Recursive Score and Hessian Computation in Regime-Switching Models

TL;DR

This paper introduces a unified recursive framework to compute the score and Hessian for general regime-switching models without relying on smoothed probabilities or Fisher–Louis transformations. The method builds on a prediction–update interpretation of likelihood evaluation and provides explicit recursions for the necessary quantities, including stabilization via normalization to prevent numerical issues. Simulation evidence shows that inference based on the outer product of the score outperforms Hessian-based inference in finite samples, particularly as sample size grows. The approach is general and reduces pre-computation, but the authors acknowledge limitations for more complex regimes such as regime-switching GARCH or state-space models, which they plan to address in future work.

Abstract

This study proposes a recursive and easy-to-implement algorithm to compute the score and Hessian matrix in general regime-switching models. We use simulation to compare the asymptotic variance estimates constructed from the Hessian matrix and the outer product of the score. The results favor the latter.