Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models

Yuma Uehara

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 4051-4081

Abstract: We consider the estimation problem of misspecified ergodic Lévy driven stochastic differential equation models based on high-frequency samples. We utilize a widely applicable and tractable Gaussian quasi-likelihood approach which focuses on mean and variance structure. It is shown that the Gaussian quasi-likelihood estimators of the drift and scale parameters still satisfy polynomial type probability estimates and asymptotic normality at the same rate as the correctly specified case. In their derivation process, the theory of extended Poisson equation for time-homogeneous Feller Markov processes plays an important role. Our result confirms the reliability of the Gaussian quasi-likelihood approach for SDE models.

Keywords: Lévy driven stochastic differential equation; Misspecified model; Gaussian quasi-likelihood estimation; Extended Poisson equation; High-frequency sampling; Stepwise estimation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:10:p:4051-4081

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DOI: 10.1016/j.spa.2018.11.007

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