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Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models

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  • Uehara, Yuma

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.

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  • Uehara, Yuma, 2019. "Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4051-4081.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:4051-4081
    DOI: 10.1016/j.spa.2018.11.007
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    1. Shoichi Eguchi & Hiroki Masuda, 2024. "Gaussian quasi-information criteria for ergodic Lévy driven SDE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 111-157, February.
    2. Shoichi Eguchi & Yuma Uehara, 2021. "Schwartz‐type model selection for ergodic stochastic differential equation models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 950-968, September.
    3. Alexander Gushchin & Ilya Pavlyukevich & Marian Ritsch, 2020. "Drift estimation for a Lévy-driven Ornstein–Uhlenbeck process with heavy tails," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 553-570, October.

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