A Bayesian MIDAS Approach to Modeling First and Second Moment Dynamics

We propose a new approach to predictive density modeling that allows for MIDAS effects in both the first and second moments of the outcome and develop Gibbs sampling methods for Bayesian estimation in the presence of stochastic volatility dynamics. When applied to quarterly U.S. GDP growth data, we find strong evidence that models that feature MIDAS terms in the conditional volatility generate more accurate forecasts than conventional benchmarks. Finally, we find that forecast combination methods such as the optimal predictive pool of Geweke and Amisano (2011) produce consistent gains in out-of-sample predictive performance.