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 13:32:36 -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/t1199737879ye2jtsfpk2dm3vv.htm/, Retrieved Mon, 07 Jan 2008 21:31:22 +0100

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Dataseries X:

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106.8 114.3 105.7 90.1 91.6 97.7 100.8 104.6 95.9 102.7 104 107.9 113.8 113.8 123.1 125.1 137.6 134 140.3 152.1 150.6 167.3 153.2 142 154.4 158.5 180.9 181.3 172.4 192 199.3 215.4 214.3 201.5 190.5 196 215.7 209.4 214.1 237.8 239 237.8 251.5 248.8 215.4 201.2 203.1 214.2

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 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[28]) 16 125.1 - - - - - - - 17 137.6 - - - - - - - 18 134 - - - - - - - 19 140.3 - - - - - - - 20 152.1 - - - - - - - 21 150.6 - - - - - - - 22 167.3 - - - - - - - 23 153.2 - - - - - - - 24 142 - - - - - - - 25 154.4 - - - - - - - 26 158.5 - - - - - - - 27 180.9 - - - - - - - 28 181.3 - - - - - - - 29 172.4 192.4368 175.8171 209.0565 0.0091 0.9055 1 0.9055 30 192 185.2191 157.4724 212.9658 0.316 0.8174 0.9999 0.609 31 199.3 197.0945 164.5015 229.6875 0.4472 0.6203 0.9997 0.8289 32 215.4 214.8096 180.4683 249.151 0.4866 0.812 0.9998 0.9721 33 214.3 215.955 180.3428 251.5672 0.4637 0.5122 0.9998 0.9718 34 201.5 235.7015 198.1745 273.2285 0.037 0.8682 0.9998 0.9978 35 190.5 213.6879 173.5883 253.7876 0.1285 0.7243 0.9984 0.9433 36 196 195.7979 153.2043 238.3914 0.4963 0.5963 0.9933 0.7477 37 215.7 211.8824 167.261 256.5038 0.4334 0.7573 0.9942 0.9104 38 209.4 218.0962 171.7606 264.4318 0.3565 0.5404 0.9941 0.9402 39 214.1 246.4577 198.4609 294.4545 0.0932 0.9349 0.9963 0.9961 40 237.8 245.8716 196.1543 295.5889 0.3752 0.8948 0.9945 0.9945 41 239 256.3253 193.9345 318.7161 0.2931 0.7197 0.9958 0.9908 42 237.8 247.4992 170.0609 324.9374 0.403 0.5852 0.9199 0.9531 43 251.5 262.0848 175.7558 348.4139 0.405 0.7093 0.923 0.9667 44 248.8 282.5905 191.5752 373.6059 0.2334 0.7484 0.926 0.9854 45 215.4 284.9405 190.0549 379.826 0.0754 0.7723 0.9277 0.9839 46 201.2 306.0928 206.4464 405.7391 0.0195 0.9628 0.9802 0.9929 47 203.1 280.3544 175.1191 385.5896 0.0751 0.9298 0.9529 0.9675 48 214.2 259.3302 148.6911 369.9693 0.212 0.8404 0.869 0.9166 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 29 0.0441 -0.1041 0.0052 401.475 20.0738 4.4804 30 0.0764 0.0366 0.0018 45.981 2.299 1.5163 31 0.0844 0.0112 6e-04 4.8643 0.2432 0.4932 32 0.0816 0.0027 1e-04 0.3485 0.0174 0.132 33 0.0841 -0.0077 4e-04 2.7391 0.137 0.3701 34 0.0812 -0.1451 0.0073 1169.7408 58.487 7.6477 35 0.0957 -0.1085 0.0054 537.6797 26.884 5.185 36 0.111 0.001 1e-04 0.0409 0.002 0.0452 37 0.1074 0.018 9e-04 14.5741 0.7287 0.8536 38 0.1084 -0.0399 0.002 75.6246 3.7812 1.9445 39 0.0994 -0.1313 0.0066 1047.0217 52.3511 7.2354 40 0.1032 -0.0328 0.0016 65.1508 3.2575 1.8049 41 0.1242 -0.0676 0.0034 300.1666 15.0083 3.8741 42 0.1596 -0.0392 0.002 94.074 4.7037 2.1688 43 0.1681 -0.0404 0.002 112.0389 5.6019 2.3668 44 0.1643 -0.1196 0.006 1141.7999 57.09 7.5558 45 0.1699 -0.2441 0.0122 4835.8801 241.794 15.5497 46 0.1661 -0.3427 0.0171 11002.4923 550.1246 23.4547 47 0.1915 -0.2756 0.0138 5968.2382 298.4119 17.2746 48 0.2177 -0.174 0.0087 2036.7372 101.8369 10.0914

Charts produced by software:

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Parameters (Session):

par1 = 20 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 20 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 1 ; par9 = 0 ; 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')

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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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