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A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

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  • Katerina Papagiannouli

    (Humboldt Universität zu Berlin)

Abstract

We suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the Lévy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepskiĭ-type stopping rule for the adaptive procedure. Consequently, we use a balancing principle for the best possible data-driven parameter. The adaptive estimator achieves almost the optimal rate. Numerical experiments with the proposed selection rule are also presented.

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  • Katerina Papagiannouli, 2022. "A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 505-535, October.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:3:d:10.1007_s11203-021-09264-2
    DOI: 10.1007/s11203-021-09264-2
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    References listed on IDEAS

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    1. Mancini, Cecilia, 2017. "Truncated Realized Covariance when prices have infinite variation jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1998-2035.
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    3. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    4. F. Comte & C. Lacour, 2011. "Data‐driven density estimation in the presence of additive noise with unknown distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 601-627, September.
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