forecasting

*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, 10 Dec 2009 08:24:18 -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/10/t1260458745clkbdz1peg3q7v0.htm/, Retrieved Thu, 10 Dec 2009 16:25:48 +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/10/t1260458745clkbdz1peg3q7v0.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:

sdws10

Dataseries X:

» Textbox « » Textfile « » CSV «

593530.00 610943.00 612613.00 611324.00 594167.00 595454.00 590865.00 589379.00 584428.00 573100.00 567456.00 569028.00 620735.00 628884.00 628232.00 612117.00 595404.00 597141.00 593408.00 590072.00 579799.00 574205.00 572775.00 572942.00 619567.00 625809.00 619916.00 587625.00 565742.00 557274.00 560576.00 548854.00 531673.00 525919.00 511038.00 498662.00 555362.00 564591.00 541657.00 527070.00 509846.00 514258.00 516922.00 507561.00 492622.00 490243.00 469357.00 477580.00 528379.00 533590.00 517945.00 506174.00 501866.00 516141.00 528222.00 532638.00 536322.00 536535.00 523597.00 536214.00 586570.00 596594.00 580523.00

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[35]) 23 572775 - - - - - - - 24 572942 - - - - - - - 25 619567 - - - - - - - 26 625809 - - - - - - - 27 619916 - - - - - - - 28 587625 - - - - - - - 29 565742 - - - - - - - 30 557274 - - - - - - - 31 560576 - - - - - - - 32 548854 - - - - - - - 33 531673 - - - - - - - 34 525919 - - - - - - - 35 511038 - - - - - - - 36 498662 512130.2152 501214.7536 523045.6769 0.0078 0.5777 0 0.5777 37 555362 549465.7592 533408.0408 565523.4777 0.2359 1 0 1 38 564591 555090.6579 531776.2661 578405.0496 0.2122 0.4909 0 0.9999 39 541657 546133.7926 519239.7878 573027.7973 0.3721 0.0893 0 0.9947 40 527070 508801.9867 478001.2313 539602.7421 0.1225 0.0183 0 0.4434 41 509846 484641.0185 449763.91 519518.127 0.0783 0.0086 0 0.069 42 514258 472528.1681 434347.4486 510708.8876 0.0161 0.0277 0 0.024 43 516922 472042.061 430408.3015 513675.8205 0.0173 0.0234 0 0.0332 44 507561 457282.9456 412278.8699 502287.0213 0.0143 0.0047 0 0.0096 45 492622 436513.2664 388350.9362 484675.5966 0.0112 0.0019 1e-04 0.0012 46 490243 427281.9954 375929.8554 478634.1353 0.0081 0.0063 1e-04 7e-04 47 469357 409088.4787 354619.1752 463557.7822 0.0151 0.0017 1e-04 1e-04 48 477580 406683.1556 344594.4641 468771.847 0.0126 0.0239 0.0018 5e-04 49 528379 440600.3053 371190.1245 510010.4861 0.0066 0.1482 6e-04 0.0233 50 533590 442829.1652 364384.1708 521274.1595 0.0117 0.0163 0.0012 0.0442 51 517945 430423.6774 345188.6284 515658.7264 0.0221 0.0088 0.0053 0.0319 52 506174 389678.7213 297415.1482 481942.2943 0.0067 0.0032 0.0018 0.005 53 501866 362101.936 262687.1985 461516.6735 0.0029 0.0023 0.0018 0.0017 54 516141 346561.4801 240655.7555 452467.2048 8e-04 0.002 0.001 0.0012 55 528222 342661.0971 230169.1137 455153.0806 6e-04 0.0013 0.0012 0.0017 56 532638 324484.5044 205507.416 443461.5927 3e-04 4e-04 0.0013 0.0011 57 536322 300296.2099 175049.5262 425542.8935 1e-04 1e-04 0.0013 5e-04 58 536535 287651.1047 156133.2612 419168.9482 1e-04 1e-04 0.0013 4e-04 59 523597 266042.6961 128343.5945 403741.7977 1e-04 1e-04 0.0019 2e-04 60 536214 260223.5134 112602.4113 407844.6155 1e-04 2e-04 0.002 4e-04 61 586570 290728.8023 133304.0188 448153.5857 1e-04 0.0011 0.0015 0.003 62 596594 289546.0375 120848.208 458243.8671 2e-04 3e-04 0.0023 0.005 63 580523 273730.1702 95468.4555 451991.8849 4e-04 2e-04 0.0036 0.0045 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 36 0.0109 -0.0263 0 181392821.2451 0 0 37 0.0149 0.0107 0.0185 34765655.2056 108079238.2254 10396.1165 38 0.0214 0.0171 0.018 90256500.4155 102138325.6221 10106.3508 39 0.0251 -0.0082 0.0156 20041671.6042 81614162.1176 9034.0557 40 0.0309 0.0359 0.0196 333720310.1956 132035391.7332 11490.6654 41 0.0367 0.052 0.025 635291091.3917 215911341.6763 14693.9219 42 0.0412 0.0883 0.0341 1741378870.9551 433835274.4304 20828.7127 43 0.045 0.0951 0.0417 2014208924.8599 631381980.7341 25127.3154 44 0.0502 0.1099 0.0493 2527882750.9526 842104288.5361 29019.0332 45 0.0563 0.1285 0.0572 3148189987.7464 1072712858.4572 32752.2955 46 0.0613 0.1474 0.0654 3964088104.7328 1335565153.5731 36545.3848 47 0.0679 0.1473 0.0722 3632294657.7545 1526959278.9216 39076.3263 48 0.0779 0.1743 0.0801 5026362549.6948 1796144145.9041 42380.9408 49 0.0804 0.1992 0.0886 7705099237.6812 2218212366.7454 47097.9019 50 0.0904 0.205 0.0964 8237529141.9434 2619500151.7586 51181.0527 51 0.101 0.2033 0.103 7659981910.258 2934530261.6648 54171.3048 52 0.1208 0.299 0.1146 13571149966.0387 3560213773.6868 59667.527 53 0.1401 0.386 0.1296 19533993585.6429 4447645985.4621 66690.6739 54 0.1559 0.4893 0.1486 28757213553.3862 5727096910.0897 75677.5853 55 0.1675 0.5415 0.1682 34432848669.88 7162384498.0792 84630.872 56 0.1871 0.6415 0.1908 43327877747.9306 8884550843.3102 94257.8954 57 0.2128 0.786 0.2178 55708173610.7393 11012897332.7388 104942.3524 58 0.2333 0.8652 0.246 61943193337.03 13227258028.5776 115009.8171 59 0.2641 0.9681 0.2761 66334219461.482 15440048088.2819 124257.99 60 0.2894 1.0606 0.3074 76170748703.5343 17869276112.892 133676.0117 61 0.2763 1.0176 0.3347 87522014269.4602 20548227580.4523 143346.5297 62 0.2973 1.0604 0.3616 94278451249.1372 23278976605.2184 152574.4953 63 0.3323 1.1208 0.3887 94121840418.4399 25809078884.2621 160652.0429

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260458745clkbdz1peg3q7v0/1109x1260458654.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260458745clkbdz1peg3q7v0/1109x1260458654.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260458745clkbdz1peg3q7v0/2zddh1260458654.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260458745clkbdz1peg3q7v0/2zddh1260458654.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 2 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; 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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