[Gretl-users] About the MLE example for GARCH

Dear all: I am a new user of gretl. I have a question about the MLE example for estimating GARCH on page 118 of the gretl user guide (chapter 17). I tried the script as shown in what follows ( scalar beta was changed to 0.5 ): ========the MLE script=================================== open djclose series y = 100*ldiff(djclose) scalar mu = 0.0 scalar omega = 1 scalar alpha = 0.4 scalar beta = 0.5 mle ll = -0.5*(log(h) + (e^2)/h) series e = y - mu series h = var(y) series h = omega + alpha*(e(-1))^2 + beta*h(-1) params mu omega alpha beta end mle =========================================== and the results are: =========MLE GARCH results================================== Using numerical derivatives Tolerance = 1.81899e-012 Function evaluations: 60 Evaluations of gradient: 14 Model 1: ML estimates using the 2526 observations 80/01/04-89/12/29 ll = -0.5*(log(h) + (e^2)/h) Standard errors based on Outer Products matrix PARAMETER ESTIMATE STDERROR T STAT P-VALUE mu 0.0601181 0.0200846 2.993 0.00276 *** omega 0.724952 936411 0.000 1.00000 alpha 0.238901 0.00594764 40.167 <0.00001 *** beta 0.132664 701184 0.000 1.00000 Log-likelihood = - 1370.26 Akaike information criterion (AIC) = 2748.53 Schwarz Bayesian criterion (BIC) = 2771.86 Hannan-Quinn criterion (HQC) = 2757 =========================================== and I found the results are different from what estimated by using the default GARCH estimation , i.e., \Model\Time series\GARCH, in which I got (as attached below) I've tried several combinations of initial values for mu, omega, alpha and, beta. But the results are basically similar. How can I get closer results from MLE as those from the default GARCH estimation? Many thanks Yi-Nung Yang ====the results from the default GARCH ======================================= Function evaluations: 75 Evaluations of gradient: 17 Model 2: GARCH estimates using the 2527 observations 80/01/03-89/12/29 Dependent variable: y Standard errors based on Hessian VARIABLE COEFFICIENT STDERROR T STAT P-VALUE const 0.0700980 0.0184927 3.791 0.00015 *** alpha(0) 0.0483241 0.0114087 4.236 0.00002 *** alpha(1) 0.0917793 0.0109744 8.363 <0.00001 *** beta(1) 0.869729 0.0179295 48.508 <0.00001 *** Mean of dependent variable = 0.047711 Standard deviation of dep. var. = 1.15563 Unconditional error variance = 1.25546 Log-likelihood = -3568.13 Akaike information criterion (AIC) = 7146.26 Schwarz Bayesian criterion (BIC) = 7175.44 Hannan-Quinn criterion (HQC) = 7156.85 ===========================================