🤖 AI Summary
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.
📝 Abstract
In this paper, a Mixed Data Sampling (MIDAS) model is studied when both low and high frequency variables are contaminated with measurement error. It is shown that the profile likelihood estimator becomes inconsistent in the presence of measurement error. Using the corrected score approach along with profile likelihood approach, a consistent estimator for parameters of MIDAS Measurement Error model is proposed. Small and large sample properties of the estimator are examined by performing a monte carlo simulation study and considering the effect of sample size, number of lags and profiling parameter.