CLT-Based Inference for QMLE in ARMA Models under Weakly Dependent Innovations: Simulation Evidence and Boundary Cases

Thomas M. Menino Convention & Exhibition Center 

This paper studies quasi-maximum likelihood estimation for ARMA(p,q) models under weakly dependent innovation structures, with emphasis on CLT-based inference and its practical behavior across different shock designs. The classical i.i.d. innovation setting is used only as a benchmark for validating the estimation and simulation framework. The main focus is on nontrivial innovation structures, including conditionally heteroskedastic and other weakly dependent cases, together with boundary designs that violate key assumptions. Within this framework, we examine the asymptotic normal approximation for the QMLE and the role of robust covariance estimation for inference. Monte Carlo results show that when the underlying innovation conditions are compatible with the inferential framework, standardized estimators are close to normal and coverage improves with sample size. In contrast, when key assumptions fail, bias persists and interval performance deteriorates even when dispersion is adjusted. The study provides a focused view of how CLT-based inference for ARMA QMLE behaves under benchmark, admissible, and failure cases, and clarifies the practical limits of the methodology.

ARMA models

Quasi-maximum likelihood estimation

central limit theorem

HAC inference

Monte Carlo simulation

Innovation mixing with summable coefficients 

Business and Economic Statistics Section