Asymptotic Distributions of Nonlinear Least Squares Estimators for Panel-MIDAS Models

In this article, we introduce the MIDAS framework into a panel data model and derive the asymptotic properties of the NLS estimator under a joint asymptotic framework where both <i>N</i> and <i>T</i> tend to infinity, allowing for heteroscedasticity and arbitrary correlation within each individual.

To facilitate valid inference, we construct robust heteroscedasticity- and autocorrelation-consistent (HAC) covariance estimators. We also analyze the asymptotic bias and variance of the LS estimator based on pre-specified aggregation weights. In addition, we propose a Wald test for the null hypothesis of equal weights and a supremum-type Wald test to address the unidentified nuisance parameter problem.