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Contrast function estimation for the drift parameter of ergodic jump diffusion process

Author

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  • Chiara Amorino
  • Arnaud Gloter

Abstract

In this paper, we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter. We suppose that the process is discretely observed. We introduce an estimator based on a contrast function, which is efficient without requiring any conditions on the rate at which the step discretization goes to zero, and where we allow the observed process to have nonsummable jumps. This extends earlier results where the condition on the step discretization was needed and where the process was supposed to have summable jumps. In general situations, our contrast function is not explicit and one has to resort to some approximation. In the case of a finite jump activity, we propose explicit approximations of the contrast function such that the efficient estimation of the drift parameter is feasible. This extends the results obtained by Kessler in the case of continuous processes.

Suggested Citation

  • Chiara Amorino & Arnaud Gloter, 2020. "Contrast function estimation for the drift parameter of ergodic jump diffusion process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 279-346, June.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:2:p:279-346
    DOI: 10.1111/sjos.12406
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    References listed on IDEAS

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    Cited by:

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    2. Amorino, Chiara & Heidari, Akram & Pilipauskaitė, Vytautė & Podolskij, Mark, 2023. "Parameter estimation of discretely observed interacting particle systems," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 350-386.
    3. Dugo, Ranieri & Giorgio, Giacomo & Pigato, Paolo, 2026. "The multivariate fractional Ornstein–Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    4. Alejandra López-Pérez & Manuel Febrero-Bande & Wencesalo González-Manteiga, 2021. "Parametric Estimation of Diffusion Processes: A Review and Comparative Study," Mathematics, MDPI, vol. 9(8), pages 1-27, April.
    5. Amorino, Chiara & Gloter, Arnaud & Halconruy, Hélène, 2025. "Evolving privacy: Drift parameter estimation for discretely observed i.i.d. diffusion processes under LDP," Stochastic Processes and their Applications, Elsevier, vol. 181(C).

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