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Schwartz‐type model selection for ergodic stochastic differential equation models
Author(s) -
Eguchi Shoichi,
Uehara Yuma
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12474
Subject(s) - mathematics , ergodic theory , stochastic differential equation , model selection , bayesian information criterion , consistency (knowledge bases) , type (biology) , selection (genetic algorithm) , stochastic modelling , statistics , mathematical analysis , computer science , artificial intelligence , discrete mathematics , biology , ecology
Abstract We study 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 Lévy 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.