# 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

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topKawai, 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 -

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