Estimation of MIDAS Regressions with Errors-in-the-Variables

TL;DR

This paper addresses measurement error issues in MIDAS models, proposing a consistent estimator using a corrected score approach and analyzing its properties through simulations.

Contribution

It introduces a new consistent estimator for MIDAS models with measurement errors, improving inference accuracy in such settings.

Findings

The profile likelihood estimator is inconsistent with measurement error.

The proposed estimator is shown to be consistent through simulations.

Sample size and lag number affect estimator performance.

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.