*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 09:37:03 -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/t1260549458gc8g8r2076zx212.htm/, Retrieved Fri, 11 Dec 2009 17:37:40 +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/t1260549458gc8g8r2076zx212.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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17 14 15 16 16 15 13 12 13 13 12 10 14 14 15 16 16 15 15 13 15 15 15 13 16 16 14 16 15 14 15 15 14 13 12 13 12 9 10 8 11 8 8 8 4 6 8 10 5 6 5 9 8 6 9 11 11 8 11 11 13

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[33]) 21 15 - - - - - - - 22 15 - - - - - - - 23 15 - - - - - - - 24 13 - - - - - - - 25 16 - - - - - - - 26 16 - - - - - - - 27 14 - - - - - - - 28 16 - - - - - - - 29 15 - - - - - - - 30 14 - - - - - - - 31 15 - - - - - - - 32 15 - - - - - - - 33 14 - - - - - - - 34 13 14.8869 12.4829 17.2909 0.062 0.7652 0.4633 0.7652 35 12 14.8694 12.0906 17.6482 0.0215 0.9063 0.4633 0.7301 36 13 13.965 11.0486 16.8814 0.2583 0.9067 0.7417 0.4906 37 12 14.7885 11.7873 17.7896 0.0343 0.8786 0.2144 0.6967 38 9 14.9268 11.907 17.9466 1e-04 0.9713 0.243 0.7263 39 10 13.9702 10.9398 17.0007 0.0051 0.9993 0.4923 0.4923 40 8 14.702 11.654 17.75 0 0.9988 0.2019 0.6742 41 11 14.986 11.9411 18.0309 0.0051 1 0.4964 0.7372 42 8 13.9938 10.948 17.0396 1e-04 0.973 0.4984 0.4984 43 8 14.6161 11.561 17.6711 0 1 0.4027 0.6537 44 8 15.0378 11.9882 18.0874 0 1 0.5097 0.7476 45 4 14.0303 10.9815 17.0791 0 0.9999 0.5078 0.5078 46 6 14.5298 11.4732 17.5863 0 1 0.8367 0.633 47 8 15.0795 12.0283 18.1308 0 1 0.976 0.756 48 10 14.078 11.0284 17.1276 0.0044 1 0.7558 0.52 49 5 14.4442 11.3875 17.501 0 0.9978 0.9415 0.6121 50 6 15.1099 12.0577 18.1622 0 1 1 0.762 51 5 14.1355 11.0856 17.1855 0 1 0.9961 0.5347 52 9 14.3612 11.3045 17.4179 3e-04 1 1 0.5916 53 8 15.1283 12.0751 18.1815 0 1 0.996 0.7656 54 6 14.2017 11.1514 17.2519 0 1 1 0.5516 55 9 14.2824 11.226 17.3389 4e-04 1 1 0.5719 56 11 15.1343 12.0801 18.1885 0.004 1 1 0.7667 57 11 14.2749 11.2244 17.3255 0.0177 0.9823 1 0.5701 58 8 14.2095 11.1534 17.2656 0 0.9802 1 0.5534 59 11 15.1278 12.0726 18.1829 0.004 1 1 0.7653 60 11 14.3537 11.3028 17.4046 0.0156 0.9844 0.9974 0.5899 61 13 14.144 11.0882 17.1998 0.2316 0.9781 1 0.5368 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 34 0.0824 -0.1267 0 3.5603 0 0 35 0.0953 -0.193 0.1599 8.2336 5.897 2.4284 36 0.1065 -0.0691 0.1296 0.9312 4.2417 2.0595 37 0.1035 -0.1886 0.1443 7.7756 5.1252 2.2639 38 0.1032 -0.3971 0.1949 35.127 11.1255 3.3355 39 0.1107 -0.2842 0.2098 15.7629 11.8984 3.4494 40 0.1058 -0.4559 0.2449 44.9165 16.6153 4.0762 41 0.1037 -0.266 0.2476 15.888 16.5244 4.065 42 0.111 -0.4283 0.2676 35.9256 18.6801 4.322 43 0.1066 -0.4527 0.2861 43.7724 21.1893 4.6032 44 0.1035 -0.468 0.3027 49.5309 23.7658 4.875 45 0.1109 -0.7149 0.337 100.6074 30.1693 5.4927 46 0.1073 -0.5871 0.3563 72.7567 33.4452 5.7832 47 0.1032 -0.4695 0.3643 50.12 34.6363 5.8853 48 0.1105 -0.2897 0.3594 16.6301 33.4359 5.7824 49 0.108 -0.6538 0.3778 89.1938 36.9208 6.0762 50 0.1031 -0.6029 0.391 82.991 39.6308 6.2953 51 0.1101 -0.6463 0.4052 83.4582 42.0656 6.4858 52 0.1086 -0.3733 0.4035 28.7428 41.3644 6.4315 53 0.103 -0.4712 0.4069 50.8127 41.8368 6.4681 54 0.1096 -0.5775 0.415 67.2674 43.0478 6.5611 55 0.1092 -0.3699 0.413 27.904 42.3595 6.5084 56 0.103 -0.2732 0.4069 17.0922 41.2609 6.4235 57 0.109 -0.2294 0.3995 10.7252 39.9886 6.3237 58 0.1097 -0.437 0.401 38.5578 39.9313 6.3191 59 0.103 -0.2729 0.3961 17.0384 39.0508 6.2491 60 0.1084 -0.2336 0.3901 11.2476 38.0211 6.1661 61 0.1102 -0.0809 0.379 1.3087 36.7099 6.0589

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260549458gc8g8r2076zx212/1ef4d1260549421.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260549458gc8g8r2076zx212/1ef4d1260549421.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260549458gc8g8r2076zx212/2pipe1260549421.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260549458gc8g8r2076zx212/2pipe1260549421.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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