Statistical inference for misspecified ergodic L\'evy driven stochastic differential equation models

Yuma Uehara

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arXiv · 1702.00908

Statistical inference for misspecified ergodic L\'evy driven stochastic differential equation models

Yuma Uehara

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Abstract

This paper deals with the estimation problem of misspecified ergodic L\'evy driven stochastic differential equation models based on high-frequency samples. We utilize the widely applicable and tractable Gaussian quasi-likelihood approach which focuses on (conditional) mean and variance structure. It is shown that the corresponding Gaussian quasi-likelihood estimators of drift and scale parameters satisfy tail probability estimates and asymptotic normality at the same rate as correctly specified case. In this process, extended Poisson equation for time-homogeneous Feller Markov processes plays an important role to handle misspecification effect. Our result confirms the practical usefulness of the Gaussian quasi-likelihood approach for SDE models, more firmly.

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Yuma Uehara. 2017-02-03. Statistical inference for misspecified ergodic L\'evy driven stochastic differential equation models. https://arxiv.org/abs/1702.00908

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