W9Q1

*Unverified author*

R Software Module: rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Sun, 14 Dec 2008 05:45:50 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/14/t1229258781zel8r9pvccf1yiq.htm/, Retrieved Sun, 14 Dec 2008 13:46:23 +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/2008/Dec/14/t1229258781zel8r9pvccf1yiq.htm/}, year = {2008}, } @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 = {2008}, 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 «

95,4 98,7 99,9 98,6 100,3 100,2 100,4 101,4 103 109,1 111,4 114,1 121,8 127,6 129,9 128 123,5 124 127,4 127,6 128,4 131,4 135,1 134 144,5 147,3 150,9 148,7 141,4 138,9 139,8 145,6 147,9 148,5 151,1 157,5 167,5 172,3 173,5 187,5 205,5 195,1 204,5 204,5 201,7 207 206,6 210,6 211,1 215 223,9 238,2 238,9 229,6 232,2 222,1 221,6 227,3 221 213,6 243,4 253,8 265,3 268,2 268,5 266,9 268,4 250,8 231,2 192

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 'George Udny Yule' @ 72.249.76.132 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[20]) 8 101.4 - - - - - - - 9 103 - - - - - - - 10 109.1 - - - - - - - 11 111.4 - - - - - - - 12 114.1 - - - - - - - 13 121.8 - - - - - - - 14 127.6 - - - - - - - 15 129.9 - - - - - - - 16 128 - - - - - - - 17 123.5 - - - - - - - 18 124 - - - - - - - 19 127.4 - - - - - - - 20 127.6 - - - - - - - 21 128.4 0 -221.0822 221.0822 0.1275 0.129 0.1806 0.129 22 131.4 0 -221.0822 221.0822 0.122 0.1275 0.1667 0.129 23 135.1 0 -221.0822 221.0822 0.1155 0.122 0.1617 0.129 24 134 0 -221.0822 221.0822 0.1174 0.1155 0.1559 0.129 25 144.5 0 -221.0822 221.0822 0.1001 0.1174 0.1401 0.129 26 147.3 0 -221.0822 221.0822 0.0958 0.1001 0.129 0.129 27 150.9 0 -221.0822 221.0822 0.0905 0.0958 0.1247 0.129 28 148.7 0 -221.0822 221.0822 0.0937 0.0905 0.1282 0.129 29 141.4 0 -221.0822 221.0822 0.105 0.0937 0.1368 0.129 30 138.9 0 -221.0822 221.0822 0.1091 0.105 0.1358 0.129 31 139.8 0 -221.0822 221.0822 0.1076 0.1091 0.1294 0.129 32 145.6 0 -221.0822 221.0822 0.0984 0.1076 0.129 0.129 33 147.9 0 -221.0822 221.0822 0.0949 0.0984 0.1275 0.129 34 148.5 0 -221.0822 221.0822 0.094 0.0949 0.122 0.129 35 151.1 0 -221.0822 221.0822 0.0902 0.094 0.1155 0.129 36 157.5 0 -221.0822 221.0822 0.0813 0.0902 0.1174 0.129 37 167.5 0 -221.0822 221.0822 0.0688 0.0813 0.1001 0.129 38 172.3 0 -221.0822 221.0822 0.0633 0.0688 0.0958 0.129 39 173.5 0 -221.0822 221.0822 0.062 0.0633 0.0905 0.129 40 187.5 0 -221.0822 221.0822 0.0482 0.062 0.0937 0.129 41 205.5 0 -221.0822 221.0822 0.0342 0.0482 0.105 0.129 42 195.1 0 -221.0822 221.0822 0.0418 0.0342 0.1091 0.129 43 204.5 0 -221.0822 221.0822 0.0349 0.0418 0.1076 0.129 44 204.5 0 -221.0822 221.0822 0.0349 0.0349 0.0984 0.129 45 201.7 0 -221.0822 221.0822 0.0369 0.0349 0.0949 0.129 46 207 0 -221.0822 221.0822 0.0332 0.0369 0.094 0.129 47 206.6 0 -221.0822 221.0822 0.0335 0.0332 0.0902 0.129 48 210.6 0 -221.0822 221.0822 0.0309 0.0335 0.0813 0.129 49 211.1 0 -221.0822 221.0822 0.0306 0.0309 0.0688 0.129 50 215 0 -221.0822 221.0822 0.0283 0.0306 0.0633 0.129 51 223.9 0 -221.0822 221.0822 0.0236 0.0283 0.062 0.129 52 238.2 0 -221.0822 221.0822 0.0174 0.0236 0.0482 0.129 53 238.9 0 -221.0822 221.0822 0.0171 0.0174 0.0342 0.129 54 229.6 0 -221.0822 221.0822 0.0209 0.0171 0.0418 0.129 55 232.2 0 -221.0822 221.0822 0.0198 0.0209 0.0349 0.129 56 222.1 0 -221.0822 221.0822 0.0245 0.0198 0.0349 0.129 57 221.6 0 -221.0822 221.0822 0.0247 0.0245 0.0369 0.129 58 227.3 0 -221.0822 221.0822 0.0219 0.0247 0.0332 0.129 59 221 0 -221.0822 221.0822 0.025 0.0219 0.0335 0.129 60 213.6 0 -221.0822 221.0822 0.0291 0.025 0.0309 0.129 61 243.4 0 -221.0822 221.0822 0.0155 0.0291 0.0306 0.129 62 253.8 0 -221.0822 221.0822 0.0122 0.0155 0.0283 0.129 63 265.3 0 -221.0822 221.0822 0.0093 0.0122 0.0236 0.129 64 268.2 0 -221.0822 221.0822 0.0087 0.0093 0.0174 0.129 65 268.5 0 -221.0822 221.0822 0.0086 0.0087 0.0171 0.129 66 266.9 0 -221.0822 221.0822 0.009 0.0086 0.0209 0.129 67 268.4 0 -221.0822 221.0822 0.0087 0.009 0.0198 0.129 68 250.8 0 -221.0822 221.0822 0.0131 0.0087 0.0245 0.129 69 231.2 0 -221.0822 221.0822 0.0202 0.0131 0.0247 0.129 70 192 0 -221.0822 221.0822 0.0444 0.0202 0.0219 0.129 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 21 Inf Inf Inf 16486.56 329.7312 18.1585 22 Inf Inf Inf 17265.96 345.3192 18.5828 23 Inf Inf Inf 18252.01 365.0402 19.106 24 Inf Inf Inf 17956 359.12 18.9505 25 Inf Inf Inf 20880.25 417.605 20.4354 26 Inf Inf Inf 21697.29 433.9458 20.8314 27 Inf Inf Inf 22770.81 455.4162 21.3405 28 Inf Inf Inf 22111.69 442.2338 21.0294 29 Inf Inf Inf 19993.96 399.8792 19.997 30 Inf Inf Inf 19293.21 385.8642 19.6434 31 Inf Inf Inf 19544.04 390.8808 19.7707 32 Inf Inf Inf 21199.36 423.9872 20.5909 33 Inf Inf Inf 21874.41 437.4882 20.9162 34 Inf Inf Inf 22052.25 441.045 21.0011 35 Inf Inf Inf 22831.21 456.6242 21.3688 36 Inf Inf Inf 24806.25 496.125 22.2739 37 Inf Inf Inf 28056.25 561.125 23.6881 38 Inf Inf Inf 29687.29 593.7458 24.3669 39 Inf Inf Inf 30102.25 602.045 24.5366 40 Inf Inf Inf 35156.25 703.125 26.5165 41 Inf Inf Inf 42230.25 844.605 29.0621 42 Inf Inf Inf 38064.01 761.2802 27.5913 43 Inf Inf Inf 41820.25 836.405 28.9207 44 Inf Inf Inf 41820.25 836.405 28.9207 45 Inf Inf Inf 40682.89 813.6578 28.5247 46 Inf Inf Inf 42849 856.98 29.2742 47 Inf Inf Inf 42683.56 853.6712 29.2177 48 Inf Inf Inf 44352.36 887.0472 29.7833 49 Inf Inf Inf 44563.21 891.2642 29.854 50 Inf Inf Inf 46225 924.5 30.4056 51 Inf Inf Inf 50131.21 1002.6242 31.6642 52 Inf Inf Inf 56739.24 1134.7848 33.6866 53 Inf Inf Inf 57073.21 1141.4642 33.7856 54 Inf Inf Inf 52716.16 1054.3232 32.4703 55 Inf Inf Inf 53916.84 1078.3368 32.838 56 Inf Inf Inf 49328.41 986.5682 31.4097 57 Inf Inf Inf 49106.56 982.1312 31.339 58 Inf Inf Inf 51665.29 1033.3058 32.1451 59 Inf Inf Inf 48841 976.82 31.2541 60 Inf Inf Inf 45624.96 912.4992 30.2076 61 Inf Inf Inf 59243.56 1184.8712 34.422 62 Inf Inf Inf 64414.44 1288.2888 35.8927 63 Inf Inf Inf 70384.09 1407.6818 37.5191 64 Inf Inf Inf 71931.24 1438.6248 37.9292 65 Inf Inf Inf 72092.25 1441.845 37.9716 66 Inf Inf Inf 71235.61 1424.7122 37.7454 67 Inf Inf Inf 72038.56 1440.7712 37.9575 68 Inf Inf Inf 62900.64 1258.0128 35.4685 69 Inf Inf Inf 53453.44 1069.0688 32.6966 70 Inf Inf Inf 36864 737.28 27.1529

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229258781zel8r9pvccf1yiq/1pl651229258748.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229258781zel8r9pvccf1yiq/1pl651229258748.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229258781zel8r9pvccf1yiq/2hdjv1229258748.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229258781zel8r9pvccf1yiq/2hdjv1229258748.ps (open in new window)

Parameters (Session):

par1 = 50 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 50 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; 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,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