ARIMAKoffie2

*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, 24 Dec 2010 12:35:59 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t1293194064zs31snzwntgrijs.htm/, Retrieved Fri, 24 Dec 2010 13:34:25 +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/2010/Dec/24/t1293194064zs31snzwntgrijs.htm/}, year = {2010}, } @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 = {2010}, 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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7,14 7,24 7,33 7,61 7,66 7,69 7,7 7,68 7,71 7,71 7,72 7,68 7,72 7,74 7,76 7,9 7,97 7,96 7,95 7,97 7,93 7,99 7,96 7,92 7,97 7,98 8 8,04 8,17 8,29 8,26 8,3 8,32 8,28 8,27 8,32 8,31 8,34 8,32 8,36 8,33 8,35 8,34 8,37 8,31 8,33 8,34 8,25 8,27 8,31 8,25 8,3 8,3 8,35 8,78 8,9

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 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk 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[28]) 16 7.9 - - - - - - - 17 7.97 - - - - - - - 18 7.96 - - - - - - - 19 7.95 - - - - - - - 20 7.97 - - - - - - - 21 7.93 - - - - - - - 22 7.99 - - - - - - - 23 7.96 - - - - - - - 24 7.92 - - - - - - - 25 7.97 - - - - - - - 26 7.98 - - - - - - - 27 8 - - - - - - - 28 8.04 - - - - - - - 29 8.17 8.1192 8.0434 8.1949 0.0941 0.9798 0.9999 0.9798 30 8.29 8.0218 7.9132 8.1304 0 0.0038 0.8676 0.3713 31 8.26 7.9436 7.7669 8.1203 2e-04 1e-04 0.4716 0.1424 32 8.3 7.9465 7.6675 8.2254 0.0065 0.0138 0.4343 0.2555 33 8.32 7.8417 7.485 8.1983 0.0043 0.0059 0.3136 0.1378 34 8.28 7.8856 7.43 8.3412 0.0449 0.0308 0.3267 0.2533 35 8.27 7.8216 7.2767 8.3666 0.0534 0.0496 0.3093 0.2161 36 8.32 7.7575 7.1221 8.393 0.0414 0.057 0.3081 0.1918 37 8.31 7.7918 7.0658 8.5178 0.0809 0.077 0.3153 0.2514 38 8.34 7.7808 6.9688 8.5927 0.0885 0.1007 0.3153 0.2657 39 8.32 7.7897 6.8919 8.6876 0.1235 0.1148 0.3231 0.2924 40 8.36 7.8163 6.8362 8.7964 0.1385 0.1569 0.3273 0.3273 41 8.33 7.8856 6.794 8.9772 0.2124 0.1971 0.3048 0.3908 42 8.35 7.7802 6.5826 8.9777 0.1755 0.1841 0.202 0.3353 43 8.34 7.694 6.3719 9.0162 0.1691 0.1654 0.2007 0.304 44 8.37 7.6913 6.2206 9.1621 0.1829 0.1937 0.2087 0.3211 45 8.31 7.5811 5.9708 9.1913 0.1875 0.1685 0.1842 0.2882 46 8.33 7.6207 5.8561 9.3853 0.2154 0.222 0.232 0.3207 47 8.34 7.5531 5.6392 9.467 0.2102 0.2131 0.2314 0.309 48 8.25 7.4858 5.4219 9.5496 0.234 0.2086 0.2141 0.2993 49 8.27 7.5175 5.3043 9.7308 0.2526 0.2583 0.2414 0.3218 50 8.31 7.5041 5.1459 9.8624 0.2515 0.2622 0.2436 0.328 51 8.25 7.5113 5.0093 10.0132 0.2814 0.2657 0.2632 0.3394 52 8.3 7.5362 4.8947 10.1778 0.2855 0.2982 0.2705 0.3543 53 8.3 7.6041 4.8015 10.4067 0.3132 0.3132 0.3058 0.3802 54 8.35 7.4976 4.5385 10.4567 0.2862 0.2975 0.2862 0.3597 55 8.78 7.4105 4.281 10.5399 0.1955 0.2781 0.2802 0.3467 56 8.9 7.407 4.0888 10.7252 0.1889 0.2087 0.2847 0.3542 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 29 0.0048 0.0063 0 0.0026 0 0 30 0.0069 0.0334 0.0198 0.0719 0.0373 0.193 31 0.0113 0.0398 0.0265 0.1001 0.0582 0.2413 32 0.0179 0.0445 0.031 0.125 0.0749 0.2737 33 0.0232 0.061 0.037 0.2288 0.1057 0.3251 34 0.0295 0.05 0.0392 0.1555 0.114 0.3376 35 0.0355 0.0573 0.0418 0.201 0.1264 0.3556 36 0.0418 0.0725 0.0456 0.3164 0.1502 0.3875 37 0.0475 0.0665 0.0479 0.2685 0.1633 0.4041 38 0.0532 0.0719 0.0503 0.3127 0.1783 0.4222 39 0.0588 0.0681 0.0519 0.2812 0.1876 0.4332 40 0.064 0.0696 0.0534 0.2956 0.1966 0.4434 41 0.0706 0.0564 0.0536 0.1975 0.1967 0.4435 42 0.0785 0.0732 0.055 0.3247 0.2058 0.4537 43 0.0877 0.084 0.057 0.4173 0.2199 0.469 44 0.0976 0.0882 0.0589 0.4606 0.235 0.4847 45 0.1084 0.0962 0.0611 0.5314 0.2524 0.5024 46 0.1181 0.0931 0.0629 0.5031 0.2663 0.5161 47 0.1293 0.1042 0.0651 0.6192 0.2849 0.5338 48 0.1407 0.1021 0.0669 0.5841 0.2999 0.5476 49 0.1502 0.1001 0.0685 0.5662 0.3125 0.5591 50 0.1603 0.1074 0.0703 0.6494 0.3279 0.5726 51 0.1699 0.0984 0.0715 0.5457 0.3373 0.5808 52 0.1788 0.1013 0.0727 0.5833 0.3476 0.5896 53 0.188 0.0915 0.0735 0.4843 0.353 0.5942 54 0.2014 0.1137 0.075 0.7266 0.3674 0.6061 55 0.2155 0.1848 0.0791 1.8757 0.4233 0.6506 56 0.2286 0.2016 0.0835 2.2292 0.4878 0.6984

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293194064zs31snzwntgrijs/1tnf81293194155.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293194064zs31snzwntgrijs/1tnf81293194155.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293194064zs31snzwntgrijs/2pxvz1293194155.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293194064zs31snzwntgrijs/2pxvz1293194155.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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