*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: Fri, 18 Dec 2009 14:28:30 -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/18/t12611717673tqxhodtovjo8o3.htm/, Retrieved Fri, 18 Dec 2009 22:29:29 +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/18/t12611717673tqxhodtovjo8o3.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:

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359640 364080 364080 359640 359640 359640 359640 359640 364080 368520 372960 377400 406780 402050 392590 368940 368940 378400 406780 420970 420970 406780 392590 392590 394250 399000 403750 399000 408500 403750 403750 399000 403750 403750 403750 403750 405450 405450 405450 405450 410220 400680 386370 381600 381600 381600 381600 376830 381420 381420 386310 396090 391200 371640 356970 342300 332520 342300 347190 352080 357130 347070 337010 337010 331980

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 '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[37]) 25 394250 - - - - - - - 26 399000 - - - - - - - 27 403750 - - - - - - - 28 399000 - - - - - - - 29 408500 - - - - - - - 30 403750 - - - - - - - 31 403750 - - - - - - - 32 399000 - - - - - - - 33 403750 - - - - - - - 34 403750 - - - - - - - 35 403750 - - - - - - - 36 403750 - - - - - - - 37 405450 - - - - - - - 38 405450 405950.2501 392171.7618 419728.7384 0.4716 0.5284 0.8386 0.5284 39 405450 405917.5792 383900.9414 427934.217 0.4834 0.5166 0.5765 0.5166 40 405450 404890.3454 376346.7675 433433.9234 0.4847 0.4847 0.6571 0.4847 41 410220 404319.501 374026.0821 434612.9199 0.3513 0.4708 0.3934 0.4708 42 400680 404132.7509 373247.6986 435017.8032 0.4133 0.3496 0.5097 0.4667 43 386370 404615.6888 373476.0959 435755.2818 0.1254 0.5978 0.5217 0.4791 44 381600 405058.9435 373008.5049 437109.3822 0.0757 0.8735 0.6445 0.4905 45 381600 405307.3295 371485.5848 439129.0743 0.0847 0.9153 0.536 0.4967 46 381600 405133.4634 368905.7529 441361.1739 0.1015 0.8985 0.5298 0.4932 47 381600 404851.4703 366759.5168 442943.4239 0.1158 0.8842 0.5226 0.4877 48 376830 404628.0525 365307.0789 443949.0261 0.0829 0.8745 0.5175 0.4837 49 381420 404647.1719 364532.9964 444761.3475 0.1282 0.913 0.4844 0.4844 50 381420 404797.5816 363894.6678 445700.4954 0.1313 0.8687 0.4875 0.4875 51 386310 404963.4051 363073.9135 446852.8967 0.1914 0.8647 0.4909 0.4909 52 396090 405006.7654 361862.3108 448151.2201 0.3427 0.8022 0.492 0.492 53 391200 404943.8305 360489.0017 449398.6592 0.2723 0.6519 0.408 0.4911 54 371640 404837.0541 359203.1328 450470.9754 0.077 0.721 0.5709 0.4895 55 356970 404780.1434 358167.8638 451392.4231 0.0222 0.9183 0.7806 0.4888 56 342300 404793.8231 357312.605 452275.0412 0.0049 0.9758 0.8308 0.4892 57 332520 404853.6975 356508.2195 453199.1755 0.0017 0.9944 0.8271 0.4904 58 342300 404902.5172 355625.0325 454180.0019 0.0064 0.998 0.823 0.4913 59 347190 404911.4986 354646.0792 455176.9179 0.0122 0.9927 0.8183 0.4916 60 352080 404883.3918 353630.7074 456136.0763 0.0217 0.9863 0.8583 0.4914 61 357130 404849.038 352665.0695 457033.0064 0.0365 0.9763 0.8106 0.491 62 347070 404833.131 351781.4723 457884.7896 0.0164 0.961 0.8065 0.4909 63 337010 404842.503 350960.6973 458724.3086 0.0068 0.9822 0.7499 0.4912 64 337010 404863.2979 350153.8804 459572.7155 0.0075 0.9925 0.6234 0.4916 65 331980 404878.3309 349327.3695 460429.2922 0.0051 0.9917 0.6853 0.492 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 38 0.0173 -0.0012 0 250250.1439 0 0 39 0.0277 -0.0012 0.0012 218630.33 234440.2369 484.1903 40 0.036 0.0014 0.0013 313213.2417 260697.9052 510.5858 41 0.0382 0.0146 0.0046 34815888.8899 8899495.6514 2983.2022 42 0.039 -0.0085 0.0054 11921488.7248 9503894.2661 3082.8387 43 0.0393 -0.0451 0.012 332905161.4036 63404105.4556 7962.6695 44 0.0404 -0.0579 0.0186 550322030.6137 132963809.0497 11530.9934 45 0.0426 -0.0585 0.0236 562037474.2529 186598017.2001 13660.0885 46 0.0456 -0.0581 0.0274 553823899.2911 227400892.988 15079.8174 47 0.048 -0.0574 0.0304 540630872.5748 258723890.9466 16084.8964 48 0.0496 -0.0687 0.0339 772731722.0958 305451875.5966 17477.1816 49 0.0506 -0.0574 0.0358 539501516.273 324956012.3196 18026.5363 50 0.0516 -0.0578 0.0375 546511319.3727 341998728.2468 18493.2076 51 0.0528 -0.0461 0.0381 347949521.542 342423784.9107 18504.6963 52 0.0544 -0.022 0.0371 79508705.8695 324896112.9746 18024.8748 53 0.056 -0.0339 0.0369 188892875.5972 316395910.6385 17787.5212 54 0.0575 -0.082 0.0395 1102044399.8308 362610527.6498 19042.3351 55 0.0588 -0.1181 0.0439 2285809814.3374 469454932.4658 21666.9087 56 0.0598 -0.1544 0.0497 3905477926.0211 650298247.9161 25500.946 57 0.0609 -0.1787 0.0561 5232163795.3625 879391525.2884 29654.5363 58 0.0621 -0.1546 0.0608 3919075160.7647 1024138365.073 32002.1619 59 0.0633 -0.1426 0.0646 3331771396.0422 1129030775.5716 33601.0532 60 0.0646 -0.1304 0.0674 2788198189.3536 1201168489.2143 34657.8777 61 0.0658 -0.1179 0.0695 2277106584.1537 1245999243.1701 35298.7145 62 0.0669 -0.1427 0.0724 3336579297.2261 1329622445.3323 36463.9883 63 0.0679 -0.1676 0.0761 4601248459.6088 1455454215.1122 38150.4157 64 0.0689 -0.1676 0.0795 4604070041.0757 1572069616.0738 39649.3331 65 0.07 -0.18 0.0831 5314166640.8791 1705715938.3883 41300.314

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611717673tqxhodtovjo8o3/1mgf21261171707.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/18/t12611717673tqxhodtovjo8o3/1mgf21261171707.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/18/t12611717673tqxhodtovjo8o3/2m93a1261171707.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/18/t12611717673tqxhodtovjo8o3/2m93a1261171707.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; 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 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

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