## 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 X_{Δ}n,X 2Δ_{n},...,X nΔ_{n} with sampling mesh Δ_{n} → 0 and the terminal sampling time nΔ_{n} → â̂ž. The rate of convergence turns out to be (aš nΔ_{n}, ǎš nΔ_{n}, ǎš n, ǎš 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.

Original language | English |
---|---|

Pages (from-to) | 13-32 |

Number of pages | 20 |

Journal | ESAIM - Probability and Statistics |

Volume | 17 |

DOIs | |

Publication status | Published - 2013 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability