Improved Maximum Likelihood Estimation of ARMA Models

TL;DR

This paper introduces a new optimization approach for maximum likelihood estimation of ARMA models that improves fit quality and computational efficiency, with added regularization enhancing out-of-sample performance.

Contribution

It proposes a novel optimization model for ARMA parameter estimation that outperforms classical methods and incorporates regularization to improve model robustness.

Findings

Outperforms classical estimation in quality and speed

Regularization improves out-of-sample accuracy

Enhanced penalty near non-causality boundary

Abstract

In this paper we propose a new optimization model for maximum likelihood estimation of causal and invertible ARMA models. Through a set of numerical experiments we show how our proposed model outperforms, both in terms of quality of the fitted model as well as in the computational time, the classical estimation procedure based on Jones reparametrization. We also propose a regularization term in the model and we show how this addition improves the out of sample quality of the fitted model. This improvement is achieved thanks to an increased penalty on models close to the non causality or non invertibility boundary.