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

Reiichiro Kawai; Hiroki Masuda

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 13-32
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Kawai, Reiichiro, and Masuda, Hiroki. "Local asymptotic normality for normal inverse gaussian Lévy processes with high-frequency sampling." ESAIM: Probability and Statistics 17 (2013): 13-32. <http://eudml.org/doc/273614>.

@article{Kawai2013,
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.},
author = {Kawai, Reiichiro, Masuda, Hiroki},
journal = {ESAIM: Probability and Statistics},
keywords = {high-frequency sampling; local asymptotic normality; normal inverse gaussian Lévy process; normal inverse Gaussian Lévy processes},
language = {eng},
pages = {13-32},
publisher = {EDP-Sciences},
title = {Local asymptotic normality for normal inverse gaussian Lévy processes with high-frequency sampling},
url = {http://eudml.org/doc/273614},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Kawai, Reiichiro
AU - Masuda, Hiroki
TI - Local asymptotic normality for normal inverse gaussian Lévy processes with high-frequency sampling
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 13
EP - 32
AB - 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.
LA - eng
KW - high-frequency sampling; local asymptotic normality; normal inverse gaussian Lévy process; normal inverse Gaussian Lévy processes
UR - http://eudml.org/doc/273614
ER -

References

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