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Functional estimation for Lvy measures of semimartingales with Poissonian jumps

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  • Shimizu, Yasutaka

Abstract

We consider semimartingales with jumps that have finite Lvy measures. The purpose of this article is to estimate integral-type functionals of the Lvy measures from discrete observations. We propose two types of estimators: kernel-type and empirical-type estimators, both of which are obtained by direct discretization from asymptotically efficient estimators of the target based on continuous observations. We show the asymptotic efficiency in the asymptotic minimax sense of our estimators as the sample size tends to infinity and the sampling interval tends to zero.

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  • Shimizu, Yasutaka, 2009. "Functional estimation for Lvy measures of semimartingales with Poissonian jumps," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1073-1092, July.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1073-1092
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    2. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
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    5. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    6. 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.
    7. Yoichi Nishiyama, 1995. "Local asymptotic normality of a sequential model for marked point processes and its applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 195-209, June.
    8. Bandi, Federico M. & Nguyen, Thong H., 2003. "On the functional estimation of jump-diffusion models," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 293-328.
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    1. Yuan Gao & Honglong You, 2021. "The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered α -Stable Lévy Subordinator," Mathematics, MDPI, vol. 9(21), pages 1-9, October.
    2. Hacène Djellout & Hui Jiang, 2018. "Large Deviations of the Threshold Estimator of Integrated (Co-)Volatility Vector in the Presence of Jumps," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1606-1624, September.
    3. Jakobsen, Nina Munkholt & Sørensen, Michael, 2019. "Estimating functions for jump–diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3282-3318.
    4. Hacène Djellout & Hui Jiang, 2015. "Large Deviations Of The Threshold Estimator Of Integrated (Co-)Volatility Vector In The Presence Of Jumps," Working Papers hal-01147189, HAL.
    5. Hiroki Masuda & Yuma Uehara, 2017. "Two-step estimation of ergodic Lévy driven SDE," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 105-137, April.
    6. Honglong You & Yuan Gao, 2019. "Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    7. Hacène Djellout & Hui Jiang, 2018. "Large Deviations Of The Threshold Estimator Of Integrated (Co-)Volatility Vector In The Presence Of Jumps," Post-Print hal-01147189, HAL.

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