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Two-step estimation of ergodic Lévy driven SDE

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Abstract

We consider high frequency samples from ergodic Lévy driven stochastic differential equation with drift coefficient \(a(x,\alpha )\) and scale coefficient \(c(x,\gamma )\) involving unknown parameters \(\alpha \) and \(\gamma \). We suppose that the Lévy measure \(\nu _{0}\), has all order moments but is not fully specified. We will prove the joint asymptotic normality of some estimators of \(\alpha \), \(\gamma \) and a class of functional parameter \(\int \varphi (z)\nu _0(dz)\), which are constructed in a two-step manner: first, we use the Gaussian quasi-likelihood for estimation of \((\alpha ,\gamma )\); and then, for estimating \(\int \varphi (z)\nu _0(dz)\) we make use of the method of moments based on the Euler-type residual with the the previously obtained quasi-likelihood estimator.

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Acknowledgments

We are grateful to the referees for careful reading and constructive comments, which led to substantial improvements of the earlier version of this paper. This work was partly supported by JSPS KAKENHI Grant Numbers 26400204 (H. Masuda) and JST, CREST.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Hiroki Masuda

  2. Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Yuma Uehara

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  1. Hiroki Masuda
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  2. Yuma Uehara
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Correspondence to Yuma Uehara.

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Masuda, H., Uehara, Y. Two-step estimation of ergodic Lévy driven SDE. Stat Inference Stoch Process 20, 105–137 (2017). https://doi.org/10.1007/s11203-016-9133-5

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  • DOI: https://doi.org/10.1007/s11203-016-9133-5

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