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

MI: Global COE Program Education-and-Research Hub for Mathematics-for-Industry グローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」We prove the local asymptotic normality for the full parameters of the normal inverse Gaussian Levy process, when we observe high-frequency and long-term data. The rates of convergence turn out to be of two kinds for the dominating parameters. The essential feature in our study is that the suitably normalized increments in small time is approximately Cauchy-distributed, which specifically comes out in the form of the asymptotic Fisher information matrix