Re: [Gretl-users] mle not finding correct maximum

On 05-12-2009, at 13:56, Davor Horvatic wrote: > Concerning mle, I like to test and check results independently and I > came across > a problem. > > Can anyone supply explicit code to determine GARCH(1,1) coefficients > with different method (OLS, MLE via R ...) for the simple example from > the user guide. > > open djclose > series y = 100*ldiff(djclose) > scalar mu = 0.0 > scalar omega = 1 > scalar alpha = 0.4 > scalar beta = 0.0 > mle ll = check ? (-0.5*(log(h) + (e > 2 > )/h)) : NA > series e = y - mu > series h = var(y) > series h = omega + alpha*(e(-1)) > 2 > + beta*h(-1) > scalar check = (alpha>0) && (beta>0) > params mu omega alpha beta > end mle Using R 2.10.0 (patched) on Mac OS X 10.6.2. Copied gretldata to folder containing R script. Inserted below are the R script and the R output. Differences with gretl are small and are not worth to worrying about. BTW. Just in case: I am not a Garch-guru. I found the R garch function by doing ??garch. Berend ----------------------------------------------------- The R script is <script> library(tseries) # load data from gretl gretldata <- read.table("gretldata.txt", header=TRUE) gretldata <- ts(gretldata, start=c(1980, 1), frequency = 5) yts <- gretldata[2:nrow(gretldata),"y"] yts.garch1 <- garch(yts) yts.garch2 <- garch(yts,start=c(1,0.4,0.01)) yts.garch3 <- garch(yts,start=c(1,0.4,0.01),control=garch.control(grad="numerical")) summary(yts.garch1) summary(yts.garch2) summary(yts.garch3) </script> Summary output is: <OUTPUT> > summary(yts.garch1) Call: garch(x = yts) Model: GARCH(1,1) Residuals: Min 1Q Median 3Q Max -11.74204 -0.49793 0.05298 0.61346 5.02039 Coefficient(s): Estimate Std. Error t value Pr(>|t|) a0 0.047597 0.005323 8.942 <2e-16 *** a1 0.090520 0.002552 35.470 <2e-16 *** b1 0.871903 0.008238 105.844 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Diagnostic Tests: Jarque Bera Test data: Residuals X-squared = 14613.68, df = 2, p-value < 2.2e-16 Box-Ljung test data: Squared.Residuals X-squared = 0.4014, df = 1, p-value = 0.5263 > summary(yts.garch2) Call: garch(x = yts, start = c(1, 0.4, 0.01)) Model: GARCH(1,1) Residuals: Min 1Q Median 3Q Max -11.74210 -0.49793 0.05298 0.61346 5.02040 Coefficient(s): Estimate Std. Error t value Pr(>|t|) a0 0.047597 0.005323 8.942 <2e-16 *** a1 0.090519 0.002552 35.470 <2e-16 *** b1 0.871903 0.008238 105.845 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Diagnostic Tests: Jarque Bera Test data: Residuals X-squared = 14613.83, df = 2, p-value < 2.2e-16 Box-Ljung test data: Squared.Residuals X-squared = 0.4015, df = 1, p-value = 0.5263 > summary(yts.garch3) Call: garch(x = yts, control = garch.control(grad = "numerical"), start = c(1, 0.4, 0.01)) Model: GARCH(1,1) Residuals: Min 1Q Median 3Q Max -11.74140 -0.49798 0.05298 0.61343 5.02026 Coefficient(s): Estimate Std. Error t value Pr(>|t|) a0 0.047649 0.005328 8.943 <2e-16 *** a1 0.090545 0.002553 35.465 <2e-16 *** b1 0.871830 0.008243 105.765 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Diagnostic Tests: Jarque Bera Test data: Residuals X-squared = 14607.92, df = 2, p-value < 2.2e-16 Box-Ljung test data: Squared.Residuals X-squared = 0.401, df = 1, p-value = 0.5266 </OUTPUT> _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users