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Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling

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journal contribution
posted on 29.02.2012, 11:06 by Reiichiro Kawai, Hiroki Masuda
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.

History

Citation

ESAIM: Probability and Statistics (in press)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

ESAIM: Probability and Statistics (in press)

Publisher

Cambridge University Press (on behalf od EDP Sciences)

issn

1292-8100

eissn

1262-3318

Copyright date

2011

Available date

29/02/2012

Publisher version

http://www.esaim-ps.org/articles/ps/abs/2013/01/ps110002/ps110002.html

Notes

The original publication is available at: www.edpsciences.org/ps

Language

en