spb/wp12_uqo

1\begin{tabular}{lccccc}2\toprule3 & \multicolumn{3}{c}{Mincer--Zarnowitz} & \multicolumn{2}{c}{Encompassing (vs HAR)} \\4\cmidrule(lr){2-4}\cmidrule(lr){5-6}5Model & Med.\ $\hat\beta$ & Med.\ $R^2$ & Rej.\ (\%) & Med.\ $\hat b_2$ & Adds info (\%) \\6\midrule7\multicolumn{6}{l}{\itshape A. GARCH family}\\8\quad GARCH & 1.08 & 0.29 & 64 & 0.39 & 60 \\9\quad GJR & 1.04 & 0.29 & 64 & 0.32 & 60 \\10\quad EGARCH & 0.54 & 0.10 & 92 & 0.13 & 64 \\11\quad RealGARCH & 1.29 & 0.45 & 52 & 0.98 & 80 \\12\multicolumn{6}{l}{\itshape B. HAR family}\\13\quad HAR & 1.03 & 0.40 & 40 & --- & --- \\14\quad HAR-J & 1.01 & 0.40 & 40 & 0.41 & 24 \\15\quad HAR-CJ & 1.01 & 0.39 & 36 & 0.35 & 28 \\16\quad SHAR & 1.02 & 0.39 & 44 & 0.39 & 40 \\17\quad HARQ & 0.94 & 0.38 & 32 & 0.32 & 32 \\18\quad LogHAR & 1.24 & 0.44 & 36 & 1.10 & 76 \\19\multicolumn{6}{l}{\itshape C. Machine learning --- HAR information set}\\20\quad Ridge-H & 1.20 & 0.44 & 28 & 1.08 & 72 \\21\quad LASSO-H & 1.25 & 0.44 & 48 & 1.09 & 60 \\22\quad ElasticNet-H & 1.22 & 0.44 & 28 & 1.08 & 72 \\23\quad RF-H & 1.14 & 0.23 & 60 & 0.06 & 20 \\24\quad XGBoost-H & 0.87 & 0.20 & 92 & 0.00 & 20 \\25\quad LightGBM-H & 0.87 & 0.21 & 92 & 0.02 & 24 \\26\multicolumn{6}{l}{\itshape D. Machine learning --- extended information set}\\27\quad Ridge-X & 1.09 & 0.46 & 20 & 0.96 & 84 \\28\quad LASSO-X & 1.10 & 0.46 & 40 & 1.01 & 84 \\29\quad ElasticNet-X & 1.13 & 0.46 & 28 & 1.01 & 88 \\30\quad RF-X & 1.32 & 0.29 & 92 & 0.38 & 40 \\31\quad XGBoost-X & 1.15 & 0.31 & 92 & 0.40 & 40 \\32\quad LightGBM-X & 1.17 & 0.27 & 96 & 0.38 & 36 \\33\multicolumn{6}{l}{\itshape E. Deep learning and pooled}\\34\quad LSTM & 0.86 & 0.16 & 92 & 0.12 & 24 \\35\quad Transformer & 0.90 & 0.03 & 92 & -0.05 & 4 \\36\quad Pooled-LGBM & 1.05 & 0.44 & 84 & 0.76 & 84 \\37\multicolumn{6}{l}{\itshape F. Forecast combinations}\\38\quad Comb-Mean & 1.27 & 0.42 & 88 & 1.05 & 76 \\39\quad Comb-InvMSE & 1.22 & 0.45 & 56 & 1.49 & 76 \\40\bottomrule41\end{tabular}42