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Likelihood Estimation of Stable Levy Processes from Discrete Data

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概要 We study the likelihood inference for real-valued non-Gaussian stable Levy processes $ X = (X_t)_{t in R_+} $ based on sampled data $ (X_{ih}_n)^n_{i=0} $, where $ h_n downarrow 0 $, focusing on cases... of either symmetric or completely skewed (one-sided) Levy density. First, the local asymptotic normality with always degenerate Fisher information matrix is obtained, so that the maximum likelihood estimation is inappropriate for joint estimation of all parameters involved. Second, supposing that either index or scale parameter is known, we obtain the uniform asymptotic normality of the maximum likelihood estimates and their asymptotic efficiency, where the resulting optimal convergence rates reveal that, as opposed to the Gaussian case, that $ nh_n \rightarrow infty $ is not necessary for consistent estimation for all parameters.続きを見る

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登録日 2009.04.22
更新日 2018.02.23