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In this paper we study the asymptotic theory for quadratic variation of aharmonizable fractional $\al$-stable process. We show a law of large numberswith a non-ergodic limit and obtain weak convergence towards a L\'evy-drivenRosenblatt random variable when the Hurst parameter satisfies $H\in (1/2,1)$and $\al(1-H)<1/2$. This result complements the asymptotic theory forfractional stable processes investigated in e.g.\cite{BHP19,BLP17,BP17,BPT20,LP18,MOP20}.

Asymptotic theory for quadratic variation of harmonizable fractional stable processes