[Gretl-users] mle not finding correct maximum

Concerning mle, I like to test and check results independently and I came across a problem. I can't send all details because this is research in progress and my colleague did not give green light to do so. But I'll describe what is going on as best as I can. I enlarged IGARCH process with additional variable call it gamma1 so that alpha+beta+gamma1=1, and I did 3D plot in Mathematica for log like. function and found maximum to be at beta=0.912565 gamma1=0.0106716 I rechecked it with the FORTRAN and result was the same, since this was the only maximum. Then I run modified script from the mentioned example in the guide. Gretl produced the following result for initial gamma1=0.01 for --robust --lbfgs options: estimate std. error t-ratio p-value ------------------------------------------------------- beta 0,916221 0,0350035 26,18 5,10e-151 *** gamma1 0,0175130 0,0164981 1,062 0,2885 ---------- for --lbfgs only: Tolerance = 1e-014 Function evaluations: 16 Evaluations of gradient: 16 Model 3: ML, using observations 1-15073 ll = check ? -0.5*(log(h) + (ep^2)/h) : NA Standard errors based on Outer Products matrix estimate std. error t-ratio p-value -------------------------------------------------------- beta 0,916221 0,00147268 622,1 0,0000 *** gamma1 0,0175130 0,000790365 22,16 8,71e-109 *** ------------ with default mle options Tolerance = 1e-014 Function evaluations: 81 Evaluations of gradient: 14 Model 5: ML, using observations 1-15073 ll = check ? -0.5*(log(h) + (ep^2)/h) : NA Standard errors based on Outer Products matrix estimate std. error t-ratio p-value --------------------------------------------------------- beta 0,932768 0,00109127 854,8 0,0000 *** gamma1 0,00513404 0,000340124 15,09 1,76e-051 *** ------------------ if I changed initial gamma1 results varied a lot. Imposed conditions were scalar check = (gamma1>0) && (beta>0) && ((beta+gamma1)<1) 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) + (e2)/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 Thanks really a lot, any help is appreciated since I really like gretl as a research tool. All the best, Davor On 30.11.2009. 8:58, Riccardo (Jack) Lucchetti wrote: