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

Reiichiro Kawai, Hiroki Masuda

Research output: Contribution to journalArticle

14 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 - Jan 1 2013

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Local Asymptotic Normality
Inverse Gaussian
Gaussian Process
High-frequency Data
Fisher Information Matrix
Skewness
Cauchy
Increment
Tail
Rate of Convergence
Mesh
Form

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling δ. / Kawai, Reiichiro; Masuda, Hiroki.

In: ESAIM - Probability and Statistics, Vol. 17, 01.01.2013, p. 13-32.

Research output: Contribution to journalArticle

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