A Ridge Approach for MIDAS Models

In this paper, I introduce the Ridge approach (see Hoerl and Kennard (1970)) as a parametrization method for the MIDAS model, introduced by Ghysels et al. (2004). The low frequency and high frequency variables are sampled quarterly and monthly respectively. The Ridge approach assumes that the MIDAS parameters are equal to some function plus an error term. Furthermore, I investigate the performance of this method by comparing it with four benchmark methods that are in the common practice often used to estimate the MIDAS model. These are U-MIDAS, the Almon lag, the Exponential Almon lag and the Beta lag. Simulation results show that the Ridge approach is a very strong method. Its performance is always better or equal than the benchmark methods. In the empirical study, the GDP of the Netherlands is tried to be explained by some high frequency variable. The empirical results are less convincing. Although, the Ridge approach does not perform worse, it is not as dominant as it was in the simulations. This can be explained by the issue that it is still a big challenge to find the optimal shrinkage factor for the Ridge approach in the empirical study.