Density forecasts with MIDAS models

In this paper we derive a general parametric bootstrapping approach to compute density forecasts for various types of mixed-data sampling (MIDAS) regressions. We consider both classical and unrestricted MIDAS regressions with and without an autoregressive component. First, we compare the forecasting performance of the different MIDAS models in Monte Carlo simulation experiments. We find that the results in terms of point and density forecasts are coherent. Moreover, the results do not clearly indicate a superior performance of one of the models under scrutiny when the persistence of the low frequency variable is low. Some differences are instead more evident when the persistence is high, for which the AR- MIDAS and the AR-U-MIDAS produce better forecasts. Second, in an empirical exercise we evaluate density forecasts for quarterly US output growth, exploiting information from typical monthly series. We find that MIDAS models provide accurate and timely density forecasts.