Asymptotic theory for quadratic variation of harmonizable fractional stable processes

02/27/2023

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In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional -stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a Lévy-driven Rosenblatt random variable when the Hurst parameter satisfies H∈ (1/2,1) and (1-H)<1/2. This result complements the asymptotic theory for fractional stable processes investigated in e.g. <cit.>.

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Asymptotic theory for quadratic variation of harmonizable fractional stable processes

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Asymptotic theory for quadratic variation of harmonizable fractional stable processes

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