gretl version 2017d-git Current session: 2017-09-08 22:34 # open phillips_aus.gdt # poe-4 ? eval $sysinfo bundle anonymous: nproc = 4 blascore = Atom hostname = DESKTOP-DE5ESQO os = windows mpi = 0 blas = openblas omp_num_threads = 4 omp = 1 blas_parallel = OpenMP mpimax = 4 wordlen = 64 ? arma 1 1; inf 0 d_u --verbose ARMA initialization: using nonlinear AR model Iteration 1: loglikelihood = -67.4802393457 Parameters: 0.76087 0.55739 0.00010000 -0.69439 Gradients: 1.7670 0.13716 -11.827 -0.17685 (norm 6.21e-001) MA root 0 = 0.00714939 MA estimate(s) out of bounds MA root 0 = 0.178747 MA estimate(s) out of bounds Iteration 2: loglikelihood = -66.8018116428 (steplength = 0.008) Parameters: 0.77501 0.55849 -0.094515 -0.69580 Gradients: 0.86167 11.492 -1.7851 0.030193 (norm 1.35e+000) MA root 0 = 1.08772e-005 MA estimate(s) out of bounds MA root 0 = 0.000271253 MA estimate(s) out of bounds MA root 0 = 0.00669765 MA estimate(s) out of bounds MA root 0 = 0.157542 MA estimate(s) out of bounds Iteration 3: loglikelihood = -66.7588545998 (steplength = 6.4e-005) Parameters: 0.77802 0.56049 -0.11391 -0.69606 Gradients: 0.60987 13.790 0.20127 0.075309 (norm 1.44e+000) MA root 0 = 5.6826e-005 MA estimate(s) out of bounds MA root 0 = 0.00141094 MA estimate(s) out of bounds MA root 0 = 0.0340963 MA estimate(s) out of bounds MA root 0 = 0.725235 MA estimate(s) out of bounds Iteration 4: loglikelihood = -66.7490818565 (steplength = 6.4e-005) Parameters: 0.77928 0.56150 -0.12240 -0.69623 Gradients: 0.49939 14.799 1.0699 0.096473 (norm 1.49e+000) MA root 0 = 0.000456117 MA estimate(s) out of bounds MA root 0 = 0.0111682 MA estimate(s) out of bounds MA root 0 = 0.252409 MA estimate(s) out of bounds Iteration 5: loglikelihood = -66.7351406040 (steplength = 0.00032) Parameters: 0.78115 0.56406 -0.13734 -0.69684 Gradients: 0.32897 16.495 2.5216 0.13464 (norm 1.58e+000) MA root 0 = 9.59176e-005 MA estimate(s) out of bounds MA root 0 = 0.00242395 MA estimate(s) out of bounds MA root 0 = 0.0640148 MA estimate(s) out of bounds Iteration 6: loglikelihood = -66.7275205987 (steplength = 6.4e-005) Parameters: 0.78001 0.56369 -0.13080 -0.69687 Gradients: 0.43540 15.635 1.7788 0.11613 (norm 1.54e+000) MA root 0 = 0.00181715 MA estimate(s) out of bounds MA root 0 = 0.047525 MA estimate(s) out of bounds Iteration 7: loglikelihood = -66.7268360446 (steplength = 0.0016) Parameters: 0.77143 0.56605 -0.093054 -0.69887 Gradients: 1.1536 10.212 -2.9294 0.017727 (norm 1.32e+000) MA root 0 = 2.01409e-006 MA estimate(s) out of bounds MA root 0 = 5.02992e-005 MA estimate(s) out of bounds MA root 0 = 0.00125087 MA estimate(s) out of bounds MA root 0 = 0.0304643 MA estimate(s) out of bounds MA root 0 = 0.67152 MA estimate(s) out of bounds Iteration 8: loglikelihood = -66.6570607886 (steplength = 6.4e-005) Parameters: 0.77915 0.56907 -0.13814 -0.69883 Gradients: 0.52109 15.850 1.9224 0.12737 (norm 1.56e+000) MA root 0 = 1.39534e-005 MA estimate(s) out of bounds MA root 0 = 0.000350281 MA estimate(s) out of bounds MA root 0 = 0.00894099 MA estimate(s) out of bounds MA root 0 = 0.24885 MA estimate(s) out of bounds Iteration 9: loglikelihood = -66.6551369639 (steplength = 6.4e-005) Parameters: 0.77608 0.56823 -0.12100 -0.69898 Gradients: 0.78793 13.608 -0.0062684 0.081643 (norm 1.45e+000) MA root 0 = 7.8642e-006 MA estimate(s) out of bounds MA root 0 = 0.000196072 MA estimate(s) out of bounds MA root 0 = 0.00483603 MA estimate(s) out of bounds MA root 0 = 0.113155 MA estimate(s) out of bounds Iteration 10: loglikelihood = -66.6510536143 (steplength = 1.28e-005) Parameters: 0.77685 0.56856 -0.12557 -0.69899 Gradients: 0.72320 14.182 0.48681 0.093230 (norm 1.48e+000) Iteration 11: loglikelihood = -65.9893564520 (steplength = 0.008) Parameters: 0.77591 0.67530 -0.12839 -0.70496 Gradients: 0.84531 -2.3277 -12.843 -0.56868 (norm 1.03e+000) MA root 0 = 0.0123591 MA estimate(s) out of bounds MA root 0 = 0.276504 MA estimate(s) out of bounds Iteration 12: loglikelihood = -63.0190095508 (steplength = 0.04) Parameters: 0.73533 0.90101 -0.48306 -0.79318 Gradients: 1.7008 -10.761 -8.7616 0.18584 (norm 1.96e+000) MA root 0 = 4.53004e-005 MA estimate(s) out of bounds MA root 0 = 0.00116255 MA estimate(s) out of bounds MA root 0 = 0.033308 MA estimate(s) out of bounds Iteration 13: loglikelihood = -62.9978519080 (steplength = 6.4e-005) Parameters: 0.73596 0.89018 -0.47352 -0.79106 Gradients: 1.8398 -7.8531 -8.1758 0.17289 (norm 1.76e+000) MA root 0 = 0.000158851 MA estimate(s) out of bounds MA root 0 = 0.00378824 MA estimate(s) out of bounds MA root 0 = 0.0759626 MA estimate(s) out of bounds MA root 0 = 0.819768 MA estimate(s) out of bounds Iteration 14: loglikelihood = -62.9465721639 (steplength = 0.00032) Parameters: 0.73137 0.90565 -0.49876 -0.79898 Gradients: 1.7685 -10.307 -7.7465 0.32620 (norm 1.92e+000) MA root 0 = 2.00151e-005 MA estimate(s) out of bounds MA root 0 = 0.000509431 MA estimate(s) out of bounds MA root 0 = 0.0139651 MA estimate(s) out of bounds MA root 0 = 0.59776 MA estimate(s) out of bounds Iteration 15: loglikelihood = -62.9245949892 (steplength = 6.4e-005) Parameters: 0.73256 0.89047 -0.48442 -0.79561 Gradients: 1.9731 -6.2001 -7.0047 0.29403 (norm 1.63e+000) MA root 0 = 6.87583e-005 MA estimate(s) out of bounds MA root 0 = 0.00166502 MA estimate(s) out of bounds MA root 0 = 0.035749 MA estimate(s) out of bounds MA root 0 = 0.478707 MA estimate(s) out of bounds Iteration 16: loglikelihood = -62.9123094653 (steplength = 6.4e-005) Parameters: 0.73138 0.89620 -0.49211 -0.79786 Gradients: 1.9272 -7.3118 -7.0349 0.33123 (norm 1.71e+000) MA root 0 = 0.0378073 MA estimate(s) out of bounds MA root 0 = 0.494347 MA estimate(s) out of bounds Iteration 17: loglikelihood = -62.9098888804 (steplength = 0.0016) Parameters: 0.72196 0.86472 -0.49955 -0.80687 Gradients: 2.9813 7.2250 -0.40844 0.73831 (norm 1.52e+000) MA root 0 = 1.49338e-006 MA estimate(s) out of bounds MA root 0 = 3.71528e-005 MA estimate(s) out of bounds MA root 0 = 0.000906601 MA estimate(s) out of bounds MA root 0 = 0.0201655 MA estimate(s) out of bounds MA root 0 = 0.305904 MA estimate(s) out of bounds Iteration 18: loglikelihood = -62.8019814118 (steplength = 6.4e-005) Parameters: 0.71732 0.91865 -0.55189 -0.81949 Gradients: 2.0523 -7.5107 -3.3891 0.87470 (norm 1.66e+000) MA root 0 = 2.40639e-006 MA estimate(s) out of bounds MA root 0 = 6.05738e-005 MA estimate(s) out of bounds MA root 0 = 0.00156776 MA estimate(s) out of bounds MA root 0 = 0.0470614 MA estimate(s) out of bounds Iteration 19: loglikelihood = -62.7724301952 (steplength = 1.28e-005) Parameters: 0.71799 0.90984 -0.54363 -0.81757 Gradients: 2.2307 -4.4717 -2.9204 0.84413 (norm 1.41e+000) MA root 0 = 0.0130666 MA estimate(s) out of bounds MA root 0 = 0.209546 MA estimate(s) out of bounds Iteration 20: loglikelihood = -62.7587661687 (steplength = 0.00032) Parameters: 0.71701 0.90672 -0.54626 -0.81899 Gradients: 2.3660 -2.3856 -1.9796 0.90125 (norm 1.19e+000) MA root 0 = 0.0171279 MA estimate(s) out of bounds MA root 0 = 0.258933 MA estimate(s) out of bounds Iteration 21: loglikelihood = -62.7548100919 (steplength = 0.00032) Parameters: 0.71613 0.90432 -0.54853 -0.82034 Gradients: 2.4788 -0.71341 -1.1940 0.95201 (norm 9.82e-001) MA root 0 = 0.0222549 MA estimate(s) out of bounds MA root 0 = 0.315802 MA estimate(s) out of bounds Iteration 22: loglikelihood = -62.7547953674 (steplength = 6.4e-005) Parameters: 0.71598 0.90396 -0.54892 -0.82060 Gradients: 2.4973 -0.44823 -1.0654 0.96100 (norm 9.44e-001) Iteration 22: loglikelihood = -62.7547953674 (steplength = 6.4e-005) Parameters: 0.71598 0.90396 -0.54892 -0.82060 Gradients: 2.4973 -0.44823 -1.0654 0.96100 (norm 9.44e-001) --- FINAL VALUES: loglikelihood = -62.7547953674 (steplength = 6.4e-005) Parameters: 0.71598 0.90396 -0.54892 -0.82060 Gradients: 2.4973 -0.44823 -1.0654 0.96100 (norm 9.44e-001) Function evaluations: 132 Evaluations of gradient: 22 Model 4: ARMAX, using observations 1987:2-2009:3 (T = 90) Estimated using Kalman filter (exact ML) Dependent variable: inf Standard errors based on Hessian coefficient std. error z p-value -------------------------------------------------------- const 0.715975 0.233031 3.072 0.0021 *** phi_1 0.903959 0.0674654 13.40 6.14e-041 *** theta_1 −0.548921 0.123771 −4.435 9.21e-06 *** d_u −0.820599 0.231340 −3.547 0.0004 *** Mean dependent var 0.791111 S.D. dependent var 0.636819 Mean of innovations 0.010436 S.D. of innovations 0.484094 Log-likelihood −62.75480 Akaike criterion 135.5096 Schwarz criterion 148.0086 Hannan-Quinn 140.5499 Real Imaginary Modulus Frequency ----------------------------------------------------------- AR Root 1 1.1062 0.0000 1.1062 0.0000 MA Root 1 1.8218 0.0000 1.8218 0.0000 -----------------------------------------------------------