*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 06:59:31 -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/t126140402373qn4cc01ju6uo3.htm/, Retrieved Mon, 21 Dec 2009 15:00:26 +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/t126140402373qn4cc01ju6uo3.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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120.9 119.6 125.9 116.1 107.5 116.7 112.5 113 126.4 114.1 112.5 112.4 113.1 116.3 111.7 118.8 116.5 125.1 113.1 119.6 114.4 114 117.8 117 120.9 115 117.3 119.4 114.9 125.8 117.6 117.6 114.9 121.9 117 106.4 110.5 113.6 114.2 125.4 124.6 120.2 120.8 111.4 124.1 120.2 125.5 116 117 105.7 102 106.4 96.9 107.6 98.8 101.1 105.7 104.6 103.2 101.6

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]) 20 119.6 - - - - - - - 21 114.4 - - - - - - - 22 114 - - - - - - - 23 117.8 - - - - - - - 24 117 - - - - - - - 25 120.9 - - - - - - - 26 115 - - - - - - - 27 117.3 - - - - - - - 28 119.4 - - - - - - - 29 114.9 - - - - - - - 30 125.8 - - - - - - - 31 117.6 - - - - - - - 32 117.6 - - - - - - - 33 114.9 118.6178 110.1747 127.0609 0.1941 0.5934 0.8362 0.5934 34 121.9 115.925 107.4703 124.3796 0.083 0.5939 0.6723 0.3489 35 117 116.715 108.1258 125.3042 0.4741 0.1184 0.4022 0.42 36 106.4 118.2934 109.7014 126.8855 0.0033 0.616 0.616 0.5628 37 110.5 116.0369 107.4259 124.6479 0.1038 0.9859 0.1342 0.361 38 113.6 116.7472 108.0584 125.436 0.2389 0.9206 0.6533 0.4237 39 114.2 118.1353 109.4443 126.8263 0.1874 0.8468 0.5747 0.548 40 125.4 116.155 107.4526 124.8573 0.0187 0.6701 0.2324 0.3724 41 124.6 116.7785 108.0143 125.5428 0.0401 0.0269 0.6628 0.4271 42 120.2 117.9969 109.2305 126.7634 0.3112 0.0699 0.0405 0.5354 43 120.8 116.2587 107.4864 125.0309 0.1551 0.1893 0.3822 0.3822 44 111.4 116.8061 107.9842 125.628 0.1149 0.1874 0.43 0.43 45 124.1 117.8755 109.0515 126.6996 0.0834 0.9248 0.7457 0.5244 46 120.2 116.3497 107.5238 125.1756 0.1963 0.0426 0.1089 0.3906 47 125.5 116.8302 107.9642 125.6962 0.0276 0.2281 0.485 0.4324 48 116 117.7689 108.9009 126.637 0.3479 0.0438 0.994 0.5149 49 117 116.4296 107.5624 125.2969 0.4498 0.5378 0.905 0.3979 50 105.7 116.8514 107.9517 125.7512 0.007 0.4869 0.763 0.4345 51 102 117.6754 108.7737 126.577 3e-04 0.9958 0.7779 0.5066 52 106.4 116.4998 107.6006 125.3989 0.0131 0.9993 0.025 0.4043 53 96.9 116.87 107.9444 125.7956 0 0.9893 0.0448 0.4363 54 107.6 117.5932 108.6658 126.5206 0.0141 1 0.2836 0.4994 55 98.8 116.5613 107.6376 125.4851 0 0.9755 0.1759 0.4098 56 101.1 116.8864 107.9409 125.8318 3e-04 1 0.8853 0.4379 57 105.7 117.5212 108.5741 126.4682 0.0048 0.9998 0.0748 0.4931 58 104.6 116.6154 107.6726 125.5582 0.0042 0.9916 0.216 0.4146 59 103.2 116.9007 107.9401 125.8613 0.0014 0.9964 0.03 0.4392 60 101.6 117.4579 108.4957 126.42 3e-04 0.9991 0.6251 0.4876 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0363 -0.0313 0 13.8222 0 0 34 0.0372 0.0515 0.0414 35.701 24.7616 4.9761 35 0.0375 0.0024 0.0284 0.0812 16.5348 4.0663 36 0.0371 -0.1005 0.0465 141.454 47.7646 6.9112 37 0.0379 -0.0477 0.0467 30.6574 44.3432 6.6591 38 0.038 -0.027 0.0434 9.9049 38.6034 6.2132 39 0.0375 -0.0333 0.042 15.4864 35.301 5.9415 40 0.0382 0.0796 0.0467 85.4705 41.5722 6.4477 41 0.0383 0.067 0.0489 61.1751 43.7503 6.6144 42 0.0379 0.0187 0.0459 4.8535 39.8606 6.3135 43 0.0385 0.0391 0.0453 20.6236 38.1118 6.1735 44 0.0385 -0.0463 0.0454 29.2256 37.3713 6.1132 45 0.0382 0.0528 0.0459 38.7443 37.4769 6.1218 46 0.0387 0.0331 0.045 14.8247 35.8589 5.9882 47 0.0387 0.0742 0.047 75.165 38.4793 6.2032 48 0.0384 -0.015 0.045 3.1291 36.2699 6.0224 49 0.0389 0.0049 0.0426 0.3253 34.1555 5.8443 50 0.0389 -0.0954 0.0455 124.3544 39.1666 6.2583 51 0.0386 -0.1332 0.0502 245.717 50.0376 7.0737 52 0.039 -0.0867 0.052 102.0053 52.636 7.2551 53 0.039 -0.1709 0.0577 398.8024 69.1201 8.3139 54 0.0387 -0.085 0.0589 99.8649 70.5176 8.3975 55 0.0391 -0.1524 0.063 315.4652 81.1675 9.0093 56 0.039 -0.1351 0.066 249.2095 88.1693 9.3898 57 0.0388 -0.1006 0.0673 139.7398 90.2321 9.4991 58 0.0391 -0.103 0.0687 144.3695 92.3143 9.608 59 0.0391 -0.1172 0.0705 187.7093 95.8475 9.7902 60 0.0389 -0.135 0.0728 251.4726 101.4055 10.07

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t126140402373qn4cc01ju6uo3/1y1dt1261403969.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t126140402373qn4cc01ju6uo3/1y1dt1261403969.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t126140402373qn4cc01ju6uo3/2crno1261403969.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t126140402373qn4cc01ju6uo3/2crno1261403969.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; 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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