*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: Mon, 21 Dec 2009 06:53:33 -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/21/t12614036664q7271c7brochpi.htm/, Retrieved Mon, 21 Dec 2009 14:54:28 +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/21/t12614036664q7271c7brochpi.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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611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581

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[32]) 20 573 - - - - - - - 21 573 - - - - - - - 22 620 - - - - - - - 23 626 - - - - - - - 24 620 - - - - - - - 25 588 - - - - - - - 26 566 - - - - - - - 27 557 - - - - - - - 28 561 - - - - - - - 29 549 - - - - - - - 30 532 - - - - - - - 31 526 - - - - - - - 32 511 - - - - - - - 33 499 512.9641 501.8939 524.0344 0.0067 0.636 0 0.636 34 555 550.6653 533.8861 567.4446 0.3063 1 0 1 35 565 557.2236 535.0119 579.4353 0.2463 0.5778 0 1 36 542 545.5172 516.9862 574.0481 0.4045 0.0904 0 0.9911 37 527 511.4433 477.8272 545.0595 0.1822 0.0374 0 0.5103 38 510 487.4066 447.3384 527.4748 0.1345 0.0264 1e-04 0.1242 39 514 474.1903 428.9498 519.4309 0.0423 0.0604 2e-04 0.0554 40 517 478.545 427.1067 529.9833 0.0714 0.0884 8e-04 0.1081 41 508 461.6379 404.8085 518.4672 0.0549 0.0281 0.0013 0.0443 42 493 445.6526 383.0198 508.2854 0.0692 0.0255 0.0034 0.0204 43 490 435.5361 367.3345 503.7376 0.0588 0.0493 0.0047 0.0151 44 469 420.861 347.2153 494.5067 0.1001 0.0329 0.0082 0.0082 45 478 420.3469 336.3682 504.3255 0.0892 0.1281 0.0332 0.0172 46 528 457.1476 363.3554 550.9398 0.0694 0.3315 0.0204 0.1302 47 534 462.8842 358.634 567.1344 0.0906 0.1104 0.0274 0.1828 48 518 449.2959 334.3357 564.256 0.1207 0.0743 0.057 0.1464 49 506 415.4631 290.155 540.7711 0.0784 0.0544 0.0405 0.0675 50 502 389.2357 252.8989 525.5726 0.0525 0.0466 0.0413 0.04 51 516 376.5328 229.9409 523.1246 0.0311 0.0467 0.033 0.0361 52 528 379.0641 221.5534 536.5749 0.0319 0.0442 0.043 0.0503 53 533 362.3342 194.6121 530.0563 0.0231 0.0264 0.0444 0.0412 54 536 345.273 166.9841 523.5619 0.018 0.0195 0.0522 0.0342 55 537 334.7642 146.3153 523.2131 0.0177 0.0182 0.0532 0.0334 56 524 319.7611 121.1738 518.3485 0.0219 0.016 0.0704 0.0295 57 536 318.4057 106.1259 530.6855 0.0223 0.0288 0.0703 0.0377 58 587 355.3506 129.5036 581.1976 0.0222 0.0585 0.067 0.0884 59 597 360.1084 120.2591 599.9578 0.0264 0.0319 0.0777 0.1088 60 581 346.7756 92.6072 600.944 0.0354 0.0268 0.0934 0.1027 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.011 -0.0272 0 194.9975 0 0 34 0.0155 0.0079 0.0175 18.7894 106.8935 10.3389 35 0.0203 0.014 0.0163 60.472 91.4196 9.5614 36 0.0267 -0.0064 0.0139 12.3705 71.6574 8.4651 37 0.0335 0.0304 0.0172 242.0099 105.7279 10.2824 38 0.0419 0.0464 0.022 510.4627 173.1837 13.1599 39 0.0487 0.084 0.0309 1584.8095 374.8445 19.3609 40 0.0548 0.0804 0.0371 1478.7859 512.8372 22.6459 41 0.0628 0.1004 0.0441 2149.4473 694.6827 26.3568 42 0.0717 0.1062 0.0503 2241.7779 849.3922 29.1443 43 0.0799 0.1251 0.0571 2966.3188 1041.8401 32.2775 44 0.0893 0.1144 0.0619 2317.3635 1148.1337 33.8841 45 0.1019 0.1372 0.0677 3323.8834 1315.4991 36.2698 46 0.1047 0.155 0.0739 5020.062 1580.1107 39.7506 47 0.1149 0.1536 0.0792 5057.457 1811.9338 42.5668 48 0.1305 0.1529 0.0838 4720.26 1993.7042 44.6509 49 0.1539 0.2179 0.0917 8196.9358 2358.6002 48.5654 50 0.1787 0.2897 0.1027 12715.7816 2933.9991 54.1664 51 0.1986 0.3704 0.1168 19451.1116 3803.3209 61.6711 52 0.212 0.3929 0.1306 22181.896 4722.2496 68.7186 53 0.2362 0.471 0.1468 29126.8128 5884.3717 76.7097 54 0.2635 0.5524 0.1653 36376.7921 7270.3908 85.2666 55 0.2872 0.6041 0.1843 40899.3167 8732.518 93.4479 56 0.3169 0.6387 0.2033 41713.5143 10106.7262 100.5322 57 0.3402 0.6834 0.2225 47347.2849 11596.3485 107.6863 58 0.3243 0.6519 0.239 53661.4315 13214.2363 114.9532 59 0.3398 0.6578 0.2545 56117.615 14803.2504 121.6686 60 0.374 0.6754 0.2695 54861.0749 16233.8869 127.4123

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614036664q7271c7brochpi/1jm241261403610.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t12614036664q7271c7brochpi/1jm241261403610.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t12614036664q7271c7brochpi/2nsvf1261403610.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t12614036664q7271c7brochpi/2nsvf1261403610.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

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