Schwartz type model selection for ergodic stochastic differential equation models

TL;DR

This paper develops a theoretical framework for model comparison in ergodic SDEs, extending Bayesian criteria to misspecified models with Wiener and Lévy noise, and proves the consistency of the proposed selection method.

Contribution

It introduces a Schwarz type model selection criterion for ergodic SDEs with misspecified models and proves its consistency, broadening the scope of Bayesian information criteria.

Findings

Proposed a Schwarz type statistic for ergodic SDEs.

Proved the model selection consistency of the criterion.

Numerical experiments support theoretical results.

Abstract

We study the construction of the theoretical foundation of model comparison for ergodic stochastic differential equation (SDE) models and an extension of the applicable scope of the conventional Bayesian information criterion. Different from previous studies, we suppose that the candidate models are possibly misspecified models, and we consider both Wiener and a pure-jump L\'{e}vy noise driven SDE. Based on the asymptotic behavior of the marginal quasi-log likelihood, the Schwarz type statistics and stepwise model selection procedure are proposed. We also prove the model selection consistency of the proposed statistics with respect to an optimal model. We conduct some numerical experiments and they support our theoretical findings.