Schwartz-type model selection for ergodic stochastic differential equation models. (English) Zbl 1473.62076
Summary: 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.
MSC:
| 62F07 | Statistical ranking and selection procedures |
| 62B10 | Statistical aspects of information-theoretic topics |
| 60G65 | Nonlinear processes (e.g., \(G\)-Brownian motion, \(G\)-Lévy processes) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
Gaussian quasi-likelihood; high-frequency sampling; Lévy-driven stochastic differential equation; stepwise model selectionReferences:
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