*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 07:56:39 -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/t1261061887d87wn7shsx3yvkz.htm/, Retrieved Thu, 17 Dec 2009 15:58:09 +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/t1261061887d87wn7shsx3yvkz.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 «

358.59 362.96 362.42 364.97 364.04 361.06 358.48 352.96 359.59 360.39 357.40 362.93 364.55 365.73 364.70 364.65 359.43 362.14 356.97 354.82 353.17 357.06 356.18 355.01 355.65 357.31 357.07 357.91 358.48 358.97 351.77 352.16 359.08 360.35 359.53 359.30 358.41 359.68 355.31 357.08 349.71 354.13 345.49 341.69 344.25 340.17 342.47 344.43 333.23 339.72 342.61 346.36 339.09 339.73 341.12 335.94 333.46 335.66 341.12 342.21 342.62 346.06 344.43 346.65 343.74 335.67 342.75 341.77 345.84 346.52 350.79 345.44 345.87 338.48 337.21 340.81 339.86 342.86 343.33 341.73 351.38 351.13 345.99 347.55 346.02 345.29 347.03 348.01 345.48 349.40 351.05 349.70 350.86 354.45 355.30 357.48 355.24 351.79 355.22 351.02 350.28 350.17 348.16 340.30 343.75 344.71 344.13 342.14 345.04 346.02 346.43 347.07 339.33 339.10 337.19 339.58 327.85 326.81 321.73 320.45 327.69 323.95 320.47 322.13 316.34 314.78 308.90 308.62 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 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[371]) 370 234.89 - - - - - - - 371 227.78 - - - - - - - 372 234.04 231.377 221.3519 241.4021 0.3013 0.7591 0.7591 0.7591 373 230.7 231.0615 218.4353 243.6878 0.4776 0.3219 0.3219 0.6948 374 230.17 230.5111 216.0835 244.9388 0.4815 0.4898 0.4898 0.6447 375 218.23 230.7691 214.4219 247.1163 0.0664 0.5286 0.5286 0.64 376 232.2 230.7691 212.7633 248.775 0.4381 0.9139 0.9139 0.6276 377 220.76 230.7233 211.2272 250.2195 0.1583 0.441 0.441 0.6163 378 215.6 230.7405 209.8417 251.6394 0.0778 0.8254 0.8254 0.6094 379 217.69 230.7422 208.5312 252.9531 0.1247 0.9093 0.9093 0.6031 380 204.35 230.7385 207.2909 254.1861 0.0137 0.8623 0.8623 0.5977 381 191.44 230.7396 206.1162 255.363 9e-04 0.9822 0.9822 0.5931 382 203.84 230.7398 204.9944 256.4853 0.0203 0.9986 0.9986 0.5891 383 211.86 230.7396 203.9191 257.56 0.0838 0.9753 0.9753 0.5856 384 210.57 230.7396 202.8856 258.5936 0.0779 0.908 0.908 0.5825 385 219.57 230.7396 201.889 259.5903 0.224 0.9147 0.9147 0.5797 386 219.98 230.7396 200.9257 260.5535 0.2397 0.7686 0.7686 0.5771 387 226.01 230.7396 199.9926 261.4867 0.3815 0.7536 0.7536 0.5748 388 207.04 230.7396 199.0869 262.3923 0.0711 0.6152 0.6152 0.5727 389 212.52 230.7396 198.2065 263.2728 0.1362 0.9233 0.9233 0.5708 390 217.92 230.7396 197.3493 264.13 0.2259 0.8576 0.8576 0.569 391 210.45 230.7396 196.5135 264.9657 0.1226 0.7686 0.7686 0.5673 392 218.53 230.7396 195.6977 265.7816 0.2473 0.8718 0.8718 0.5657 393 223.32 230.7396 194.9004 266.5788 0.3425 0.7478 0.7478 0.5643 394 218.76 230.7396 194.1205 267.3588 0.2607 0.6544 0.6544 0.5629 395 217.63 230.7396 193.3568 268.1224 0.2459 0.735 0.735 0.5617 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 372 0.0221 0.0115 5e-04 7.0914 0.2955 0.5436 373 0.0279 -0.0016 1e-04 0.1307 0.0054 0.0738 374 0.0319 -0.0015 1e-04 0.1164 0.0048 0.0696 375 0.0361 -0.0543 0.0023 157.229 6.5512 2.5595 376 0.0398 0.0062 3e-04 2.0474 0.0853 0.2921 377 0.0431 -0.0432 0.0018 99.2682 4.1362 2.0338 378 0.0462 -0.0656 0.0027 229.235 9.5515 3.0905 379 0.0491 -0.0566 0.0024 170.3593 7.0983 2.6643 380 0.0518 -0.1144 0.0048 696.3534 29.0147 5.3865 381 0.0544 -0.1703 0.0071 1544.4578 64.3524 8.022 382 0.0569 -0.1166 0.0049 723.6011 30.15 5.4909 383 0.0593 -0.0818 0.0034 356.4375 14.8516 3.8538 384 0.0616 -0.0874 0.0036 406.8133 16.9506 4.1171 385 0.0638 -0.0484 0.002 124.7609 5.1984 2.28 386 0.0659 -0.0466 0.0019 115.7694 4.8237 2.1963 387 0.068 -0.0205 9e-04 22.3693 0.9321 0.9654 388 0.07 -0.1027 0.0043 561.6722 23.403 4.8377 389 0.0719 -0.079 0.0033 331.9547 13.8314 3.7191 390 0.0738 -0.0556 0.0023 164.3428 6.8476 2.6168 391 0.0757 -0.0879 0.0037 411.6688 17.1529 4.1416 392 0.0775 -0.0529 0.0022 149.0749 6.2115 2.4923 393 0.0792 -0.0322 0.0013 55.0508 2.2938 1.5145 394 0.081 -0.0519 0.0022 143.5114 5.9796 2.4453 395 0.0827 -0.0568 0.0024 171.8622 7.1609 2.676

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261061887d87wn7shsx3yvkz/1dhdm1261061798.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261061887d87wn7shsx3yvkz/1dhdm1261061798.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261061887d87wn7shsx3yvkz/28qhr1261061798.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261061887d87wn7shsx3yvkz/28qhr1261061798.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 1 ; 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 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,fx)) (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.se <- array(0, dim=fx) perf.mse <- 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$pred[i] perf.mape[i] = perf.mape[i] + abs(perf.pe[i]) perf.se[i] = (x[nx+i] - forecast$pred[i])^2 perf.mse[i] = perf.mse[i] + perf.se[i] 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 = perf.mape / fx perf.mse = perf.mse / fx perf.rmse = sqrt(perf.mse) 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[1:12] <- 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.mape[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse[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