gretl version 2017b-git Copyright Ramu Ramanathan, Allin Cottrell and Riccardo "Jack" Lucchetti This is free software with ABSOLUTELY NO WARRANTY Current session: 2017-05-23 14:47 ? run gdp_midas.inp /home/cottrell/stats/midas/ghysels/gdp_midas.inp Read datafile /opt/esl/share/gretl/data/misc/gdp_midas.gdt === U-MIDAS === Model 1: MIDAS (OLS), using observations 1985:1-2009:1 (T = 97) Dependent variable: ld_qgdp estimate std. error t-ratio p-value -------------------------------------------------------------- const 0.723275 0.150154 4.817 6.20e-06 *** ld_qgdp_1 0.266596 0.121229 2.199 0.0306 ** ld_payems_m1_1 1.21945 0.663836 1.837 0.0697 * ld_payems_m3_2 0.628388 0.667840 0.9409 0.3494 ld_payems_m2_2 0.480515 0.691798 0.6946 0.4892 ld_payems_m1_2 1.31695 0.694126 1.897 0.0611 * ld_payems_m3_3 -0.422915 0.717003 -0.5898 0.5568 ld_payems_m2_3 -0.551077 0.696004 -0.7918 0.4307 ld_payems_m1_3 -0.906465 0.717446 -1.263 0.2098 ld_payems_m3_4 0.0392873 0.684595 0.05739 0.9544 ld_payems_m2_4 -0.0957314 0.605121 -0.1582 0.8747 Mean dependent var 1.274925 S.D. dependent var 0.682517 Sum squared resid 27.67322 S.E. of regression 0.567258 R-squared 0.381184 Adjusted R-squared 0.309228 F(10, 86) 5.297501 P-value(F) 4.78e-06 Log-likelihood -76.80612 Akaike criterion 175.6122 Schwarz criterion 203.9341 Hannan-Quinn 187.0642 rho -0.018919 Durbin's h -0.186333 midas coefficients: 1.21945 0.62839 0.48052 1.31695 -0.42291 -0.55108 -0.90647 0.03929 -0.09573 === beta (zero last lag) === Convergence achieved after 24 iterations Model 2: MIDAS (NLS), using observations 1985:1-2009:1 (T = 97) Using L-BFGS-B with conditional OLS Dependent variable: ld_qgdp estimate std. error t-ratio p-value ------------------------------------------------------ const 0.665560 0.139647 4.766 7.00e-06 *** ld_qgdp_1 0.284700 0.118466 2.403 0.0183 ** MIDAS list dXL, high-frequency lags 3 to 11 HF_slope 1.91207 0.574921 3.326 0.0013 *** Beta1 0.990377 0.106112 9.333 5.77e-15 *** Beta2 6.61572 17.1396 0.3860 0.7004 Mean dependent var 1.274925 S.D. dependent var 0.682517 Sum squared resid 29.64215 S.E. of regression 0.567624 R-squared 0.337155 Adjusted R-squared 0.308336 Log-likelihood -80.13963 Akaike criterion 170.2793 Schwarz criterion 183.1528 Hannan-Quinn 175.4847 rho -0.036012 Durbin's h -0.354681 GNR: R-squared = 0, max |t| = 8.6119e-09 Convergence seems to be reasonably complete midas coefficients: 1.23218 0.41982 0.17547 0.06279 0.01788 0.00355 0.00036 0.00001 0.00000 === beta (non-zero last lag) === Convergence achieved after 28 iterations Model 3: MIDAS (NLS), using observations 1985:1-2009:1 (T = 97) Using L-BFGS-B with conditional OLS Dependent variable: ld_qgdp estimate std. error t-ratio p-value -------------------------------------------------------- const 0.748578 0.146404 5.113 1.74e-06 *** ld_qgdp_1 0.248055 0.118903 2.086 0.0398 ** MIDAS list dXL, high-frequency lags 3 to 11 HF_slope 1.72167 0.582076 2.958 0.0039 *** Beta1 0.998501 0.0269479 37.05 1.10e-56 *** Beta2 2.95148 2.93404 1.006 0.3171 Beta3 -0.0743143 0.0271273 -2.739 0.0074 *** Mean dependent var 1.274925 S.D. dependent var 0.682517 Sum squared resid 28.78262 S.E. of regression 0.562399 R-squared 0.356376 Adjusted R-squared 0.321012 Log-likelihood -78.71248 Akaike criterion 169.4250 Schwarz criterion 184.8732 Hannan-Quinn 175.6715 rho -0.020400 Durbin's h -0.200918 GNR: R-squared = 6.55032e-15, max |t| = 6.08607e-07 Convergence seems to be reasonably complete midas coefficients: 1.28108 0.83480 0.51662 0.24590 0.02252 -0.15320 -0.28069 -0.35903 -0.38634 === normalized exponential Almon === Convergence achieved after 36 iterations Model 4: MIDAS (NLS), using observations 1985:1-2009:1 (T = 97) Using L-BFGS-B with conditional OLS Dependent variable: ld_qgdp estimate std. error t-ratio p-value --------------------------------------------------------- const 0.666700 0.140031 4.761 7.14e-06 *** ld_qgdp_1 0.284320 0.118552 2.398 0.0185 ** MIDAS list dXL, high-frequency lags 3 to 11 HF_slope 1.90769 0.575425 3.315 0.0013 *** Almon1 -0.783321 6.26276 -0.1251 0.9007 Almon2 -0.0660584 1.65472 -0.03992 0.9682 Mean dependent var 1.274925 S.D. dependent var 0.682517 Sum squared resid 29.64939 S.E. of regression 0.567694 R-squared 0.336994 Adjusted R-squared 0.308167 Log-likelihood -80.15146 Akaike criterion 170.3029 Schwarz criterion 183.1765 Hannan-Quinn 175.5084 rho -0.037671 Durbin's h -0.371015 GNR: R-squared = 6.66134e-16, max |t| = 1.71216e-07 Convergence seems to be reasonably complete midas coefficients: 1.23510 0.46285 0.15199 0.04373 0.01103 0.00244 0.00047 0.00008 0.00001 === Almon polynomial === Convergence achieved after 3 iterations Model 5: MIDAS (NLS), using observations 1985:1-2009:1 (T = 97) Using Levenberg-Marquardt algorithm Dependent variable: ld_qgdp estimate std. error t-ratio p-value -------------------------------------------------------- const 0.741403 0.146433 5.063 2.14e-06 *** ld_qgdp_1 0.255099 0.119139 2.141 0.0349 ** MIDAS list dXL, high-frequency lags 3 to 11 Almon0 1.06035 1.53491 0.6908 0.4914 Almon1 0.193615 1.30812 0.1480 0.8827 Almon2 -0.140466 0.299446 -0.4691 0.6401 Almon3 0.0116034 0.0198686 0.5840 0.5607 Mean dependent var 1.274925 S.D. dependent var 0.682517 Sum squared resid 28.66623 S.E. of regression 0.561261 R-squared 0.358979 Adjusted R-squared 0.323758 Log-likelihood -78.51596 Akaike criterion 169.0319 Schwarz criterion 184.4802 Hannan-Quinn 175.2784 rho -0.026829 Durbin's h -0.264233 GNR: R-squared = 0, max |t| = 6.00575e-14 Convergence seems to be reasonably complete midas coefficients: 1.12511 0.97855 0.69029 0.32997 -0.03280 -0.32840 -0.48721 -0.43961 -0.11598 Forecast RMSEs: U-MIDAS 0.5424 Beta0 0.5650 BetaNZ 0.5210 neAlmon 0.5642 Almonp 0.5329