A theoretically sound bootstrap procedure is proposed for building accurate confidence intervals of parameters describing the extremal behavior of instantaneous functionals of a Harris Markov chain, namely the extremal and tail indexes. Regenerative properties of the chain (or of a Nummelin extension of the latter) are here exploited in order to construct consistent estimators of these parameters, following the approach developed in Bertail, Clémençon & Tressou (Extremes, 2009). Their asymptotic normality is first established and the standardization problem is also tackled. It is then proved that, based on these estimators, the (approximate) regenerative block-bootstrap introduced in Bertail &Clémençon (2006) yields asymptotically valid confidence intervals. In order to illustrate the performance of the methodology studied in this paper, simulation results are additionally displayed.
