Adaptive Group LASSO for the GARCH-MIDAS Model

This article investigates the variable selection problem in the generalized autoregressive conditional heteroscedasticity-mixed-data sampling (GARCH-MIDAS) model of Engle, Ghysels, and Sohn (2013), and establishes the corresponding theoretical properties along with a feasible computational algorithm. The proposed method is based on a penalized log-partial likelihood with an adaptively group-weighted L2 penalty on the long-term component coefficients. The variable selection mechanism is implemented by assigning smaller penalties to important variables compared to unimportant ones. Simulation results indicate that the proposed method performs as effectively as if the correct submodel were known. In a comprehensive empirical comparison with existing volatility models, our approach is shown to be the preferred model for forecasting long-horizon stock market volatility.