -0.09 0.0519 0.611 0.2715 0.521 48 0.0301 -0.1181 0.0684 1.1187 0.4833 0.6952 49 0.031 -0.1086 0.0765 0.9504 0.5767 0.7594 50 0.0335 -0.0702 0.0754 0.3643 0.5413 0.7357 51 0.0356 -0.0236 0.068 0.0365 0.4692 0.685 52 0.0388 0.0339 0.0638 0.0689 0.4192 0.6474 53 0.0442 0.0091 0.0577 0.0049 0.3731 0.6108 54 0.0482 -0.0674 0.0587 0.2706 0.3629 0.6024 55 0.0458 -0.1139 0.0637 0.9288 0.4143 0.6437 56 0.0456 -0.1467 0.0706 1.5745 0.511 0.7148 57 0.0473 -0.1734 0.0785 2.1561 0.6375 0.7985 58 0.0508 -0.1507 0.0837 1.5436 0.7023 0.838 59 0.0548 -0.1357 0.0871 1.2088 0.736 0.8579 60 0.0563 -0.1287 0.0897 1.1313 0.7607 0.8722 61 0.0572 -0.1376 0.0925 1.3571 0.7958 0.8921 62 0.0594 -0.1555 0.096 1.7089 0.8465 0.9201 63 0.0636 -0.1623 0.0995 1.7349 0.8933 0.9451 64 0.0692 -0.1738 0.1032 1.8132 0.9393 0.9692 65 0.0755 -0.1805 0.1069 1.805 0.9805 0.9902 66 0.0812 -0.1099 0.1071 0.6437 0.9652 0.9824 67 0.0787 -0.0322 0.1038 0.0656 0.9261 0.9623 68 0.0814 -0.0224 0.1004 0.0328 0.8889 0.9428 69 0.0869 -0.0766 0.0995 0.3873 0.8688 0.9321 70 0.0941 -0.1392 0.101 1.2441 0.8832 0.9398 71 0.1007 -0.1659 0.1034 1.7243 0.9144 0.9562 72 0.1034 -0.1395 0.1047 1.2511 0.9264 0.9625

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261040025w4yde9vrz6yozij/1t22w1261039867.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261040025w4yde9vrz6yozij/1t22w1261039867.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261040025w4yde9vrz6yozij/28y171261039867.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261040025w4yde9vrz6yozij/28y171261039867.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; 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 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

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