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Identifying the successive Blumenthal–Getoor indices of a discretely observed process

Author(s): Ait-Sahalia, Yacine; Jacod, Jean

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Abstract: This paper studies the identification of the Lévy jump measure of a discretely-sampled semimartingale. We define successive Blumenthal– Getoor indices of jump activity, and show that the leading index can always be identified, but that higher order indices are only identifiable if they are sufficiently close to the previous one, even if the path is fully observed. This result establishes a clear boundary on which aspects of the jump measure can be identified on the basis of discrete observations, and which cannot. We then propose an estimation procedure for the identifiable indices and compare the rates of convergence of these estimators with the optimal rates in a special parametric case, which we can compute explicitly.
Publication Date: Jun-2012
Citation: Ait-Sahalia, Yacine, Jacod, Jean. (2012). Identifying the successive Blumenthal–Getoor indices of a discretely observed process. The Annals of Statistics, 40 (3), 1430 - 1464. doi:10.1214/12-AOS976
DOI: doi:10.1214/12-AOS976
ISSN: 0090-5364
Pages: 1430 - 1464
Type of Material: Journal Article
Journal/Proceeding Title: The Annals of Statistics
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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