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. Specifically, our modeling approach allows for MIDAS stochastic volatility dynamics, generalizing a large literature focusing on MIDAS effects in the conditional mean, and allows the models to be estimated by means of standard Gibbs sampling methods. When applied to monthly time series on growth in industrial production and inflation, we find strong evidence that the introduction of MIDAS effects in the volatility equation leads to improved in-sample and out-of-sample density forecasts. Our results also suggest that model combination schemes assign high weight to MIDAS-in-volatility models and produce consistent gains in out-of-sample predictive performance.