Hierarchical Regularizers for Reverse Unrestricted Mixed Data Sampling Regressions

Reverse Unrestricted MIxed DAta Sampling (RU‐MIDAS) regressions are used to model high‐frequency responses by means of low‐frequency variables. However, due to the periodic structure of RU‐MIDAS regressions, the dimensionality grows quickly if the frequency mismatch between the high‐ and low‐frequency variables is large. Additionally, the number of high‐frequency observations available for estimation decreases. We propose to counteract this reduction in sample size by pooling the high‐frequency coefficients and further reducing the dimensionality through a sparsity‐inducing convex regularizer that accounts for the temporal ordering among the different lags. To this end, the regularizer prioritizes the inclusion of lagged coefficients according to the recency of the information they contain. We demonstrate the proposed method on two empirical applications, one on realized volatility forecasting with macroeconomic data and another on demand forecasting for a bicycle‐sharing system with ridership data on other transportation types.