Asymptotic theory for quadratic variation of harmonizable fractional stable processes

02/27/2023

∙

by   Andreas Basse-O'Connor, et al.

∙

0

∙

share

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.>.