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Threshold estimation for jump-diffusions under small noise asymptotics

Author

Listed:
  • Mitsuki Kobayashi

    (Waseda University)

  • Yasutaka Shimizu

    (Waseda University)

Abstract

We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and asymptotic normality under new asymptotics. One of the novelties of the paper is that we give a new localization argument, which enables us to avoid truncation in the contrast function that has been used in earlier works and to deal with a wider class of jumps in threshold estimation than ever before.

Suggested Citation

  • Mitsuki Kobayashi & Yasutaka Shimizu, 2023. "Threshold estimation for jump-diffusions under small noise asymptotics," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 361-411, July.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:2:d:10.1007_s11203-023-09286-y
    DOI: 10.1007/s11203-023-09286-y
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    References listed on IDEAS

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    1. Gloter, Arnaud & Sørensen, Michael, 2009. "Estimation for stochastic differential equations with a small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 679-699, March.
    2. Long, Hongwei & Shimizu, Yasutaka & Sun, Wei, 2013. "Least squares estimators for discretely observed stochastic processes driven by small Lévy noises," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 422-439.
    3. Yasutaka Shimizu, 2006. "M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely Many Jumps," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 179-225, July.
    4. Yasutaka Shimizu, 2017. "Threshold Estimation for Stochastic Processes with Small Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 951-988, December.
    5. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    6. Yasutaka Shimizu, 2010. "Threshold selection in jump-discriminant filter for discretely observed jump processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 355-378, August.
    7. Yasutaka Shimizu & Nakahiro Yoshida, 2006. "Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 227-277, October.
    8. Chiara Amorino & Arnaud Gloter, 2021. "Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 61-148, April.
    9. T. Ogihara & N. Yoshida, 2011. "Quasi-likelihood analysis for the stochastic differential equation with jumps," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 189-229, October.
    10. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
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