*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, 11 Dec 2009 08:13:47 -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/11/t1260544522k89wxdf2byzblh2.htm/, Retrieved Fri, 11 Dec 2009 16:15:25 +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/11/t1260544522k89wxdf2byzblh2.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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95.6 74.3 88.5 88 84.3 112.8 105.3 97.2 112.4 123.2 143.7 205.1 102.8 89.4 90.7 101.1 93.6 119.3 106.4 105.2 106.5 117.6 144.2 195.5 109.5 84.9 102.9 93.9 104.6 115.2 104.9 114.9 115.1 126.4 156.7 197.3 116.1 89.1 107.8 100.4 113.6 128.3 113.3 113.7 116.1 133.6 167.7 214.6 120.3 106 103.9 118 116.3 134.8 117.8 123.3 125.2 135.8 158.9 217.9

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[32]) 20 105.2 - - - - - - - 21 106.5 - - - - - - - 22 117.6 - - - - - - - 23 144.2 - - - - - - - 24 195.5 - - - - - - - 25 109.5 - - - - - - - 26 84.9 - - - - - - - 27 102.9 - - - - - - - 28 93.9 - - - - - - - 29 104.6 - - - - - - - 30 115.2 - - - - - - - 31 104.9 - - - - - - - 32 114.9 - - - - - - - 33 115.1 114.3724 65.7392 163.0056 0.4883 0.4915 0.6245 0.4915 34 126.4 110.4728 54.0386 166.907 0.2901 0.4362 0.4022 0.4389 35 156.7 110.9939 54.4604 167.5274 0.0565 0.2966 0.1248 0.4461 36 197.3 110.9195 54.2728 167.5661 0.0014 0.0566 0.0017 0.4452 37 116.1 110.1983 53.4113 166.9854 0.4193 0.0013 0.5096 0.4355 38 89.1 111.2124 54.4978 167.927 0.2224 0.4329 0.8184 0.4493 39 107.8 110.052 53.0829 167.0211 0.4691 0.7645 0.5972 0.4338 40 100.4 111.1974 54.2913 168.1034 0.355 0.5466 0.7243 0.4493 41 113.6 110.1507 53.0153 167.286 0.4529 0.631 0.5755 0.4353 42 128.3 111.0491 53.9769 168.1212 0.2768 0.4651 0.4433 0.4474 43 113.3 110.3167 53.0981 167.5354 0.4593 0.2689 0.5736 0.4376 44 113.7 110.8848 53.7204 168.0493 0.4616 0.467 0.4453 0.4453 45 116.1 110.4663 53.2271 167.7055 0.4235 0.4559 0.437 0.4397 46 133.6 110.7566 53.5519 167.9613 0.2169 0.4274 0.296 0.4436 47 167.7 110.5707 53.3356 167.8057 0.0252 0.2152 0.0571 0.4411 48 214.6 110.6757 53.4553 167.8962 2e-04 0.0254 0.0015 0.4425 49 120.3 110.6301 53.4023 167.858 0.3703 2e-04 0.4257 0.4419 50 106 110.6346 53.4079 167.8612 0.4369 0.3703 0.7696 0.4419 51 103.9 110.6564 53.4324 167.8805 0.4085 0.5634 0.539 0.4422 52 118 110.6198 53.3908 167.8487 0.4002 0.591 0.6368 0.4417 53 116.3 110.6628 53.4395 167.8861 0.4234 0.4008 0.4599 0.4423 54 134.8 110.6193 53.3899 167.8487 0.2038 0.4229 0.2724 0.4417 55 117.8 110.6596 53.4357 167.8835 0.4034 0.2042 0.464 0.4423 56 123.3 110.6246 53.3957 167.8535 0.3321 0.4029 0.4581 0.4418 57 125.2 110.6534 53.4285 167.8783 0.3092 0.3325 0.426 0.4422 58 135.8 110.6308 53.4026 167.859 0.1943 0.3089 0.2157 0.4419 59 158.9 110.6476 53.4218 167.8734 0.0492 0.1945 0.0253 0.4421 60 217.9 110.6358 53.4083 167.8633 1e-04 0.0492 2e-04 0.4419 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.2169 0.0064 0 0.5294 0 0 34 0.2606 0.1442 0.0753 253.676 127.1027 11.274 35 0.2599 0.4118 0.1874 2089.0475 781.0843 27.9479 36 0.2606 0.7788 0.3353 7461.5978 2451.2127 49.5097 37 0.2629 0.0536 0.2789 34.8299 1967.9361 44.3614 38 0.2602 -0.1988 0.2656 488.9587 1721.4399 41.4902 39 0.2641 -0.0205 0.2306 5.0714 1476.2444 38.4219 40 0.2611 -0.0971 0.2139 116.583 1306.2867 36.1426 41 0.2646 0.0313 0.1936 11.898 1162.4657 34.095 42 0.2622 0.1553 0.1898 297.5951 1075.9787 32.8021 43 0.2646 0.027 0.175 8.8999 978.9715 31.2885 44 0.263 0.0254 0.1625 7.9251 898.051 29.9675 45 0.2644 0.051 0.1539 31.7387 831.4116 28.8342 46 0.2635 0.2062 0.1577 521.8205 809.2979 28.4482 47 0.2641 0.5167 0.1816 3263.7611 972.9288 31.1918 48 0.2638 0.939 0.2289 10800.25 1587.1364 39.8389 49 0.2639 0.0874 0.2206 93.5061 1499.2758 38.7205 50 0.2639 -0.0419 0.2107 21.4792 1417.176 37.6454 51 0.2638 -0.0611 0.2028 45.6496 1344.9904 36.6741 52 0.264 0.0667 0.196 54.4677 1280.4642 35.7836 53 0.2638 0.0509 0.1891 31.7781 1221.003 34.9429 54 0.264 0.2186 0.1904 584.7077 1192.0805 34.5265 55 0.2638 0.0645 0.185 50.9857 1142.4677 33.8004 56 0.2639 0.1146 0.182 160.6665 1101.5593 33.1897 57 0.2639 0.1315 0.18 211.6038 1065.9611 32.6491 58 0.2639 0.2275 0.1818 633.4883 1049.3275 32.3933 59 0.2639 0.4361 0.1913 2328.2913 1096.6965 33.1164 60 0.2639 0.9695 0.219 11505.6077 1468.4434 38.3203

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260544522k89wxdf2byzblh2/1x64v1260544424.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260544522k89wxdf2byzblh2/1x64v1260544424.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260544522k89wxdf2byzblh2/2grv81260544424.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260544522k89wxdf2byzblh2/2grv81260544424.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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