Density Forecasts with MIDAS Models

In this paper we propose a parametric block wild bootstrap approach to compute density forecasts for various types of mixed-data sampling (MIDAS) regressions. First, Monte Carlo simulations show that predictive densities for the various MIDAS models derived from the block wild bootstrap approach are more accurate, in terms of coverage rates, than predictive densities derived from either a residual-based bootstrap approach or by drawing errors from a normal distribution. This result holds irrespective of the data generating errors being normally independently distributed, serially correlated, heteroskedastic or a mixture of normal distributions. Second, in an empirical exercise we evaluate density forecasts for quarterly U.S. real output growth, exploiting information from typical monthly and weekly series. We show that the block wild bootstrapping approach, applied to the various MIDAS regressions, produces predictive densities for U.S. real output growth that are well-calibrated. Moreover, the relative accuracy, measured in terms of the logarithmic score or the continuous ranked probability score, improves for the various MIDAS specifications as more information becomes available