[Gretl-users] GARCH estimation

Dear all I use gretl 1.7.4 to estimate a GARCH model by using default menu function (i.e., \Model\Time series\GARCH ) and by the command in console. But they generate different results. The details of iterations are as follows. Any idea? ==== results by menu===== Automatic initialization of parameters Regression coefficients: theta[0] = 0.0511825 theta[1] = 1.08508 Variance parameters: alpha[0] = 0.1 beta[0] = 0.9 Iteration 1: Log-likelihood = -168.929078042 Parameters: 0.11038 1.0851 0.10000 0.90000 Gradients: -26.738 17.074 481.64 14.243 Iteration 2: Log-likelihood = -139.605272823 (steplength = 0.0016) Parameters: 0.067597 1.1124 0.87063 0.92279 Gradients: -4.4061 0.82275 -15.175 -8.1703 Iteration 3: Log-likelihood = -138.361721087 (steplength = 0.04) Parameters: -0.13607 1.1652 0.87232 0.62335 Gradients: 14.823 -0.51238 -14.088 -6.9177 Iteration 4: Log-likelihood = -137.371894269 (steplength = 0.008) Parameters: -0.12485 1.1848 0.87847 0.47302 Gradients: 13.892 -1.0676 -13.148 -5.2299 Iteration 5: Log-likelihood = -137.147777193 (steplength = 0.04) Parameters: -0.12168 1.1207 0.88177 0.43192 Gradients: 13.651 0.40209 -12.854 -4.5731 Iteration 6: Log-likelihood = -136.065550003 (steplength = 0.2) Parameters: -0.055939 1.1709 0.88165 0.29403 Gradients: 7.6020 -1.0743 -11.185 -0.64410 Iteration 7: Log-likelihood = -135.589722350 (steplength = 1) Parameters: 0.054295 1.1305 0.86108 0.32088 Gradients: -3.2400 -0.48930 -11.296 -1.6096 Iteration 8: Log-likelihood = -135.332923963 (steplength = 1) Parameters: 0.044387 1.1121 0.84171 0.26964 Gradients: -2.1320 -0.080313 -9.7947 0.99314 Iteration 9: Log-likelihood = -134.612248244 (steplength = 1) Parameters: 0.014804 1.0933 0.76024 0.27015 Gradients: 0.83895 0.60996 -7.3230 3.3510 Iteration 10: Log-likelihood = -133.876720666 (steplength = 1) Parameters: -0.034438 1.0938 0.46226 0.40605 Gradients: 6.1180 0.99752 10.528 6.9157 Iteration 11: Log-likelihood = -133.215756120 (steplength = 0.008) Parameters: 0.014505 1.1018 0.54648 0.46137 Gradients: -0.55270 0.72059 -1.2327 0.43556 Iteration 12: Log-likelihood = -133.185323523 (steplength = 0.04) Parameters: 0.010238 1.1316 0.52856 0.49641 Gradients: -0.25051 -0.14061 -0.71733 -0.28480 Iteration 13: Log-likelihood = -133.185060907 (steplength = 0.008) Parameters: 0.011028 1.1308 0.52769 0.49709 Gradients: -0.36195 -0.11592 -0.65345 -0.28715 Iteration 14: Log-likelihood = -133.185045046 (steplength = 0.04) Parameters: 0.0087095 1.1249 0.52597 0.50187 Gradients: -0.053499 0.085396 -0.65223 -0.41383 Iteration 15: Log-likelihood = -133.181789118 (steplength = 1) Parameters: 0.0081963 1.1273 0.52065 0.49465 Gradients: -0.016645 -0.0072318 0.043542 -0.00045134 Iteration 16: Log-likelihood = -133.181774062 (steplength = 1) Parameters: 0.0081232 1.1271 0.52128 0.49410 Gradients: -0.00074809 -0.00035241 -0.0012373 0.00028761 Iteration 17: Log-likelihood = -133.181774041 (steplength = 1) Parameters: 0.0081164 1.1271 0.52126 0.49413 Gradients: 6.7268e-006 4.3038e-006-1.6833e-005-1.9424e-005 Iteration 17: Log-likelihood = -133.181774041 (steplength = 1) Parameters: 0.0081164 1.1271 0.52126 0.49413 Gradients: 6.7268e-006 4.3038e-006-1.6833e-005-1.9424e-005 --- FINAL VALUES: Log-likelihood = -133.181774041 (steplength = 6.4e-005) Parameters: 0.0081164 1.1271 0.52126 0.49413 Gradients: 6.7268e-006 4.3038e-006-1.6833e-005-1.9424e-005 theta[0]: 0.00381941 (0.0406031) theta[1]: 0.530368 (0.0834569) theta[2]: 0.115430 (0.0264921) theta[3]: 0.494127 (0.192625) Function evaluations: 47 Evaluations of gradient: 17 Model 11: GARCH estimates using the 99 observations 1980:02-1988:04 Dependent variable: Y Standard errors based on Hessian VARIABLE COEFFICIENT STDERROR T STAT P-VALUE const 0.00381941 0.0406031 0.094 0.92506 Y_1 0.530368 0.0834569 6.355 <0.00001 *** alpha(0) 0.115430 0.0264921 4.357 0.00001 *** alpha(1) 0.494127 0.192625 2.565 0.01031 ** Mean of dependent variable = 0.0519415 Standard deviation of dep. var. = 0.544934 Unconditional error variance = 0.22818 Log-likelihood = -58.5562 Akaike information criterion (AIC) = 127.112 Schwarz Bayesian criterion (BIC) = 140.088 Hannan-Quinn criterion (HQC) = 132.362 ==== results by the command in console===== ? garch 0 1; Y Y(-1) --verbose Automatic initialization of parameters Regression coefficients: theta[0] = 0.0511825 theta[1] = 1.08508 Variance parameters: alpha[0] = 0.1 beta[0] = 0.9 Iteration 1: Log-likelihood = -270.911199903 Parameters: 0.11038 1.0851 0.10000 0.90000 Gradients: -125.16 -125.16 1010.7 30.388 Iteration 2: Log-likelihood = -170.537739660 (steplength = 0.0016) Parameters: -0.089875 0.88483 1.7171 0.94862 Gradients: -25.749 -25.749 -8.7587 -8.4495 Iteration 3: Log-likelihood = -161.761522666 (steplength = 0.008) Parameters: -0.29926 0.67545 1.6788 0.88214 Gradients: -11.183 -11.183 -10.840 -8.8715 Iteration 4: Log-likelihood = -158.391619816 (steplength = 0.04) Parameters: -0.31167 0.66303 1.6896 0.51071 Gradients: -10.407 -10.407 -10.879 -8.1069 Iteration 5: Log-likelihood = -157.154680098 (steplength = 0.04) Parameters: -0.31888 0.65583 1.6928 0.36062 Gradients: -10.000 -10.000 -10.621 -6.6638 Iteration 6: Log-likelihood = -155.742679661 (steplength = 0.2) Parameters: -0.35479 0.61992 1.6858 0.22820 Gradients: -7.1755 -7.1755 -10.191 -3.8497 Iteration 7: Log-likelihood = -154.844791246 (steplength = 1) Parameters: -0.48452 0.49018 1.6370 0.10641 Gradients: 5.3640 5.3640 -8.7104 3.1207 Iteration 8: Log-likelihood = -154.573226547 (steplength = 1) Parameters: -0.45621 0.51850 1.6312 0.19907 Gradients: 2.1978 2.1978 -10.062 -2.3733 Iteration 9: Log-likelihood = -154.393792855 (steplength = 1) Parameters: -0.41196 0.56275 1.6201 0.14415 Gradients: -2.0434 -2.0434 -9.3522 0.38397 Iteration 10: Log-likelihood = -153.968693027 (steplength = 1) Parameters: -0.42290 0.55181 1.5786 0.15683 Gradients: -0.97944 -0.97944 -9.3680 0.21026 Iteration 11: Log-likelihood = -150.992406742 (steplength = 0.04) Parameters: -0.46207 0.51263 1.2039 0.16524 Gradients: 3.4088 3.4088 -6.1548 7.6249 Iteration 12: Log-likelihood = -148.359103161 (steplength = 0.008) Parameters: -0.43062 0.54409 0.75562 0.32000 Gradients: -2.3822 -2.3822 1.9263 6.8635 Iteration 13: Log-likelihood = -148.097032678 (steplength = 0.008) Parameters: -0.45911 0.51560 0.71943 0.36973 Gradients: 0.75946 0.75946 1.8664 4.7097 Iteration 14: Log-likelihood = -147.949161098 (steplength = 1) Parameters: -0.45122 0.52348 0.75142 0.44913 Gradients: -0.66911 -0.66911 -1.6394 -0.55287 Iteration 15: Log-likelihood = -147.921370789 (steplength = 1) Parameters: -0.45617 0.51854 0.69072 0.47194 Gradients: -0.69320 -0.69320 0.78234 -0.15366 Iteration 16: Log-likelihood = -147.911096499 (steplength = 1) Parameters: -0.46083 0.51388 0.71098 0.45901 Gradients: 0.15242 0.15242 -0.086460 0.020146 Iteration 17: Log-likelihood = -147.910849840 (steplength = 1) Parameters: -0.45975 0.51495 0.70935 0.46012 Gradients: -0.0033672 -0.0033672 -0.010763 -0.0083438 Iteration 18: Log-likelihood = -147.910848410 (steplength = 1) Parameters: -0.45979 0.51491 0.70914 0.46007 Gradients: 0.00068169 0.00068169 0.00046165 -0.00074704 Iteration 19: Log-likelihood = -147.910848385 (steplength = 1) Parameters: -0.45979 0.51492 0.70917 0.46004 Gradients: 8.9567e-005 8.9567e-005 8.2642e-006 -0.00017120 Iteration 20: Log-likelihood = -147.910848385 (steplength = 0.008) Parameters: -0.45979 0.51492 0.70917 0.46004 Gradients: 1.1075e-005 1.1075e-005 4.6432e-005 -0.00012421 Iteration 21: Log-likelihood = -147.910848385 (steplength = 0.008) Parameters: -0.45979 0.51492 0.70917 0.46004 Gradients: 5.2761e-005 5.2761e-005 3.4521e-005-8.0059e-005 Iteration 22: Log-likelihood = -147.910848385 (steplength = 0.008) Parameters: -0.45979 0.51492 0.70917 0.46004 Gradients: 4.1306e-005 4.1306e-005 5.3314e-006-9.2102e-005 Iteration 23: Log-likelihood = -147.910848385 (steplength = 1) Parameters: -0.45978 0.51492 0.70917 0.46003 Gradients: -2.4463e-006-2.4463e-006 2.1778e-006 7.0214e-006 Iteration 23: Log-likelihood = -147.910848385 (steplength = 1) Parameters: -0.45978 0.51492 0.70917 0.46003 Gradients: -2.4463e-006-2.4463e-006 2.1778e-006 7.0214e-006 --- FINAL VALUES: Log-likelihood = -147.910848385 (steplength = 0.0016) Parameters: -0.45978 0.51492 0.70917 0.46003 Gradients: -2.4463e-006-2.4463e-006 2.1778e-006 7.0214e-006 theta[0]: -0.216364 (0.171258) theta[1]: 0.242311 (0.0635179) theta[2]: 0.157041 (0.0421745) theta[3]: 0.460033 (0.177473) Function evaluations: 58 Evaluations of gradient: 23 Model 10: GARCH estimates using the 99 observations 1980:02-1988:04 Dependent variable: Y Standard errors based on Hessian VARIABLE COEFFICIENT STDERROR T STAT P-VALUE const -0.216364 0.171258 -1.263 0.20645 Y_1 0.242311 0.0635179 3.815 0.00014 *** alpha(0) 0.157041 0.0421745 3.724 0.00020 *** alpha(1) 0.460033 0.177473 2.592 0.00954 *** Mean of dependent variable = 0.0519415 Standard deviation of dep. var. = 0.544934 Unconditional error variance = 0.290835 Log-likelihood = -73.2853 Akaike information criterion (AIC) = 156.571 Schwarz Bayesian criterion (BIC) = 169.546 Hannan-Quinn criterion (HQC) = 161.82