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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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dc.contributor.authorAit-Sahalia, Yacine-
dc.contributor.authorJacod, Jean-
dc.date.accessioned2019-12-04T19:05:31Z-
dc.date.available2019-12-04T19:05:31Z-
dc.date.issued2012-06en_US
dc.identifier.citationAit-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-AOS976en_US
dc.identifier.issn0090-5364-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1v17m-
dc.description.abstractThis 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.en_US
dc.format.extent1430 - 1464en_US
dc.language.isoen_USen_US
dc.relation.ispartofThe Annals of Statisticsen_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleIdentifying the successive Blumenthal–Getoor indices of a discretely observed processen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1214/12-AOS976-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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