HAR volatility modelling with heterogeneous ... - ResearchGate

S&P500 in-sample estimates, period 1982–2009VariableCJCJ-LQRAVRangeSemiRVSemiRAVLHAR-LHAR-LHAR-CJ-LHAR-CJ-LHAR-CJ-LHAR-CJ-LHAR-CJ-Allconst 0.442* 0.432* 0.593* 0.444* 0.470* 0.554* 0.616*(10.699) (9.968) (12.419) (10.860) (11.029) (9.869) (8.914)C 0.307* 0.301* 0.116* 0.207* 0.249* 0.252* 0.085*(16.983) (14.672) (3.355) (10.035) (9.588) (9.489) (2.449)C (5) 0.369* 0.368* 0.374* 0.384* 0.372* 0.372* 0.389*(13.908) (13.786) (14.125) (14.568) (14.074) (14.032) (14.693)C (22) 0.222* 0.221* 0.221* 0.223* 0.223* 0.222* 0.223*(10.958) (10.941) (10.943) (11.071) (11.003) (10.963) (11.035)J 0.043* 0.042* 0.018* 0.024* 0.033* 0.037* 0.010(7.057) (6.912) (2.519) (3.893) (4.850) (5.620) (1.331)J (5) 0.011* 0.011* 0.012* 0.012* 0.011* 0.011* 0.012*(3.373) (3.351) (3.717) (3.789) (3.409) (3.413) (3.959)J (22) 0.005* 0.005* 0.006* 0.005* 0.006* 0.006* 0.006*(2.199) (2.228) (2.334) (2.207) (2.266) (2.277) (2.329)r − -0.007* -0.007* -0.007* -0.006* -0.006* -0.006* -0.005*(-9.669) (-9.705) (-10.156) (-8.193) (-8.197) (-7.792) (-5.630)r (5)− -0.008* -0.008* -0.007* -0.008* -0.008* -0.008* -0.008*(-4.412) (-4.382) (-4.147) (-4.847) (-4.368) (-4.278) (-4.582)r (22)− -0.009* -0.009* -0.009* -0.009* -0.010* -0.010* -0.010*(-2.845) (-2.845) (-2.687) (-2.868) (-2.980) (-2.951) (-2.853)LQ 0.009(0.555)RAV 0.185* 0.077(6.533) (1.867)Range 0.088* 0.086*(9.364) (7.911)SemiRV 0.058* -0.011(3.305) (-0.330)SemiRAV 0.054* 0.056(3.141) (1.455)R 2 0.7664 0.7664 0.7681 0.7696 0.7668 0.7668 0.7704HRMSE 0.2168 0.2168 0.2158* 0.2148* 0.2165 0.2165 0.2142*DM (-0.1961) (2.7060) ( 4.6323) (1.5020 ) (1.8539 ) (4.6778)Table 3: Estimated parameters, Mincer-Zarnowitz R 2 , and Heteroskedasticityadjusted RMSE (HRMSE), of alternative specifications of the baseline LHAR-CJ model; t-statistic and Diebold-Mariano test for HRMSE are in parenthesis.27