Estimation of MIDAS Regressions with Errors-in-the-Variables
This study addresses the inconsistency of conventional estimators in mixed-data sampling (MIDAS) regression when both high- and low-frequency variables are subject to measurement error. To resolve this issue, the paper introduces the corrected score method into the MIDAS framework for the first time and combines it with profile likelihood to construct a consistent estimator. This approach effectively overcomes the inconsistency that plagues existing profile likelihood estimators under measurement error. Through comprehensive Monte Carlo simulations, the authors systematically investigate the impacts of sample size, lag order, and nuisance parameters on estimation performance. The results demonstrate that the proposed estimator exhibits strong consistency and favorable finite-sample properties across a range of sample sizes and model specifications.