gretl version 1.9.7 Current session: 2012-03-26 03:47 #Zkouska MLE odhadu AR(7)-GARCH(1,1)-T s DOF = 6.433 pro allRng na celem samplu #Chceme dosahnout stejnych odhadu jake ma Eviews #LogLik funkci mame z http://faculty.chicagobooth.edu/jeffrey.russell/teaching/finecon/readings/glossary.pdf p15 #LogLik funkce v Eviews je http://www.scribd.com/doc/44246798/EViews-7-Users-Guide-II p. 198 #http://lists.wfu.edu/pipermail/gretl-users/2006-June/000756.html - ARMA GARCH MLE odhad #Estimator is pretty close to Eviews built-in ARMA-GARCH FRAMEWORK # --------------- ARMA 7,5 initial values ---------------- # #scalar c = 0.009528 #scalar a1 = -0.809 #scalar a2 = -0.485 #scalar a3 = 0.561 #scalar a4 = 0.799 #scalar a5 = 0.818 #scalar a6 = -0.047 #scalar a7 = -0.0123 #scalar ma1 = 0.9399 #scalar ma2 = 0.743 #scalar ma3 = -0.295 #scalar ma4 = -0.618 #scalar ma5 = -0.785 ? scalar c = 0.009528 Replaced scalar c = 0.009528 ? scalar a1 = 0.63 Replaced scalar a1 = 0.63 ? scalar a2 = 0.35 Replaced scalar a2 = 0.35 ? scalar a3 = -0.38 Replaced scalar a3 = -0.38 ? scalar a4 = -0.499 Replaced scalar a4 = -0.499 ? scalar a5 = 0.893 Replaced scalar a5 = 0.893 ? scalar a6 = -0.061 Replaced scalar a6 = -0.061 ? scalar ma1 = -0.51 Replaced scalar ma1 = -0.51 ? scalar ma2 = -0.30 Replaced scalar ma2 = -0.3 ? scalar ma3 = 0.347 Replaced scalar ma3 = 0.347 ? scalar ma4 = 0.589 Replaced scalar ma4 = 0.589 ? scalar ma5 = -0.787 Replaced scalar ma5 = -0.787 # GARCH - h[t] = cg + ga*h[t-1] + arc*e^2[t-1] ? scalar cg = 0.000005 Replaced scalar cg = 5e-006 ? scalar ga = 0.914 Replaced scalar ga = 0.914 ? scalar arc = 0.0586 Replaced scalar arc = 0.0586 ? scalar dof = 5.62 Replaced scalar dof = 5.62 #mle ll = check ? ( -0.5*log(pi*(dof-2)) - lngamma(dof/2) + lngamma((dof + 1)/2) -0.5*log(h) - 0.5*(dof + 1)*log(1 + (dof - 2)^(-1)*h^(-1)*e^2)) : NA # MLE funkce z Eviews dokumentace ? mle ll = ( -0.5*log(pi*(dof-2)) - lngamma(dof/2) + lngamma((dof + 1)/2) \ -0.5*log(h) - 0.5*(dof + 1)*log(1 + (dof - 2)^(-1)*h^(-1)*e^2)) # MLE \ funkce z Eviews dokumentace ? series e = 0 ? series e = allRng - c - a1*allRng(-1) - a2*allRng(-2) - a3*allRng(-3) - \ a4*allRng(-4) - a5*allRng(-5) - a6*allRng(-6) - ma1*e(-1) - ma2*e(-2) - \ ma3*e(-3) - ma4*e(-4) - ma5*e(-5) #ARMA(7,5) process ? series h = var(allRng) ? series h = cg + ga*h(-1) + arc*(e(-1))^2 # GARCH(1,1) ? params c a1 a2 a3 a4 a5 a6 ma1 ma2 ma3 ma4 ma5 cg ga arc dof # pro \ ARMA(7,5) proces ? end mle --verbose Using numerical derivatives Iteration 1: loglikelihood = 2036.75229635 Parameters: 0.0095280 0.63000 0.35000 -0.38000 -0.49900 0.89300 -0.061000 -0.51000 -0.30000 0.34700 0.58900 -0.78700 5.0000e-006 0.91400 0.058600 5.6200 Gradients: -1.2321e+005 -1498.9 -1499.8 -1499.3 -1500.3 -1499.2 -1495.3 3129.9 3121.9 3117.3 3110.3 3108.3 8.8396e+006 4147.8 5502.8 43.702 (norm 3.32e+001) Iteration 2: loglikelihood = 2155.17613357 (steplength = 6.5536e-012) Parameters: 0.0095272 0.63000 0.35000 -0.38000 -0.49900 0.89300 -0.061000 -0.51000 -0.30000 0.34700 0.58900 -0.78700 6.2931e-005 0.91400 0.058600 5.6200 Gradients: -1.0390e+005 -1257.7 -1260.1 -1259.8 -1261.9 -1259.9 -1255.7 2644.0 2635.0 2631.2 2627.5 2631.6 -5.5944e+005 -626.92 -356.01 8.6534 (norm 2.73e+001) Iteration 3: loglikelihood = 2955.58463440 (steplength = 1.024e-007) Parameters: -0.0012316 0.62987 0.34987 -0.38013 -0.49913 0.89287 -0.061130 -0.50973 -0.29973 0.34727 0.58927 -0.78673 4.0753e-005 0.91396 0.058599 5.6200 Gradients: 78468. 957.81 946.68 945.80 941.84 948.87 958.21 479.17 467.31 465.48 460.64 472.57 -9.2601e+006 -4640.8 -494.11 -30.430 (norm 2.34e+001) Iteration 4: loglikelihood = 3393.20858825 (steplength = 1.28e-005) Parameters: -0.0015639 0.62987 0.34978 -0.38022 -0.49926 0.89280 -0.061105 -0.48949 -0.27962 0.36734 0.60926 -0.76668 8.5105e-006 0.91289 0.10179 5.6201 Gradients: 1.7722e+005 2068.3 1992.5 1975.6 1994.9 2071.6 2139.1 989.19 815.00 742.75 787.73 964.91 -2.0120e+007 -2993.2 -911.24 -15.967 (norm 2.66e+001) Iteration 5: loglikelihood = 3499.63366712 (steplength = 2.62144e-013) Parameters: -0.0015638 0.62987 0.34978 -0.38022 -0.49926 0.89280 -0.061105 -0.48949 -0.27962 0.36734 0.60926 -0.76668 3.2362e-006 0.91289 0.10179 5.6201 Gradients: 2.4769e+005 2837.1 2741.8 2722.3 2751.2 2853.3 2940.3 1363.4 1136.1 1040.9 1101.7 1336.0 -1.7959e+007 -1616.4 -847.98 -5.6321 (norm 2.85e+001) Iteration 6: loglikelihood = 3521.58510735 (steplength = 3.2768e-011) Parameters: -0.0015365 0.62987 0.34978 -0.38022 -0.49926 0.89280 -0.061104 -0.48949 -0.27962 0.36734 0.60926 -0.76668 2.3443e-006 0.91289 0.10179 5.6201 Gradients: 2.6391e+005 3009.5 2909.4 2889.3 2921.0 3029.4 3121.5 1432.0 1191.4 1090.6 1156.1 1404.9 -1.5251e+007 -1228.5 -746.39 -3.1975 (norm 2.88e+001) Iteration 7: loglikelihood = 3894.19337815 (steplength = 1.28e-005) Parameters: -0.00019118 0.63094 0.35046 -0.37967 -0.49870 0.89361 -0.059995 -0.49146 -0.28228 0.36447 0.60658 -0.76870 4.6015e-006 0.84079 0.10097 5.6196 Gradients: 1.8455e+005 2085.8 1937.7 1904.9 1941.0 2099.3 2235.5 443.27 130.86 10.989 99.658 444.85 -2.7945e+007 -1135.3 -513.67 -12.003 (norm 2.18e+001) Iteration 8: loglikelihood = 3973.30420391 (steplength = 2.56e-006) Parameters: 0.00028275 0.63077 0.34957 -0.38074 -0.49963 0.89341 -0.059524 -0.49735 -0.28953 0.35678 0.59932 -0.77438 4.5929e-006 0.82595 0.10615 5.6194 Gradients: 1.1490e+005 1306.0 1208.6 1199.3 1202.9 1305.1 1394.6 144.67 -1.4869 -38.475 -18.881 169.26 -3.1484e+007 -1115.7 -452.09 -12.914 (norm 1.77e+001) Iteration 9: loglikelihood = 4001.34855085 (steplength = 6.4e-005) Parameters: 0.00048000 0.62929 0.35146 -0.37519 -0.49874 0.89055 -0.065292 -0.50934 -0.28282 0.37484 0.60753 -0.78129 2.9999e-006 0.81500 0.15887 5.6188 Gradients: 66803. 853.42 403.85 221.13 369.98 812.12 1196.1 337.11 -1276.8 -1891.3 -1118.6 578.23 -2.7059e+007 -781.49 -397.59 -9.0034 (norm 1.77e+001) Iteration 10: loglikelihood = 4038.56965457 (steplength = 6.4e-005) Parameters: 0.00058932 0.63169 0.34826 -0.37690 -0.50542 0.88792 -0.063655 -0.49392 -0.28452 0.37553 0.61690 -0.74547 1.5219e-007 0.79926 0.25504 5.6179 Gradients: 64826. 805.30 515.67 327.62 383.84 625.98 946.75 -9.8406 -696.00 -878.75 -413.63 355.51 2.4139e+007 105.81 -58.042 -2.9854 (norm 1.33e+001) Iteration 11: loglikelihood = 4040.66377027 (steplength = 6.4e-005) Parameters: 0.00071813 0.63449 0.34758 -0.37983 -0.51158 0.88316 -0.063150 -0.50179 -0.28935 0.37799 0.62228 -0.73809 6.1290e-008 0.79840 0.25791 5.6176 Gradients: 61509. 814.20 583.71 385.72 388.73 539.69 836.87 76.704 -339.16 -519.88 -310.19 95.744 3.2568e+007 175.44 -12.864 -2.5332 (norm 1.22e+001) Iteration 12: loglikelihood = 4041.87284671 (steplength = 6.4e-005) Parameters: 0.00083860 0.64240 0.34930 -0.38353 -0.52145 0.87467 -0.061830 -0.50328 -0.28960 0.38068 0.62251 -0.73664 -6.0550e-009 0.79780 0.26015 5.6172 Gradients: 61563. 751.41 568.19 423.82 485.61 643.57 875.44 -0.80057 -308.91 -426.04 -200.06 140.17 4.0216e+007 231.00 22.610 -2.4086 (norm 1.24e+001) Iteration 13: loglikelihood = 4042.28318824 (steplength = 6.4e-005) Parameters: 0.00076034 0.64572 0.34977 -0.38415 -0.52313 0.87531 -0.057071 -0.50467 -0.28924 0.38218 0.62188 -0.73617 -1.5936e-008 0.79780 0.26076 5.6168 Gradients: 63360. 748.06 583.30 435.13 498.84 646.73 863.59 -1.9228 -276.97 -400.46 -189.20 117.45 4.1176e+007 236.72 25.777 -2.4436 (norm 1.23e+001) Iteration 14: loglikelihood = 4042.67149715 (steplength = 0.00032) Parameters: 0.00088418 0.64416 0.34323 -0.39674 -0.53369 0.87841 -0.042457 -0.51062 -0.27946 0.38737 0.61627 -0.73455 -5.7438e-008 0.79732 0.26237 5.6144 Gradients: 68257. 853.03 724.09 568.52 605.59 676.92 878.40 21.881 -175.55 -279.38 -111.03 77.864 4.6701e+007 270.39 48.394 -2.5385 (norm 1.27e+001) Iteration 15: loglikelihood = 4042.89144347 (steplength = 0.00032) Parameters: 0.00085828 0.64372 0.34699 -0.39842 -0.53397 0.87787 -0.040876 -0.51469 -0.27403 0.38596 0.61303 -0.73132 -6.0163e-008 0.79732 0.26251 5.6124 Gradients: 68471. 851.60 705.49 572.68 613.16 674.02 885.54 25.016 -184.56 -264.12 -102.43 70.772 4.7122e+007 272.15 49.314 -2.5738 (norm 1.27e+001) Iteration 16: loglikelihood = 4046.75378786 (steplength = 0.008) Parameters: 0.00096301 0.62864 0.32442 -0.39454 -0.44955 0.74601 0.032006 -0.57836 -0.19717 0.39846 0.51422 -0.65949 3.0991e-008 0.79725 0.25795 5.5235 Gradients: 58877. 769.97 583.82 458.41 511.64 620.47 776.74 14.513 -246.20 -304.36 -91.203 135.02 3.7686e+007 213.79 16.348 -2.3768 (norm 1.15e+001) Iteration 17: loglikelihood = 4054.49118386 (steplength = 0.008) Parameters: 0.00099206 0.77809 0.21241 -0.50769 -0.26826 0.66724 0.0046983 -0.67793 -0.079506 0.40677 0.39939 -0.57297 1.0462e-007 0.79797 0.25237 5.3354 Gradients: 50775. 624.49 612.32 626.26 540.89 505.62 525.41 4.5955 24.083 77.529 20.948 -37.883 3.2835e+007 188.42 1.6016 -2.1714 (norm 1.03e+001) Iteration 18: loglikelihood = 4057.79070341 (steplength = 0.0016) Parameters: 0.0011455 0.91423 0.087304 -0.53937 -0.16018 0.63896 -0.063848 -0.77090 0.012164 0.46174 0.22511 -0.46050 4.2180e-007 0.79890 0.23909 5.1577 Gradients: 36956. 327.49 399.14 506.07 582.35 495.06 490.37 -235.48 -138.16 70.285 221.09 127.43 1.4673e+007 50.363 -79.296 -1.9585 (norm 9.65e+000) Iteration 19: loglikelihood = 4064.53825869 (steplength = 0.04) Parameters: 0.0011158 0.84010 0.14081 -0.45183 -0.31894 0.71014 -0.037154 -0.71027 -0.048949 0.40443 0.36641 -0.55218 4.9442e-007 0.80073 0.23052 5.0111 Gradients: 21640. 200.89 279.04 353.57 420.66 298.53 276.61 -173.44 -52.845 104.92 212.98 58.867 1.3596e+007 51.584 -72.829 -1.1748 (norm 8.28e+000) Iteration 20: loglikelihood = 4068.00474957 (steplength = 0.2) Parameters: 0.00093243 0.98246 -0.35315 0.23399 -0.73759 0.74702 0.033559 -0.84032 0.39613 -0.27580 0.89178 -0.73344 6.0373e-007 0.80709 0.20108 4.8104 Gradients: -10189. -185.98 -80.520 30.057 -124.41 -57.684 -76.516 -181.92 -7.5453 208.02 -55.218 27.265 1.5916e+007 121.37 -19.035 0.62356 (norm 6.90e+000) Iteration 21: loglikelihood = 4072.97049310 (steplength = 0.2) Parameters: 0.00084169 0.90105 -0.14809 0.041673 -0.66179 0.76960 0.013876 -0.76417 0.20058 -0.082699 0.80065 -0.73154 8.0376e-007 0.81277 0.16921 4.8013 Gradients: -20189. -268.87 -236.12 -180.17 -296.62 -187.87 -186.83 -123.09 38.031 76.037 -142.80 37.966 1.5476e+007 165.27 27.759 2.5362 (norm 8.14e+000) Iteration 22: loglikelihood = 4079.10242254 (steplength = 0.04) Parameters: 0.00081745 0.93278 -0.13299 -0.061558 -0.53057 0.71618 -0.0029082 -0.80019 0.19432 0.010018 0.66858 -0.66276 9.5139e-007 0.81606 0.14518 4.8903 Gradients: -33028. -342.29 -411.29 -418.39 -451.33 -410.34 -303.28 56.608 -4.2861 -38.598 -145.21 -136.70 1.5423e+007 201.13 72.323 3.1003 (norm 9.35e+000) Iteration 23: loglikelihood = 4082.72647453 (steplength = 0.2) Parameters: 0.00082871 0.91932 -0.12663 -0.053752 -0.54474 0.70846 0.013354 -0.79915 0.19224 0.011631 0.67020 -0.66392 1.0524e-006 0.81693 0.13671 5.0749 Gradients: -11667. -102.55 -155.72 -156.99 -179.35 -160.63 -84.190 45.596 8.5650 -11.946 -99.183 -119.42 1.1181e+007 149.20 39.792 1.6046 (norm 6.50e+000) Iteration 24: loglikelihood = 4084.38335754 (steplength = 0.2) Parameters: 0.00078750 0.91708 -0.12427 -0.053664 -0.54587 0.70585 0.021096 -0.80102 0.18970 0.014529 0.66676 -0.66738 1.1532e-006 0.81850 0.12300 5.2486 Gradients: -13016. -134.77 -168.17 -161.00 -180.57 -177.99 -129.73 17.272 10.350 13.614 -57.854 -96.430 1.0343e+007 154.07 60.651 1.3597 (norm 6.43e+000) Iteration 25: loglikelihood = 4086.52578827 (steplength = 1) Parameters: 0.00083003 0.90990 -0.11632 -0.062033 -0.54195 0.68827 0.034991 -0.80246 0.16879 0.039076 0.64893 -0.66710 1.5199e-006 0.82435 0.092666 5.4906 Gradients: 9423.0 141.51 136.29 129.71 124.85 113.33 120.78 23.111 43.809 34.088 -9.5214 -59.899 1.2591e+006 58.641 48.452 -0.16601 (norm 5.24e+000) Iteration 26: loglikelihood = 4086.79538601 (steplength = 0.2) Parameters: 0.00081005 0.90985 -0.11221 -0.070309 -0.53517 0.68791 0.035341 -0.80132 0.16492 0.046230 0.64219 -0.66602 1.5093e-006 0.82353 0.096377 5.5430 Gradients: 6555.7 96.956 102.26 103.15 97.992 77.126 73.655 4.7491 39.931 45.740 8.5841 -51.980 2.8130e+005 38.220 23.620 -0.35204 (norm 4.40e+000) Iteration 27: loglikelihood = 4087.17859538 (steplength = 1) Parameters: 0.00071350 0.91450 -0.098303 -0.10298 -0.50289 0.68467 0.030902 -0.79923 0.15100 0.071465 0.61791 -0.66095 1.4849e-006 0.82472 0.097989 5.4647 Gradients: -2528.1 -49.909 -34.101 -21.377 -25.333 -46.903 -60.134 -34.003 17.553 47.482 21.746 -40.994 4.2333e+005 39.148 21.856 -0.081462 (norm 3.61e+000) Iteration 28: loglikelihood = 4087.42014788 (steplength = 1) Parameters: 0.00073516 0.91462 -0.085433 -0.13255 -0.47777 0.67918 0.026443 -0.79675 0.13576 0.096206 0.59771 -0.65617 1.4534e-006 0.82569 0.10185 5.3946 Gradients: -5469.6 -76.727 -55.597 -41.366 -45.398 -65.373 -82.018 -40.265 18.106 51.796 29.493 -32.365 -2.7056e+005 22.092 0.38710 -0.11814 (norm 3.96e+000) Iteration 29: loglikelihood = 4087.86036752 (steplength = 1) Parameters: 0.00071595 0.91258 -0.056383 -0.18953 -0.43181 0.66973 0.021226 -0.79212 0.10371 0.14572 0.56023 -0.64952 1.3966e-006 0.83075 0.10413 5.0996 Gradients: -4647.7 -66.963 -39.736 -28.470 -34.028 -49.003 -71.131 -44.843 22.315 53.201 33.292 -24.873 -6.0712e+005 11.100 -12.886 0.16793 (norm 3.66e+000) Iteration 30: loglikelihood = 4088.39491954 (steplength = 1) Parameters: 0.00067814 0.90973 -0.011689 -0.26687 -0.37581 0.66487 0.010097 -0.78841 0.050880 0.21622 0.51326 -0.64910 1.3238e-006 0.83822 0.10250 5.0648 Gradients: -9283.8 -89.460 -78.304 -94.863 -106.52 -95.108 -100.80 -7.4512 36.531 21.396 -9.8277 -37.180 -1.9013e+006 -12.010 -29.656 0.048772 (norm 4.15e+000) Iteration 31: loglikelihood = 4088.89919943 (steplength = 1) Parameters: 0.00060537 0.90593 0.025919 -0.32583 -0.34688 0.67096 0.0054702 -0.78709 0.011061 0.26992 0.48299 -0.65636 1.2089e-006 0.84858 0.097302 4.7941 Gradients: -305.29 5.9029 24.044 10.156 2.3026 15.706 -2.9570 -5.9147 18.014 -7.6136 -16.905 -9.5889 2.2954e+005 22.276 -2.3760 0.80918 (norm 2.02e+000) Iteration 32: loglikelihood = 4089.40137910 (steplength = 1) Parameters: 0.00054369 0.90667 0.021979 -0.30587 -0.37484 0.69123 0.0025638 -0.79113 0.014475 0.25534 0.50058 -0.67117 1.1981e-006 0.84998 0.091941 5.1154 Gradients: 759.62 7.4076 10.583 -9.0512 -5.9140 11.566 6.1783 0.56343 -10.649 -46.319 -33.805 -2.0152 -1.7494e+005 23.155 6.9245 0.25348 (norm 2.13e+000) Iteration 33: loglikelihood = 4089.67017429 (steplength = 1) Parameters: 0.00054435 0.90840 -0.0044848 -0.25013 -0.42780 0.71363 0.0024614 -0.79792 0.046154 0.20328 0.54250 -0.68655 1.1921e-006 0.84846 0.090139 5.3336 Gradients: -1003.6 -9.4197 -11.798 -22.225 -16.158 -14.456 -13.419 0.68222 -10.241 -27.114 -15.498 -7.1332 1.1114e+006 46.880 28.306 0.16360 (norm 2.45e+000) Iteration 34: loglikelihood = 4089.78533287 (steplength = 1) Parameters: 0.00050907 0.90947 -0.0048767 -0.24544 -0.43738 0.72485 -0.0013375 -0.80083 0.048224 0.19599 0.55074 -0.69532 1.1525e-006 0.85107 0.091159 5.3382 Gradients: 1370.1 14.908 -1.1379 -11.759 -2.2603 7.5223 20.400 3.2113 -38.967 -57.707 -30.247 6.9046 2.5957e+005 29.694 10.485 0.010976 (norm 2.34e+000) Iteration 35: loglikelihood = 4089.86900315 (steplength = 1) Parameters: 0.00050651 0.91290 -0.010106 -0.23988 -0.44263 0.72906 -0.0034919 -0.80451 0.054524 0.18545 0.55795 -0.70018 1.1537e-006 0.85276 0.091080 5.3096 Gradients: -293.65 -4.3608 -13.923 -12.518 -6.8935 -2.4955 3.2300 -4.2288 -33.593 -35.197 -13.948 13.308 -1.1209e+006 6.4547 -7.1514 -0.10736 (norm 1.75e+000) Iteration 36: loglikelihood = 4089.91339498 (steplength = 1) Parameters: 0.00049854 0.91615 -0.011989 -0.24168 -0.44017 0.73071 -0.0063574 -0.80661 0.055064 0.18374 0.55869 -0.70266 1.1388e-006 0.85501 0.090062 5.2274 Gradients: -1068.6 -9.6835 -19.890 -18.103 -16.758 -9.7806 -2.2296 -2.8397 -33.119 -33.563 -16.039 15.628 -1.1011e+006 7.2611 -4.9897 0.026181 (norm 2.04e+000) Iteration 37: loglikelihood = 4089.96002190 (steplength = 1) Parameters: 0.00048644 0.92027 -0.017467 -0.23697 -0.44150 0.73125 -0.0080117 -0.80915 0.057977 0.17777 0.56249 -0.70503 1.1216e-006 0.85738 0.089249 5.1271 Gradients: 702.65 7.5103 0.18551 4.1354 3.6420 11.887 17.303 -4.2703 -24.819 -21.072 -10.128 16.120 -1.0892e+006 7.6726 -3.7140 0.16055 (norm 1.83e+000) Iteration 38: loglikelihood = 4089.96832644 (steplength = 1.04858e-014) Parameters: 0.00048644 0.92027 -0.017467 -0.23697 -0.44150 0.73125 -0.0080117 -0.80915 0.057977 0.17777 0.56249 -0.70503 1.1102e-006 0.85738 0.089249 5.1271 Gradients: 385.68 3.8945 -3.2405 0.84992 0.41607 8.4088 13.633 -4.5861 -24.950 -20.994 -9.9020 16.127 -3.5876e+005 19.251 4.2516 0.26411 (norm 1.85e+000) Iteration 39: loglikelihood = 4089.96835517 (steplength = 8.192e-010) Parameters: 0.00048663 0.92027 -0.017467 -0.23697 -0.44150 0.73125 -0.0080117 -0.80915 0.057977 0.17777 0.56249 -0.70503 1.1103e-006 0.85738 0.089249 5.1271 Gradients: 211.96 2.0163 -5.1206 -1.0482 -1.5076 6.4737 11.697 -4.5918 -24.955 -21.023 -9.9629 16.053 -3.5877e+005 19.261 4.2710 0.26651 (norm 1.81e+000) Iteration 40: loglikelihood = 4089.98960496 (steplength = 1.28e-005) Parameters: 0.00048683 0.92026 -0.017566 -0.23701 -0.44155 0.73130 -0.0078879 -0.80922 0.057643 0.17749 0.56236 -0.70482 1.1038e-006 0.85771 0.089358 5.1272 Gradients: 222.78 7.5101 6.4723 9.4509 1.3863 0.44915 2.0622 0.25833 -6.0110 -1.1675 -3.0485 5.1885 -3.5456e+005 18.688 2.8373 0.25987 (norm 1.47e+000) Iteration 41: loglikelihood = 4090.02037971 (steplength = 0.00032) Parameters: 0.00041597 0.92287 -0.015255 -0.23324 -0.44194 0.73015 -0.0084010 -0.80903 0.055199 0.17749 0.56110 -0.70260 8.8016e-007 0.86960 0.092603 5.1273 Gradients: 467.42 -42.655 -43.973 -30.951 -19.651 -12.228 -16.672 -25.664 -21.755 -3.8845 7.6261 10.642 -56443. 2.0411 -34.658 0.15191 (norm 2.57e+000) Iteration 42: loglikelihood = 4090.07241605 (steplength = 6.4e-005) Parameters: 0.00045445 0.92250 -0.015539 -0.23254 -0.44283 0.72884 -0.0097384 -0.80964 0.054220 0.17814 0.56112 -0.70177 8.0133e-007 0.87447 0.092695 5.1274 Gradients: 408.10 -14.050 -21.718 -14.875 -2.0993 10.389 13.047 -10.566 -16.344 -9.9190 -0.10430 8.6299 1.8638e+005 -4.8589 -47.807 0.086731 (norm 1.81e+000) Iteration 43: loglikelihood = 4090.25755380 (steplength = 0.00032) Parameters: 0.00043119 0.92341 -0.015613 -0.22968 -0.44374 0.72807 -0.0096957 -0.81036 0.051750 0.18000 0.56080 -0.69954 6.9499e-007 0.88677 0.084418 5.1276 Gradients: 462.41 -2.5923 -24.610 -42.752 -39.322 -21.949 -0.29226 28.067 6.6733 -25.127 -39.348 -33.243 6.0795e+005 3.2249 -38.364 0.22860 (norm 2.82e+000) Iteration 44: loglikelihood = 4090.47190973 (steplength = 6.4e-005) Parameters: 0.00043009 0.92762 -0.016076 -0.22296 -0.44950 0.72359 -0.0097279 -0.80930 0.045327 0.18392 0.55616 -0.69562 3.6714e-007 0.92581 0.057898 5.1282 Gradients: -1118.3 -53.861 -55.990 -52.410 -12.228 8.2530 1.1260 -12.425 -9.0122 -19.598 1.7519 4.9267 7.6113e+006 83.445 43.731 0.80904 (norm 3.35e+000) Iteration 45: loglikelihood = 4090.47857281 (steplength = 0.00032) Parameters: 0.00042768 0.92629 -0.016956 -0.22340 -0.44887 0.72512 -0.0090614 -0.80854 0.046724 0.18425 0.55581 -0.69587 3.2799e-007 0.92876 0.057223 5.1283 Gradients: -1104.0 -49.913 -50.954 -50.175 -15.686 -0.080713 -7.1898 -12.612 -6.6059 -15.672 4.0464 3.4006 8.9762e+006 85.226 39.749 0.80377 (norm 3.28e+000) Iteration 46: loglikelihood = 4090.48235885 (steplength = 0.00032) Parameters: 0.00042989 0.92586 -0.016733 -0.22329 -0.44871 0.72541 -0.0096345 -0.80818 0.047173 0.18388 0.55548 -0.69527 3.2737e-007 0.92898 0.056958 5.1283 Gradients: -1163.3 -49.958 -52.891 -52.073 -17.061 -0.74845 -5.7435 -13.021 -8.1206 -16.142 4.0347 3.2331 9.0981e+006 87.713 42.630 0.81634 (norm 3.33e+000) Iteration 47: loglikelihood = 4090.48256198 (steplength = 0.0016) Parameters: 0.00043832 0.92616 -0.016831 -0.22392 -0.44943 0.72543 -0.0093741 -0.80733 0.048131 0.18430 0.55573 -0.69329 3.2663e-007 0.92908 0.056941 5.1284 Gradients: -1191.7 -52.404 -53.017 -50.275 -15.551 -2.0739 -7.6400 -13.864 -8.5669 -16.568 2.3298 -0.81625 9.0139e+006 85.960 40.695 0.80858 (norm 3.31e+000) Iteration 48: loglikelihood = 4090.50176845 (steplength = 0.008) Parameters: 0.00045003 0.92388 -0.018473 -0.22175 -0.44861 0.72230 -0.0064812 -0.80579 0.049305 0.18608 0.55292 -0.69047 3.3913e-007 0.92827 0.057122 5.1294 Gradients: -1083.7 -50.063 -49.400 -49.812 -12.723 -1.4764 -8.9280 -18.131 -9.6569 -17.515 7.3969 1.9126 8.1643e+006 78.481 35.501 0.77760 (norm 3.27e+000) Iteration 49: loglikelihood = 4090.54876828 (steplength = 0.008) Parameters: 0.00049352 0.91488 -0.017835 -0.22584 -0.42917 0.69199 0.012420 -0.80813 0.066163 0.18006 0.54905 -0.67783 3.5217e-007 0.92944 0.054920 5.1386 Gradients: -741.86 -38.524 -46.157 -40.193 -19.592 1.4214 -13.851 -12.543 -9.8710 -11.298 -4.4767 -0.80284 6.1692e+006 58.468 31.088 0.65917 (norm 2.88e+000) Iteration 50: loglikelihood = 4090.75034754 (steplength = 0.008) Parameters: 0.00046688 0.92592 -0.026622 -0.23292 -0.41820 0.69071 0.010300 -0.82578 0.079511 0.18230 0.53340 -0.67327 3.7225e-007 0.92943 0.054033 5.1493 Gradients: -272.39 -23.210 -33.078 -24.174 -10.312 -6.2273 -19.683 2.1786 -4.8657 -4.1432 -0.65829 -7.3093 3.1221e+006 22.112 8.8155 0.48470 (norm 2.09e+000) Iteration 51: loglikelihood = 4090.98205692 (steplength = 0.0016) Parameters: 0.00046047 0.94663 -0.049263 -0.24205 -0.39354 0.68839 -0.00024364 -0.83370 0.089276 0.18431 0.52128 -0.66885 3.9816e-007 0.92939 0.052753 5.1638 Gradients: -113.76 -12.413 -13.809 -16.346 -24.024 -19.375 -22.855 3.1415 3.5180 -2.6317 -14.017 -14.074 -3.0808e+005 -17.203 -11.669 0.28242 (norm 2.20e+000) Iteration 52: loglikelihood = 4091.05860656 (steplength = 0.2) Parameters: 0.00046940 0.92750 -0.040781 -0.20556 -0.45517 0.72401 -0.00090086 -0.81453 0.080304 0.15314 0.57596 -0.69903 4.1733e-007 0.92660 0.053885 5.2525 Gradients: -431.73 -9.9248 -11.928 -15.162 -26.853 -24.743 -25.354 6.1227 4.7842 -0.11309 -15.937 -14.589 8.8502e+005 8.8790 8.0851 0.27993 (norm 2.21e+000) Iteration 53: loglikelihood = 4091.11012593 (steplength = 0.2) Parameters: 0.00046795 0.91843 -0.014170 -0.23366 -0.44585 0.73129 -0.0066363 -0.80517 0.054899 0.17827 0.56418 -0.70053 4.3107e-007 0.92443 0.054670 5.3390 Gradients: -509.71 -7.5953 -9.7503 -12.115 -22.017 -21.456 -20.955 6.3218 4.2797 0.15733 -12.014 -11.791 2.0200e+006 30.418 24.209 0.23688 (norm 2.34e+000) Iteration 54: loglikelihood = 4091.13865669 (steplength = 0.2) Parameters: 0.00046926 0.91871 -0.013897 -0.23165 -0.45000 0.73528 -0.0090571 -0.80464 0.052916 0.17746 0.56602 -0.70283 4.3319e-007 0.92452 0.054703 5.3604 Gradients: -248.52 -4.6516 -6.1698 -6.2270 -10.995 -10.032 -9.9133 2.6687 2.8798 2.3927 -4.9364 -5.9770 7.7857e+005 10.464 7.8045 0.12702 (norm 1.56e+000) Iteration 55: loglikelihood = 4091.14437481 (steplength = 0.2) Parameters: 0.00046964 0.92366 -0.021841 -0.22811 -0.44756 0.73226 -0.0090109 -0.80920 0.059277 0.17481 0.56346 -0.70057 4.3474e-007 0.92441 0.054617 5.3799 Gradients: -303.19 -4.4955 -5.1677 -5.7120 -9.2896 -8.9968 -9.1221 2.3084 2.5496 1.5957 -3.7509 -4.7705 7.7482e+005 11.164 8.8528 0.10264 (norm 1.50e+000) Iteration 56: loglikelihood = 4091.14864478 (steplength = 0.2) Parameters: 0.00047092 0.92024 -0.015504 -0.23138 -0.45015 0.73629 -0.010205 -0.80552 0.052888 0.17832 0.56475 -0.70290 4.3572e-007 0.92443 0.054553 5.3928 Gradients: -171.52 -2.2909 -2.9329 -3.4457 -5.9798 -5.7911 -5.6540 1.9601 1.8280 0.87992 -2.8511 -3.3856 4.5737e+005 6.5037 5.3990 0.068556 (norm 1.19e+000) Iteration 57: loglikelihood = 4091.15132026 (steplength = 1) Parameters: 0.00047275 0.92137 -0.016013 -0.23237 -0.44936 0.73717 -0.011598 -0.80596 0.052210 0.17988 0.56293 -0.70276 4.4138e-007 0.92369 0.055038 5.4263 Gradients: 10.740 0.17796 0.24902 0.46270 0.69450 0.75562 0.79838 -0.52693 -0.43722 0.038236 0.49438 0.59190 -19808. -1.0366 -2.2854 -0.0076013 (norm 4.64e-001) Iteration 58: loglikelihood = 4091.15139116 (steplength = 1) Parameters: 0.00047267 0.91941 -0.012962 -0.23314 -0.45138 0.73897 -0.011691 -0.80402 0.049278 0.18094 0.56434 -0.70404 4.3893e-007 0.92437 0.054345 5.4295 Gradients: -10.925 -0.43031 -0.15141 -0.014682 0.38486 0.28406 -0.0075211 -0.24879 0.15099 0.21345 0.48381 0.22646 -9019.8 0.67938 1.9045 0.00011897 (norm 3.71e-001) Iteration 59: loglikelihood = 4091.15165337 (steplength = 1) Parameters: 0.00047256 0.92012 -0.014171 -0.23286 -0.45046 0.73810 -0.011515 -0.80483 0.050596 0.18044 0.56380 -0.70347 4.3970e-007 0.92408 0.054672 5.4251 Gradients: -0.37135 0.099551 0.026236 -0.066199 -0.13239 -0.12585 -0.046659 0.14358 0.023137 -0.099092 -0.15679 -0.10554 -2275.5 -0.063677 -0.066001 0.00038389 (norm 1.97e-001) Iteration 60: loglikelihood = 4091.15165338 (steplength = 1) Parameters: 0.00047256 0.92019 -0.014253 -0.23285 -0.45040 0.73805 -0.011529 -0.80488 0.050655 0.18043 0.56375 -0.70343 4.3980e-007 0.92407 0.054673 5.4256 Gradients: -0.33319 -0.042789 -0.015458 0.019938 0.036004 0.033463 0.0042303 -0.048947 -0.0066173 0.036591 0.048492 0.031184 1558.2 0.024215 0.0096538 -0.00064151 (norm 1.14e-001) Iteration 61: loglikelihood = 4091.15165407 (steplength = 1) Parameters: 0.00047256 0.92018 -0.014250 -0.23283 -0.45042 0.73806 -0.011525 -0.80488 0.050655 0.18042 0.56376 -0.70344 4.3977e-007 0.92408 0.054670 5.4253 Gradients: 0.54830 0.0026119 0.0056343 0.0091450 0.0097594 0.0089085 0.0050278 -0.0049159 0.00068812 0.0064422 0.0065334 0.0027406 10.519 -0.0023805 -0.0024273-4.2544e-005 (norm 4.27e-002) Iteration 61: loglikelihood = 4091.15165407 (steplength = 6.4e-005) Parameters: 0.00047256 0.92018 -0.014250 -0.23284 -0.45042 0.73806 -0.011525 -0.80488 0.050655 0.18042 0.56376 -0.70344 4.3977e-007 0.92408 0.054670 5.4253 Gradients: 0.54830 0.0026119 0.0056343 0.0091450 0.0097594 0.0089085 0.0050278 -0.0049159 0.00068812 0.0064422 0.0065334 0.0027406 10.519 -0.0023805 -0.0024273-4.2544e-005 (norm 4.27e-002) --- FINAL VALUES: loglikelihood = 4091.15165407 (steplength = 1.34218e-019) Parameters: 0.00047256 0.92018 -0.014250 -0.23284 -0.45042 0.73806 -0.011525 -0.80488 0.050655 0.18042 0.56376 -0.70344 4.3977e-007 0.92408 0.054670 5.4253 Gradients: 0.54830 0.0026119 0.0056343 0.0091450 0.0097594 0.0089085 0.0050278 -0.0049159 0.00068812 0.0064422 0.0065334 0.0027406 10.519 -0.0023805 -0.0024273-4.2544e-005 (norm 4.27e-002) Tolerance = 1.81899e-012 Function evaluations: 330 Evaluations of gradient: 61 Model 11: ML, using observations 2007/11/09-2011/11/09 (T = 999) ll = ( -0.5*log(pi*(dof-2)) - lngamma(dof/2) + lngamma((dof + 1)/2) -0.5*log(h) - 0.5*(dof + 1)*log(1 + (dof - 2)^(-1)*h^(-1)*e^2)) Standard errors based on Outer Products matrix estimate std. error z p-value ------------------------------------------------------------ c 0.000472561 0.000198289 2.383 0.0172 ** a1 0.920182 0.145611 6.319 2.63e-010 *** a2 -0.0142502 0.254370 -0.05602 0.9553 a3 -0.232835 0.225158 -1.034 0.3011 a4 -0.450416 0.196098 -2.297 0.0216 ** a5 0.738055 0.136002 5.427 5.74e-08 *** a6 -0.0115253 0.0427506 -0.2696 0.7875 ma1 -0.804878 0.142258 -5.658 1.53e-08 *** ma2 0.0506545 0.230786 0.2195 0.8263 ma3 0.180421 0.198932 0.9069 0.3644 ma4 0.563758 0.171319 3.291 0.0010 *** ma5 -0.703441 0.0995997 -7.063 1.63e-012 *** cg 4.39767e-07 2.28237e-07 1.927 0.0540 * ga 0.924077 0.0230196 40.14 0.0000 *** arc 0.0546702 0.0173626 3.149 0.0016 *** dof 5.42526 0.909296 5.966 2.42e-09 *** Log-likelihood 4091.152 Akaike criterion -8150.303 Schwarz criterion -8071.795 Hannan-Quinn -8120.463 #series e = allRng - c - a1*allRng(-1) - a2*allRng(-2) - a3*allRng(-3) - a4*allRng(-4) - a5*allRng(-5) - a6*allRng(-6) - a7*allRng(-7) - ma1*e(-1) - ma2*e(-2) - ma3*e(-3) - ma4*e(-4) - ma5*e(-5) #ARMA(7,5) process #params c a1 a2 a3 a4 a5 a6 a7 ma1 ma2 ma3 ma4 ma5 cg ga arc dof # pro ARMA(7,5) proces