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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 06:50:06 -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/t1197121230jyfobyjbemwdbgm.htm/, Retrieved Sat, 08 Dec 2007 14:40:33 +0100

User-defined keywords:

Dataseries X:

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96.8 91.2 97.1 104.9 110.9 104.8 94.1 95.8 99.3 101.1 104.0 99.0 105.4 107.1 110.7 117.1 118.7 126.5 127.5 134.6 131.8 135.9 142.7 141.7 153.4 145.0 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179.0 190.6 190.0 181.6 174.8 180.5 196.8 193.8 197.0 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244.0 234.7 250.2

Text written by user:

lambda 0,7 d=1 D=0 ARIMA parameters op maxx

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 6 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 99 - - - - - - - 13 105.4 - - - - - - - 14 107.1 - - - - - - - 15 110.7 - - - - - - - 16 117.1 - - - - - - - 17 118.7 - - - - - - - 18 126.5 - - - - - - - 19 127.5 - - - - - - - 20 134.6 - - - - - - - 21 131.8 - - - - - - - 22 135.9 - - - - - - - 23 142.7 - - - - - - - 24 141.7 - - - - - - - 25 153.4 141.1261 134.4193 147.93 2e-04 0.4343 1 0.4343 26 145 134.8476 128.1969 141.5981 0.0016 0 1 0.0233 27 137.7 141.4653 134.6835 148.3461 0.1417 0.157 1 0.4733 28 148.3 150.1703 143.2628 157.1746 0.3004 0.9998 1 0.9911 29 152.2 156.8302 149.8349 163.9204 0.1003 0.9908 1 1 30 169.4 150.058 143.135 157.0782 0 0.2749 1 0.9902 31 168.6 138.1141 131.3311 144.9986 0 0 0.9987 0.1537 32 161.1 140.0247 133.1975 146.9533 0 0 0.9376 0.3178 33 174.1 143.9352 137.0511 150.9195 0 0 0.9997 0.7348 34 179 145.9426 139.0201 152.965 0 0 0.9975 0.8818 35 190.6 149.1769 142.1805 156.2731 0 0 0.9632 0.9805 36 190 143.6052 136.6656 150.6468 0 0 0.702 0.702 37 181.6 150.7371 143.6832 157.8914 0 0 0.2328 0.9934 38 174.8 152.6205 145.5396 159.8013 0 0 0.9812 0.9986 39 180.5 156.6185 149.4711 163.8651 0 0 1 1 40 196.8 163.7058 156.4424 171.0672 0 0 1 1 41 193.8 165.4792 158.1792 172.877 0 0 0.9998 1 42 197 174.063 166.6456 181.5764 0 0 0.8881 1 43 216.3 175.15 167.7119 182.6841 0 0 0.9558 1 44 221.4 182.9376 175.3854 190.5844 0 0 1 1 45 217.9 179.8739 172.3455 187.498 0 0 0.9311 1 46 229.7 184.3676 176.7739 192.0563 0 0 0.9144 1 47 227.4 191.8017 184.1096 199.5874 0 0 0.6189 1 48 204.2 190.7042 183.0143 198.4881 3e-04 0 0.5704 1 49 196.6 190.0841 175.3101 205.2109 0.1993 0.0337 0.8642 1 50 198.8 183.2212 168.5636 198.2394 0.021 0.0404 0.8641 1 51 207.5 190.4607 175.5832 205.6954 0.0142 0.1417 0.9 1 52 190.7 199.9556 184.8424 215.4196 0.1204 0.1695 0.6554 1 53 201.6 207.196 191.9077 222.8306 0.2415 0.9807 0.9535 1 54 210.5 199.8426 184.6881 215.3501 0.089 0.4121 0.6403 1 55 223.5 186.8153 171.9276 202.0679 0 0.0012 1e-04 1 56 223.8 188.9102 173.9453 204.2396 0 0 0 1 57 231.2 193.1763 178.0976 208.6168 0 1e-04 8e-04 1 58 244 195.3692 180.2156 210.884 0 0 0 1 59 234.7 198.8992 183.6212 214.5377 0 0 2e-04 1 60 250.2 192.826 177.6583 208.3606 0 0 0.0756 1 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 25 0.0246 0.087 0.0024 150.6483 4.1847 2.0456 26 0.0255 0.0753 0.0021 103.0722 2.8631 1.6921 27 0.0248 -0.0266 7e-04 14.1776 0.3938 0.6276 28 0.0238 -0.0125 3e-04 3.4981 0.0972 0.3117 29 0.0231 -0.0295 8e-04 21.439 0.5955 0.7717 30 0.0239 0.1289 0.0036 374.1123 10.392 3.2237 31 0.0254 0.2207 0.0061 929.3891 25.8164 5.081 32 0.0252 0.1505 0.0042 444.1686 12.338 3.5126 33 0.0248 0.2096 0.0058 909.9167 25.2755 5.0275 34 0.0245 0.2265 0.0063 1092.7942 30.3554 5.5096 35 0.0243 0.2777 0.0077 1715.8764 47.6632 6.9039 36 0.025 0.3231 0.009 2152.4798 59.7911 7.7325 37 0.0242 0.2047 0.0057 952.5213 26.4589 5.1438 38 0.024 0.1453 0.004 491.9315 13.6648 3.6966 39 0.0236 0.1525 0.0042 570.3263 15.8424 3.9803 40 0.0229 0.2022 0.0056 1095.2248 30.4229 5.5157 41 0.0228 0.1711 0.0048 802.0693 22.2797 4.7201 42 0.022 0.1318 0.0037 526.1065 14.6141 3.8228 43 0.0219 0.2349 0.0065 1693.3261 47.0368 6.8583 44 0.0213 0.2102 0.0058 1479.3589 41.0933 6.4104 45 0.0216 0.2114 0.0059 1445.9862 40.1663 6.3377 46 0.0213 0.2459 0.0068 2055.0308 57.0842 7.5554 47 0.0207 0.1856 0.0052 1267.2422 35.2012 5.9331 48 0.0208 0.0708 0.002 182.1379 5.0594 2.2493 49 0.0406 0.0343 0.001 42.4576 1.1794 1.086 50 0.0418 0.085 0.0024 242.7004 6.7417 2.5965 51 0.0408 0.0895 0.0025 290.3386 8.065 2.8399 52 0.0395 -0.0463 0.0013 85.6653 2.3796 1.5426 53 0.0385 -0.027 8e-04 31.3152 0.8699 0.9327 54 0.0396 0.0533 0.0015 113.5806 3.155 1.7762 55 0.0417 0.1964 0.0055 1345.7648 37.3824 6.1141 56 0.0414 0.1847 0.0051 1217.2974 33.8138 5.815 57 0.0408 0.1968 0.0055 1445.801 40.1611 6.3373 58 0.0405 0.2489 0.0069 2364.959 65.6933 8.1051 59 0.0401 0.18 0.005 1281.6986 35.6027 5.9668 60 0.0411 0.2975 0.0083 3291.773 91.4381 9.5623

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121230jyfobyjbemwdbgm/1z6nj1197121798.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121230jyfobyjbemwdbgm/1z6nj1197121798.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121230jyfobyjbemwdbgm/2opgu1197121798.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121230jyfobyjbemwdbgm/2opgu1197121798.ps (open in new window)

Parameters:

par1 = 36 ; par2 = 0.7 ; 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')

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Software written by Ed van Stee & Patrick Wessa

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