| 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, X2 Δn, ..., XnΔ n with sampling mesh Δn → 0 and the terminal sampling time nΔ n → ∞. The rate of convergence turns out to be (√ nΔ n, √ nΔ n, √ 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.
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