Discrete and asymptotically normal estimators for both parameters of the Harmonizable fractional stable motion

Statistical estimation of the Hurst parameter and the stability parameter of harmonizable fractional stable motion (HFSM) is a difficult issue mainly due to the lack of ergodicity of this process and heaviness of tails of its marginal distributions. Very few estimators have been introduced in the literature so far. Those proposed in \cite{AA24} offer the advantages to be strongly consistent and asymptotically normal. Yet, they have the drawback to require the knowledge of a whole continuous trajectory of HFSM on the real line, whereas, in practice, only a discretized one is available. The goal of the present article is to overcome this drawback by introducing discretized versions of them, obtained through values of HFSM on dyadic numbers.