Re: [Gretl-users] About the MLE example for GARCH

2007/10/5, Riccardo (Jack) Lucchetti <r.lucchetti(a)univpm.it&gt;: Yes. Please see below and thanks. Yi-Nung Yang Chung Yuan Christian University, Taiwan ======================================== gretl version 1.6.5 Current session: 2007/10/05 10:28 ? open djclose Read datafile c:\progra~1\userdata\gretl-1.6.5\data\misc\djclose.gdt periodicity: 5, maxobs: 2528, observations range: 1980/01/02-1989/12/29 Listing 2 variables: 0) const 1) djclose ? series y = 100*ldiff(djclose) Generated series y (ID 2) ? scalar mu = 0.0 Generated scalar mu (ID 3) = 0 ? scalar omega = 1 Generated scalar omega (ID 4) = 1 ? scalar alpha = 0.4 Generated scalar alpha (ID 5) = 0.4 ? scalar beta = 0.5 Generated scalar beta (ID 6) = 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 --verbose Using numerical derivatives Iteration 1: Log-likelihood = -1561.46147443 Parameters: 0.00000 1.0000 0.40000 0.50000 Gradients: 89.979 -296.97 -181.84 -396.60 Iteration 2: Log-likelihood = -1472.96367506 (steplength = 0.00032) Parameters: 0.028793 0.90497 0.34181 0.37309 Gradients: 53.018 -274.09 -163.79 -366.04 Iteration 3: Log-likelihood = -1447.77404259 (steplength = 0.00032) Parameters: -0.064045 0.85520 0.32585 0.30662 Gradients: 231.08 -235.92 -149.60 -315.06 Iteration 4: Log-likelihood = -1444.66210893 (steplength = 0.008) Parameters: -0.048367 0.80389 0.50576 0.23805 Gradients: 219.45 -197.62 -190.94 -263.91 Iteration 5: Log-likelihood = -1400.66087235 (steplength = 0.04) Parameters: -0.020901 0.76422 0.39267 0.18469 Gradients: 177.60 -130.52 -156.37 -174.31 Iteration 6: Log-likelihood = -1378.72010975 (steplength = 0.2) Parameters: 0.0018002 0.75301 0.26579 0.16997 Gradients: 133.04 -86.134 -62.471 -115.03 Iteration 7: Log-likelihood = -1375.43661347 (steplength = 1) Parameters: 0.088888 0.69792 0.23498 0.095992 Gradients: -74.989 112.68 41.097 150.49 Iteration 8: Log-likelihood = -1370.89509923 (steplength = 1) Parameters: 0.064386 0.73628 0.22325 0.14732 Gradients: -10.259 -30.131 17.878 -40.239 Iteration 9: Log-likelihood = -1370.84179073 (steplength = 1) Parameters: 0.053937 0.72411 0.26523 0.13111 Gradients: 15.082 -5.7174 -39.239 -7.6353 Iteration 10: Log-likelihood = -1370.28526304 (steplength = 1) Parameters: 0.056917 0.72388 0.23809 0.13085 Gradients: 7.8871 4.6573 2.7641 6.2198 Iteration 11: Log-likelihood = -1370.26428037 (steplength = 0.00032) Parameters: 0.059441 0.72537 0.23898 0.13284 Gradients: 1.6561 -0.82962 -0.38197 -1.1079 Iteration 12: Log-likelihood = -1370.26343966 (steplength = 0.00032) Parameters: 0.060046 0.72515 0.23888 0.13254 Gradients: 0.17639 -0.021055 0.026967 -0.028467 Iteration 13: Log-likelihood = -1370.26343939 (steplength = 0.00032) Parameters: 0.060046 0.72515 0.23889 0.13253 Gradients: 0.17676 -0.018224 0.011653 -0.024374 Iteration 14: Log-likelihood = -1370.26343279 (steplength = 1) Parameters: 0.060119 0.72501 0.23890 0.13262 Gradients: -0.0018076 0.00079581 -0.0017053 0.0013415 Iteration 14: Log-likelihood = -1370.26343279 (steplength = 0.2) Parameters: 0.060119 0.72499 0.23890 0.13263 Gradients: -0.0018076 0.00079581 -0.0017053 0.0013415 --- FINAL VALUES: Iteration 14: Log-likelihood = -1370.26343279 (steplength = 0.00032) Parameters: 0.060118 0.72499 0.23890 0.13263 Gradients: -0.0018076 0.00079581 -0.0017053 0.0013415 Tolerance = 1.81899e-012 Function evaluations: 53 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 0.0200801 2.994 0.00275 *** omega 0.724990 233390 0.000 1.00000 alpha 0.238901 0.00564566 42.316 <0.00001 *** beta 0.132635 174763 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