Asymptotic theory for quadratic variation of harmonizable fractional stable processes

In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional α-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 α(1−H) < 1/2. This result complements the asymptotic theory for fractional stable processes.