*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: Wed, 09 Dec 2009 09:55:31 -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/09/t12603777813hkjem8l5j2am1v.htm/, Retrieved Wed, 09 Dec 2009 17:56:23 +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/09/t12603777813hkjem8l5j2am1v.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 «

106370 109375 116476 123297 114813 117925 126466 131235 120546 123791 129813 133463 122987 125418 130199 133016 121454 122044 128313 131556 120027 123001 130111 132524 123742 124931 133646 136557 127509 128945 137191 139716 129083 131604 139413 143125 133948 137116 144864 149277 138796 143258 150034 154708 144888 148762 156500 161088 152772 158011 163318 169969 162269 165765 170600 174681 166364 170240 176150 182056 172218 177856 182253 188090 176863 183273 187969 194650 183036 189516 193805 200499 188142 193732 197126 205140 191751 196700 199784 207360 196101 200824 205743 212489 200810 203683 207286 210910 194915 217920

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[66]) 62 177856 - - - - - - - 63 182253 - - - - - - - 64 188090 - - - - - - - 65 176863 - - - - - - - 66 183273 - - - - - - - 67 187969 187555.6073 185025.0604 190086.1541 0.3744 0.9995 1 0.9995 68 194650 193409.5576 190085.3762 196733.7391 0.2323 0.9993 0.9991 1 69 183036 182180.046 178187.6381 186172.4539 0.3372 0 0.9955 0.2958 70 189516 188590.4182 184030.5807 193150.2556 0.3454 0.9915 0.9889 0.9889 71 193805 192872.9703 186299.596 199446.3445 0.3905 0.8416 0.9282 0.9979 72 200499 198726.9288 190839.2997 206614.558 0.3298 0.8893 0.8445 0.9999 73 188142 187497.416 178458.1733 196536.6586 0.4444 0.0024 0.8333 0.8202 74 193732 193907.7883 183851.5238 203964.0528 0.4863 0.8694 0.804 0.9809 75 197126 198190.3404 185972.5986 210408.0822 0.4322 0.7628 0.7591 0.9916 76 205140 204044.2989 190175.1732 217913.4247 0.4385 0.8359 0.6918 0.9983 77 191751 192814.7861 177447.129 208182.4431 0.446 0.058 0.7244 0.8882 78 196700 199225.1584 182495.8983 215954.4185 0.3837 0.8094 0.7401 0.9692 79 199784 203507.7105 184443.2019 222572.2191 0.3509 0.758 0.7441 0.9813 80 207360 209361.6691 188377.7736 230345.5645 0.4258 0.8145 0.6533 0.9926 81 196101 198132.1562 175368.8066 220895.5058 0.4306 0.2134 0.7086 0.8996 82 200824 204542.5286 180132.0592 228952.9979 0.3826 0.7511 0.7356 0.9562 83 205743 208825.0806 181906.39 235743.7712 0.4112 0.7199 0.7448 0.9686 84 212489 214679.0392 185610.3586 243747.7198 0.4413 0.7266 0.6892 0.9829 85 200810 203449.5263 172359.6028 234539.4498 0.4339 0.2844 0.6784 0.8983 86 203683 209859.8987 176875.1006 242844.6968 0.3568 0.7046 0.7043 0.9429 87 207286 214142.4508 178482.7494 249802.1521 0.3531 0.7173 0.6778 0.9551 88 210910 219996.4093 181980.5514 258012.2673 0.3197 0.7439 0.6506 0.9708 89 194915 208766.8965 168514.3872 249019.4057 0.25 0.4584 0.6508 0.8928 90 217920 215177.2688 172808.5816 257545.956 0.4495 0.8257 0.7025 0.93 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 67 0.0069 0.0022 0 170893.5613 0 0 68 0.0088 0.0064 0.0043 1538697.2385 854795.3999 924.5515 69 0.0112 0.0047 0.0044 732657.2774 814082.6924 902.2653 70 0.0123 0.0049 0.0046 856701.7525 824737.4574 908.1506 71 0.0174 0.0048 0.0046 868679.4309 833525.8521 912.9764 72 0.0203 0.0089 0.0053 3140236.2562 1217977.5861 1103.6202 73 0.0246 0.0034 0.0051 415488.5946 1103336.3016 1050.3982 74 0.0265 -9e-04 0.0045 30901.5272 969281.9548 984.5212 75 0.0315 -0.0054 0.0046 1132820.4528 987452.899 993.7066 76 0.0347 0.0054 0.0047 1200560.7953 1008763.6887 1004.3723 77 0.0407 -0.0055 0.0048 1131640.8169 1019934.3367 1009.918 78 0.0428 -0.0127 0.0054 6376425.08 1466308.5653 1210.9123 79 0.0478 -0.0183 0.0064 13866019.95 2420132.518 1555.6775 80 0.0511 -0.0096 0.0067 4006679.0757 2533457.2721 1591.6838 81 0.0586 -0.0103 0.0069 4125595.5133 2639599.8215 1624.6845 82 0.0609 -0.0182 0.0076 13827454.5859 3338840.7443 1827.2495 83 0.0658 -0.0148 0.008 9499221.0271 3701216.055 1923.8545 84 0.0691 -0.0102 0.0081 4796271.684 3762052.4789 1939.6011 85 0.078 -0.013 0.0084 6967099.2233 3930739.1496 1982.6092 86 0.0802 -0.0294 0.0094 38154077.2489 5641906.0546 2375.2697 87 0.085 -0.032 0.0105 47010916.9867 7611858.9561 2758.9598 88 0.0882 -0.0413 0.0119 82562834.3555 11018721.4743 3319.446 89 0.0984 -0.0664 0.0143 191875035.2618 18882039.465 4345.3469 90 0.1005 0.0127 0.0142 7522574.435 18408728.4221 4290.5394

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t12603777813hkjem8l5j2am1v/1khr61260377730.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t12603777813hkjem8l5j2am1v/1khr61260377730.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t12603777813hkjem8l5j2am1v/2y9521260377730.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t12603777813hkjem8l5j2am1v/2y9521260377730.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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 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