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

The Mixed Data Sampling (MIDAS) approach provides a flexible framework for incorporating mixed-frequency data into econometric models. In this paper, 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 N and T tend to infinity, allowing for heteroskedasticity and arbitrary correlation within each individual. To facilitate valid inference, we construct robust heteroskedasticity- 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. The theoretical results are evaluated via an extensive Monte Carlo simulation study and an empirical application.