Arima Forecast

*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: Fri, 11 Dec 2009 10:36:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t1260553050idgrqwo5zlx8szb.htm/, Retrieved Fri, 11 Dec 2009 18:37:32 +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/2009/Dec/11/t1260553050idgrqwo5zlx8szb.htm/}, year = {2009}, } @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 = {2009}, 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:

SHWWS10

Dataseries X:

» Textbox « » Textfile « » CSV «

7.3 7.6 7.5 7.6 7.9 7.9 8.1 8.2 8 7.5 6.8 6.5 6.6 7.6 8 8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5

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 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[45]) 33 8.2 - - - - - - - 34 8.2 - - - - - - - 35 8.2 - - - - - - - 36 7.9 - - - - - - - 37 7.3 - - - - - - - 38 6.9 - - - - - - - 39 6.6 - - - - - - - 40 6.7 - - - - - - - 41 6.9 - - - - - - - 42 7 - - - - - - - 43 7.1 - - - - - - - 44 7.2 - - - - - - - 45 7.1 - - - - - - - 46 6.9 7.1717 6.7773 7.5662 0.0885 0.6393 0 0.6393 47 7 7.166 6.5314 7.8006 0.3041 0.7943 7e-04 0.5808 48 6.8 7.2994 6.4098 8.1889 0.1356 0.7452 0.0929 0.6698 49 6.4 7.4436 6.4658 8.4213 0.0182 0.9015 0.6132 0.7545 50 6.7 7.5102 6.5237 8.4967 0.0537 0.9863 0.8873 0.7925 51 6.6 7.5134 6.5276 8.4991 0.0347 0.9471 0.9653 0.7944 52 6.4 7.4989 6.5139 8.4838 0.0144 0.9632 0.9441 0.7863 53 6.3 7.4919 6.5071 8.4767 0.0088 0.9851 0.8806 0.7823 54 6.2 7.4935 6.5082 8.4789 0.005 0.9912 0.8369 0.7831 55 6.5 7.4971 6.5113 8.4828 0.0237 0.995 0.7851 0.7851 56 6.8 7.4987 6.5129 8.4845 0.0824 0.9765 0.7237 0.786 57 6.8 7.4985 6.5128 8.4843 0.0824 0.9176 0.7859 0.7859 58 6.4 7.498 6.5123 8.4836 0.0145 0.9174 0.8828 0.7856 59 6.1 7.4977 6.512 8.4834 0.0027 0.9855 0.8388 0.7855 60 5.8 7.4977 6.512 8.4834 4e-04 0.9973 0.9173 0.7855 61 6.1 7.4979 6.5121 8.4836 0.0027 0.9996 0.9855 0.7856 62 7.2 7.4979 6.5122 8.4836 0.2768 0.9973 0.9437 0.7856 63 7.3 7.4979 6.5122 8.4836 0.347 0.7232 0.9629 0.7856 64 6.9 7.4979 6.5122 8.4836 0.1173 0.653 0.9855 0.7856 65 6.1 7.4979 6.5122 8.4836 0.0027 0.8827 0.9914 0.7856 66 5.8 7.4979 6.5122 8.4836 4e-04 0.9973 0.9951 0.7856 67 6.2 7.4979 6.5122 8.4836 0.0049 0.9996 0.9764 0.7856 68 7.1 7.4979 6.5122 8.4836 0.2144 0.9951 0.9174 0.7856 69 7.7 7.4979 6.5122 8.4836 0.3439 0.7856 0.9174 0.7856 70 7.9 7.4979 6.5122 8.4836 0.212 0.3439 0.9855 0.7856 71 7.7 7.4979 6.5122 8.4836 0.3439 0.212 0.9973 0.7856 72 7.4 7.4979 6.5122 8.4836 0.4229 0.3439 0.9996 0.7856 73 7.5 7.4979 6.5122 8.4836 0.4983 0.5771 0.9973 0.7856 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 46 0.0281 -0.0379 0 0.0738 0 0 47 0.0452 -0.0232 0.0305 0.0276 0.0507 0.2252 48 0.0622 -0.0684 0.0432 0.2494 0.1169 0.3419 49 0.067 -0.1402 0.0674 1.089 0.3599 0.6 50 0.067 -0.1079 0.0755 0.6564 0.4192 0.6475 51 0.0669 -0.1216 0.0832 0.8342 0.4884 0.6989 52 0.067 -0.1465 0.0922 1.2075 0.5911 0.7689 53 0.0671 -0.1591 0.1006 1.4206 0.6948 0.8336 54 0.0671 -0.1726 0.1086 1.6732 0.8035 0.8964 55 0.0671 -0.133 0.111 0.9941 0.8226 0.907 56 0.0671 -0.0932 0.1094 0.4882 0.7922 0.89 57 0.0671 -0.0932 0.1081 0.488 0.7668 0.8757 58 0.0671 -0.1464 0.111 1.2055 0.8006 0.8947 59 0.0671 -0.1864 0.1164 1.9536 0.8829 0.9396 60 0.0671 -0.2264 0.1237 2.8823 1.0162 1.0081 61 0.0671 -0.1864 0.1276 1.954 1.0748 1.0367 62 0.0671 -0.0397 0.1225 0.0887 1.0168 1.0084 63 0.0671 -0.0264 0.1171 0.0392 0.9625 0.9811 64 0.0671 -0.0797 0.1152 0.3575 0.9307 0.9647 65 0.0671 -0.1864 0.1187 1.954 0.9818 0.9909 66 0.0671 -0.2264 0.1239 2.8827 1.0724 1.0355 67 0.0671 -0.1731 0.1261 1.6845 1.1002 1.0489 68 0.0671 -0.0531 0.1229 0.1583 1.0592 1.0292 69 0.0671 0.027 0.1189 0.0409 1.0168 1.0084 70 0.0671 0.0536 0.1163 0.1617 0.9826 0.9913 71 0.0671 0.027 0.1129 0.0409 0.9464 0.9728 72 0.0671 -0.0131 0.1092 0.0096 0.9117 0.9548 73 0.0671 3e-04 0.1053 0 0.8791 0.9376

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260553050idgrqwo5zlx8szb/1g4zg1260552977.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260553050idgrqwo5zlx8szb/1g4zg1260552977.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260553050idgrqwo5zlx8szb/2d5901260552977.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260553050idgrqwo5zlx8szb/2d5901260552977.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

par1 <- as.numeric(par1) #cut off periods par1 <- 28 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 par6 <- 3 par7 <- as.numeric(par7) #q par7 <- 3 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')

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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