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Title: Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling
Authors: Kawai, Reiichiro
Masuda, Hiroki
First Published: 14-Mar-2011
Publisher: Cambridge University Press (on behalf od EDP Sciences)
Citation: ESAIM: Probability and Statistics (in press)
Abstract: We prove the local asymptotic normality for the full parameters of the normal inverse Gaussian Lévy process X, when we observe high-frequency data XΔn ,X2Δn , . . . ,XnΔn with sampling mesh Δn→0 and the terminal sampling time nΔn→∞. The rate of convergence turns out to be (√nΔn,√nΔn,√n,√n) for the dominating parameter (α,β ,δ ,μ), where α stands for the heaviness of the tails, β the degree of skewness, δ the scale, and μ the location. The essential feature in our study is that the suitably normalized increments of X in small time is approximately Cauchy-distributed, which specifically comes out in the form of the asymptotic Fisher information matrix.
DOI Link: 10.1051/ps/2011101
ISSN: 1292-8100
eISSN: 1262-3318
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: © 2011 EDP Sciences and S.M.A.I. Deposited with reference to the publisher's archiving policy available both on the SHERPA/RoMEO website and on the journal's website.
Description: The original publication is available at:
Appears in Collections:Published Articles, Dept. of Mathematics

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