  We consider a stationary regularly varying time series which can be
expressedas a function of a geometrically ergodic Markov chain. We obtain
practical conditionsfor the weak convergence of the tail array sums and
feasible estimators ofcluster statistics. These conditions include the
so-called geometric drift or Foster-Lyapunovcondition and can be easily checked
for most usual time series models witha Markovian structure. We illustrate
these conditions on several models and statisticalapplications. A
counterexample is given to show a different limiting behaviorwhen the geometric
drift condition is not fulfilled.
