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Recovering Brownian and jump parts from high-frequency observations of a Lévy process
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González Cázares, Jorge and Ivanovs, Jevgenijs (2021) Recovering Brownian and jump parts from high-frequency observations of a Lévy process. Bernoulli, 27 (4). pp. 2413-2436. doi:10.3150/20-bej1314 ISSN 1350-7265.
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Official URL: https://doi.org/10.3150/20-bej1314
Abstract
We introduce two general non-parametric methods for recovering paths of the Brownian and jump components from high-frequency observations of a Lévy process. The first procedure relies on reordering of independently sampled normal increments and thus avoids tuning parameters. The functionality of this method is a consequence of the small time predominance of the Brownian component, the presence of exchangeable structures, and fast convergence of normal empirical quantile functions. The second procedure amounts to filtering the increments and compensating with the final value. It requires a carefully chosen threshold, in which case both methods yield the same rate of convergence. This rate depends on the small-jump activity and is given in terms of the Blumenthal–Getoor index. Finally, we discuss possible extensions, including the multidimensional case, and provide numerical illustrations.
| Item Type: | Journal Article | ||||||||
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| SWORD Depositor: | Library Publications Router | ||||||||
| Journal or Publication Title: | Bernoulli | ||||||||
| Publisher: | Bernoulli Society for Mathematical Statistics and Probability | ||||||||
| ISSN: | 1350-7265 | ||||||||
| Official Date: | 1 November 2021 | ||||||||
| Dates: |
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| Volume: | 27 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | pp. 2413-2436 | ||||||||
| DOI: | 10.3150/20-bej1314 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | ** From Crossref journal articles via Jisc Publications Router ** History: ppub 01-11-2021; issued 01-11-2021. | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Copyright Holders: | Copyright © 2021 ISI/BS | ||||||||
| Open Access Version: |
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