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On the Local Asymptotic Behavior of the Likelihood Function for Meixner Lévy Processes under High-Frequency Sampling

By Reiichiro Kawai and Hiroki Masuda


We discuss the local asymptotic behavior of the likelihood function associated with all the four characterizing parameters (α,β,δ,μ) of the Meixner Lévy process under high-frequency sampling scheme. We derive the optimal rate of convergence for each parameter and the Fisher information matrix in a closed form. The skewness parameter β exhibits a slower rate alone, relative to the other three parameters free of sampling rate. An unusual aspect is that the Fisher information matrix is constantly singular for full joint estimation of the four parameters. This is a particular phenomenon in the regular high-frequency sampling setting and is of essentially different nature from low-frequency sampling. As soon as either α or δ is fixed, the Fisher information matrix becomes diagonal, implying that the corresponding maximum likelihood estimators are asymptotically orthogonal

Topics: Fisher information matrix, High-frequency sampling, Lévy process, Local asymptotic normality, Meixner process
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.spl.2010.12.011
OAI identifier:

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