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

Reiichiro Kawai, Hiroki Masuda

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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,X 2Δn,...,X nΔn with sampling mesh Δn → 0 and the terminal sampling time nΔn → â̂ž. The rate of convergence turns out to be (aš nΔn, ǎš nΔn, 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 languageEnglish
Pages (from-to)13-32
Number of pages20
JournalESAIM - Probability and Statistics
Volume17
DOIs
Publication statusPublished - 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Fingerprint Dive into the research topics of 'Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling δ'. Together they form a unique fingerprint.

Cite this