Moving Average Estimation by Geometric Optimization

Alex Nguyen-Le, Nikolai Matni

Abstract: We propose a new geometric-optimization framework for maximum likelihood estimation of moving-average models. Instead of optimizing directly over the moving average parameters, we formulate the estimation problem over the reflection coefficients and show how to perform gradient descent over a reflection-coefficient manifold. This choice leads to simpler expressions in the objective function and in the constraints, which can yield more convenient expressions for theoretical analysis. Finally, we numerically implement and compare the proposed estimation schemes in the reflection coefficients to those based on moving-average parmeterizations. We show that our novel formulation works in practice and yields equivalent solutions to currently employed formulations.