Forecast Yuan

*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: Sun, 26 Dec 2010 19:15:44 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/26/t12933908222b5k9kn19bcswve.htm/, Retrieved Sun, 26 Dec 2010 20:13:42 +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/2010/Dec/26/t12933908222b5k9kn19bcswve.htm/}, year = {2010}, } @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 = {2010}, 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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7,4271 7,7662 7,6289 7,5281 7,3831 7,2355 7,0617 7,1237 7,4533 7,5411 7,4978 7,3525 7,3862 7,311 7,2013 7,249 7,3321 7,59 7,9082 8,2123 8,0929 8,118 8,1206 8,2883 8,4281 8,7917 8,9168 8,9446 8,9786 9,5862 9,6533 9,4125 9,2195 9,2882 9,6774 9,6857 10,1688 10,4399 10,4675 10,149 9,9163 9,9268 10,0529 10,1622 10,083 10,1134 10,3423 10,7536 11,0967 10,8588 10,7719 10,9262 10,708 10,5062 10,0683 9,8954 9,9589 9,9177 9,7189 9,5273 9,5746 9,763 9,6117 9,6581 9,8361 10,2353 10,1285 10,1347 10,2141 10,0971 9,9651 10,1286 10,3356 10,1238 10,1326 10,2467 10,44 10,3689 10,2415 10,3899 10,3162 10,4533 10,6741 10,8957 10,7404 10,6568 10,5682 10,9833 11,0237 10,8462 10,7287 10,7809 10,2609 9,8252 9,1071 8,695 9,2205 9,0496 8,7406 8,921 9,011 9,3157 9,5786 9,6246 9,7485 9,9431 10,1152 10,1827 9,9777 9,7436 9,3462 9,2623 9,1505 8,5794 8,3245 8,6538 8,752 8,8104 9,2665 9,0895

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 9 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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[108]) 96 8.695 - - - - - - - 97 9.2205 - - - - - - - 98 9.0496 - - - - - - - 99 8.7406 - - - - - - - 100 8.921 - - - - - - - 101 9.011 - - - - - - - 102 9.3157 - - - - - - - 103 9.5786 - - - - - - - 104 9.6246 - - - - - - - 105 9.7485 - - - - - - - 106 9.9431 - - - - - - - 107 10.1152 - - - - - - - 108 10.1827 - - - - - - - 109 9.9777 10.1882 9.7852 10.5913 0.153 0.5107 1 0.5107 110 9.7436 10.2462 9.5511 10.9413 0.0782 0.7755 0.9996 0.5711 111 9.3462 10.2712 9.3753 11.167 0.0215 0.8758 0.9996 0.5767 112 9.2623 10.2823 9.2279 11.3366 0.029 0.9591 0.9943 0.5734 113 9.1505 10.2625 9.0485 11.4765 0.0363 0.9468 0.9783 0.5513 114 8.5794 10.2685 8.8967 11.6403 0.0079 0.9449 0.9133 0.5488 115 8.3245 10.2179 8.7112 11.7247 0.0069 0.9835 0.7972 0.5183 116 8.6538 10.2292 8.6087 11.8498 0.0284 0.9894 0.7677 0.5224 117 8.752 10.1602 8.4309 11.8896 0.0552 0.9561 0.6796 0.4898 118 8.8104 10.1115 8.2727 11.9502 0.0827 0.9263 0.5712 0.4697 119 9.2665 10.0641 8.122 12.0062 0.2104 0.8971 0.4794 0.4523 120 9.0895 10.0671 8.0315 12.1026 0.1733 0.7796 0.4557 0.4557 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 109 0.0202 -0.0207 0 0.0443 0 0 110 0.0346 -0.0491 0.0349 0.2526 0.1485 0.3853 111 0.0445 -0.0901 0.0533 0.8556 0.3842 0.6198 112 0.0523 -0.0992 0.0647 1.0403 0.5482 0.7404 113 0.0604 -0.1084 0.0735 1.2365 0.6859 0.8282 114 0.0682 -0.1645 0.0886 2.853 1.0471 1.0233 115 0.0752 -0.1853 0.1024 3.5851 1.4096 1.1873 116 0.0808 -0.154 0.1089 2.482 1.5437 1.2425 117 0.0868 -0.1386 0.1122 1.9831 1.5925 1.262 118 0.0928 -0.1287 0.1138 1.6928 1.6025 1.2659 119 0.0985 -0.0792 0.1107 0.6361 1.5147 1.2307 120 0.1032 -0.0971 0.1096 0.9556 1.4681 1.2117

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933908222b5k9kn19bcswve/1rlwx1293390933.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933908222b5k9kn19bcswve/1rlwx1293390933.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933908222b5k9kn19bcswve/2ndco1293390933.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t12933908222b5k9kn19bcswve/2ndco1293390933.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 2 ; par8 = 2 ; par9 = 1 ; par10 = TRUE ;

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,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')

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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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