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

Title produced by software: ARIMA Forecasting

Date of computation: Sat, 08 Dec 2007 07:02:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/08/t1197121799dechwu8vjk1vsk2.htm/, Retrieved Sat, 08 Dec 2007 14:50:02 +0100

User-defined keywords:

Dataseries X:

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95,4 101,2 101,5 101,9 101,7 100,1 97,4 96,5 99,2 102,2 105,3 111,1 114,9 124,5 142,2 159,7 165,2 198,6 207,8 219,6 239,6 235,3 218,5 213,8 205,5 198,4 198,5 190,2 180,7 193,6 192,8 195,5 197,2 196,9 178,9 172,4 156,4 143,7 153,6 168,8 185,8 199,9 205,4 197,5 199,6 200,5 193,7 179,6 169,1 169,8 195,5 194,8 204,5 203,8 204,8 204,9 240,0 248,3 258,4 254,9

Text written by user:

lambda -0,6 d=1 D=0 ARIMA parameters op max

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 4 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]) 12 111.1 - - - - - - - 13 114.9 - - - - - - - 14 124.5 - - - - - - - 15 142.2 - - - - - - - 16 159.7 - - - - - - - 17 165.2 - - - - - - - 18 198.6 - - - - - - - 19 207.8 - - - - - - - 20 219.6 - - - - - - - 21 239.6 - - - - - - - 22 235.3 - - - - - - - 23 218.5 - - - - - - - 24 213.8 - - - - - - - 25 205.5 189.9999 190.3194 189.6813 1 1 0 1 26 198.4 174.616 175.0706 174.1633 1 1 0 1 27 198.5 174.1792 174.9014 173.4616 1 1 0 1 28 190.2 173.4605 174.468 172.4624 1 1 0 1 29 180.7 173.9903 175.2336 172.761 1 1 0 1 30 193.6 178.2154 179.7441 176.7075 1 0.9994 1 1 31 192.8 185.4642 187.3753 183.5841 1 1 1 1 32 195.5 188.1295 190.3381 185.9616 1 1 1 1 33 197.2 180.8274 183.1154 178.5848 1 1 1 1 34 196.9 173.398 175.7537 171.0924 1 1 1 1 35 178.9 166.4637 168.8622 164.1192 1 1 1 1 36 172.4 155.4856 157.7898 153.2347 1 1 1 1 37 156.4 149.2025 151.51 146.9507 1 1 1 1 38 143.7 136.3709 138.4978 134.2959 1 1 1 1 39 153.6 119.7744 121.5995 117.9927 1 1 1 1 40 168.8 108.5699 110.2122 106.9664 1 1 1 1 41 185.8 105.7459 107.4001 104.1321 1 1 1 1 42 199.9 93.0277 94.4355 91.6531 1 1 1 1 43 205.4 90.4741 91.8775 89.1046 1 1 1 1 44 197.5 87.5749 88.9608 86.2233 1 1 1 1 45 199.6 83.4321 84.7621 82.1351 1 1 1 1 46 200.5 84.2218 85.6191 82.8606 1 1 1 1 47 193.7 87.757 89.2995 86.2566 1 1 1 1 48 179.6 88.836 90.4585 87.2595 1 1 1 1 49 169.1 95.6101 97.4631 93.8129 1 1 1 1 50 169.8 101.2807 103.3305 99.2952 1 1 1 1 51 195.5 101.347 103.4091 99.3499 1 1 1 1 52 194.8 101.5556 103.6265 99.5501 1 1 1 1 53 204.5 101.3052 103.3729 99.3029 1 1 1 1 54 203.8 99.454 101.4659 97.5052 1 1 1 1 55 204.8 96.7249 98.6494 94.8597 1 1 1 1 56 204.9 95.7688 97.6641 93.9318 1 1 1 1 57 240 98.33 100.3098 96.4121 1 1 1 1 58 248.3 101.3091 103.3869 99.2973 1 1 1 1 59 258.4 104.4643 106.6477 102.3515 1 1 1 1 60 254.9 110.2211 112.6028 107.9189 1 1 1 1 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 25 -9e-04 0.0816 0.0023 240.2518 6.6737 2.5833 26 -0.0013 0.1362 0.0038 565.6795 15.7133 3.964 27 -0.0021 0.1396 0.0039 591.5036 16.4307 4.0535 28 -0.0029 0.0965 0.0027 280.2098 7.7836 2.7899 29 -0.0036 0.0386 0.0011 45.0207 1.2506 1.1183 30 -0.0043 0.0863 0.0024 236.6848 6.5746 2.5641 31 -0.0052 0.0396 0.0011 53.8143 1.4948 1.2226 32 -0.0059 0.0392 0.0011 54.3241 1.509 1.2284 33 -0.0063 0.0905 0.0025 268.0625 7.4462 2.7288 34 -0.0068 0.1355 0.0038 552.3451 15.3429 3.917 35 -0.0072 0.0747 0.0021 154.6623 4.2962 2.0727 36 -0.0074 0.1088 0.003 286.0986 7.9472 2.8191 37 -0.0077 0.0482 0.0013 51.8044 1.439 1.1996 38 -0.0078 0.0537 0.0015 53.7152 1.4921 1.2215 39 -0.0076 0.2824 0.0078 1144.1716 31.7825 5.6376 40 -0.0075 0.5548 0.0154 3627.6658 100.7685 10.0384 41 -0.0078 0.757 0.021 6408.656 178.0182 13.3423 42 -0.0075 1.1488 0.0319 11421.6976 317.2694 17.8121 43 -0.0077 1.2703 0.0353 13207.9712 366.8881 19.1543 44 -0.0079 1.2552 0.0349 12083.5195 335.6533 18.3208 45 -0.0079 1.3924 0.0387 13494.9863 374.8607 19.3613 46 -0.0082 1.3806 0.0384 13520.6238 375.5729 19.3797 47 -0.0087 1.2072 0.0335 11223.9251 311.7757 17.6572 48 -0.0091 1.0217 0.0284 8238.1124 228.8365 15.1273 49 -0.0096 0.7686 0.0214 5400.7602 150.0211 12.2483 50 -0.01 0.6765 0.0188 4694.8951 130.4138 11.4199 51 -0.0101 0.929 0.0258 8864.7944 246.2443 15.6922 52 -0.0101 0.9182 0.0255 8694.5243 241.5146 15.5407 53 -0.0101 1.0187 0.0283 10649.1649 295.8101 17.1991 54 -0.01 1.0492 0.0291 10888.0889 302.4469 17.391 55 -0.0098 1.1173 0.031 11680.2341 324.4509 18.0125 56 -0.0098 1.1395 0.0317 11909.6117 330.8225 18.1885 57 -0.01 1.4408 0.04 20070.3819 557.5106 23.6117 58 -0.0101 1.4509 0.0403 21606.3321 600.1759 24.4985 59 -0.0103 1.4736 0.0409 23696.2043 658.2279 25.656 60 -0.0107 1.3126 0.0365 20931.9919 581.4442 24.1132

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121799dechwu8vjk1vsk2/1qlv11197122571.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121799dechwu8vjk1vsk2/1qlv11197122571.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121799dechwu8vjk1vsk2/2k2nd1197122572.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121799dechwu8vjk1vsk2/2k2nd1197122572.ps (open in new window)

Parameters:

par1 = 36 ; par2 = -0.6 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 2 ; par8 = 2 ; 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) } (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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