forecasting

R Software Module: rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Mon, 07 Jan 2008 12:49:31 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/07/t1199735331kbh5pwt94mk3jmx.htm/, Retrieved Mon, 07 Jan 2008 20:48:53 +0100

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Dataseries X:

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104.2 103.2 112.7 106.4 102.6 110.6 95.2 89 112.5 116.8 107.2 113.6 101.8 102.6 122.7 110.3 110.5 121.6 100.3 100.7 123.4 127.1 124.1 131.2 111.6 114.2 130.1 125.9 119 133.8 107.5 113.5 134.4 126.8 135.6 139.9 129.8 131 153.1 134.1 144.1 155.9 123.3 128.1 144.3 153 149.9 150.9

Text written by user:

Output produced by software:

Summary of compuational 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[24]) 12 113.6 - - - - - - - 13 101.8 - - - - - - - 14 102.6 - - - - - - - 15 122.7 - - - - - - - 16 110.3 - - - - - - - 17 110.5 - - - - - - - 18 121.6 - - - - - - - 19 100.3 - - - - - - - 20 100.7 - - - - - - - 21 123.4 - - - - - - - 22 127.1 - - - - - - - 23 124.1 - - - - - - - 24 131.2 - - - - - - - 25 111.6 117.7975 109.0424 126.5526 0.0827 0.0013 0.9998 0.0013 26 114.2 118.3287 108.7158 127.9416 0.1999 0.915 0.9993 0.0043 27 130.1 133.8961 123.5802 144.2121 0.2354 0.9999 0.9833 0.6958 28 125.9 123.536 112.1437 134.9284 0.3421 0.1294 0.9886 0.0937 29 119 121.8798 109.718 134.0416 0.3213 0.2585 0.9667 0.0665 30 133.8 131.4493 118.5974 144.3013 0.36 0.9712 0.9335 0.5152 31 107.5 112.3903 98.8494 125.9312 0.2395 0.001 0.9599 0.0032 32 113.5 109.7397 95.5833 123.8961 0.3013 0.6218 0.8946 0.0015 33 134.4 132.5162 117.7872 147.2452 0.401 0.9943 0.8875 0.5695 34 126.8 136.3211 121.0421 151.6001 0.111 0.5973 0.8816 0.7444 35 135.6 130.2159 114.4404 145.9913 0.2518 0.6644 0.7763 0.4513 36 139.9 136.541 120.2943 152.7876 0.3427 0.5452 0.7403 0.7403 37 129.8 124.2507 105.6273 142.8741 0.2796 0.0498 0.9085 0.2323 38 131 124.3355 104.8561 143.8148 0.2512 0.2912 0.8461 0.2449 39 153.1 139.7255 119.4685 159.9825 0.0978 0.8007 0.8242 0.7953 40 134.1 129.4727 108.3278 150.6176 0.334 0.0143 0.6297 0.4364 41 144.1 127.7115 105.8026 149.6204 0.0713 0.2838 0.7821 0.3775 42 155.9 137.2061 114.5813 159.8309 0.0527 0.2752 0.616 0.6986 43 123.3 118.115 94.7912 141.4387 0.3315 7e-04 0.8138 0.1358 44 128.1 115.4039 91.4284 139.3795 0.1497 0.2593 0.5618 0.0983 45 144.3 138.1235 113.5281 162.7188 0.3113 0.7878 0.6167 0.7094 46 153 141.8782 116.6806 167.0758 0.1935 0.4253 0.8796 0.7969 47 149.9 135.7194 109.9691 161.4697 0.1402 0.0942 0.5036 0.6346 48 150.9 141.9916 115.7095 168.2738 0.2532 0.2777 0.562 0.7895 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 25 0.0379 -0.0526 0.0022 38.409 1.6004 1.2651 26 0.0414 -0.0349 0.0015 17.046 0.7102 0.8428 27 0.0393 -0.0284 0.0012 14.4105 0.6004 0.7749 28 0.0471 0.0191 8e-04 5.5883 0.2328 0.4825 29 0.0509 -0.0236 0.001 8.293 0.3455 0.5878 30 0.0499 0.0179 7e-04 5.5256 0.2302 0.4798 31 0.0615 -0.0435 0.0018 23.9152 0.9965 0.9982 32 0.0658 0.0343 0.0014 14.1398 0.5892 0.7676 33 0.0567 0.0142 6e-04 3.5486 0.1479 0.3845 34 0.0572 -0.0698 0.0029 90.6519 3.7772 1.9435 35 0.0618 0.0413 0.0017 28.9888 1.2079 1.099 36 0.0607 0.0246 0.001 11.2832 0.4701 0.6857 37 0.0765 0.0447 0.0019 30.7953 1.2831 1.1328 38 0.0799 0.0536 0.0022 44.4158 1.8507 1.3604 39 0.074 0.0957 0.004 178.8768 7.4532 2.7301 40 0.0833 0.0357 0.0015 21.4121 0.8922 0.9445 41 0.0875 0.1283 0.0053 268.5842 11.191 3.3453 42 0.0841 0.1362 0.0057 349.4619 14.5609 3.8159 43 0.1007 0.0439 0.0018 26.8845 1.1202 1.0584 44 0.106 0.11 0.0046 161.1907 6.7163 2.5916 45 0.0909 0.0447 0.0019 38.1492 1.5896 1.2608 46 0.0906 0.0784 0.0033 123.6942 5.1539 2.2702 47 0.0968 0.1045 0.0044 201.0898 8.3787 2.8946 48 0.0944 0.0627 0.0026 79.3587 3.3066 1.8184

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t1199735331kbh5pwt94mk3jmx/1pv4z1199735368.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t1199735331kbh5pwt94mk3jmx/1pv4z1199735368.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t1199735331kbh5pwt94mk3jmx/2oo4l1199735368.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t1199735331kbh5pwt94mk3jmx/2oo4l1199735368.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods 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 par7 <- as.numeric(par7) #q 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,fx)) (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.se <- array(0, dim=fx) perf.mse <- 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$pred[i] perf.mape[i] = perf.mape[i] + abs(perf.pe[i]) perf.se[i] = (x[nx+i] - forecast$pred[i])^2 perf.mse[i] = perf.mse[i] + perf.se[i] 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 = perf.mape / fx perf.mse = perf.mse / fx perf.rmse = sqrt(perf.mse) 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[1:12] <- 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.mape[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse[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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