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
===========================================