Enforcing an Admissible Parameter Space for Vector Multiplicative Error Models: The Fundamental Role of Matrix Inequality Constraints

Abstract

We derive an admissible parameter space for vector multiplicative error models (vMEMs), explicitly formulating it in terms of the model’s matrix parameters through a set of matrix inequalities. Another key contribution is the adoption of constrained maximum likelihood estimation for the multivariate process, which ensures compliance with these matrix inequalities and addresses the limitations of unconstrained approaches used in previous studies. To demonstrate the effectiveness of the proposed method, we apply it to four empirical cases in financial volatility modeling, emphasizing its practical relevance.