The asymptotic behavior of quadratic forms in heavy - tailedstrongly dependent random

Suppose that X t = P 1 j=0 c j Z t?j is a stationary linear sequence with regularly varying c j 's and with innovations fZ j g that have innnite variance. Such a sequence can exhibit both high variability and strong dependence. The quadratic form Q n = P n t1s=1 b (t ? s)X t X s plays an important role in the estimation of the intensity of strong dependence. In contrast with the nite variance case, n ?1=2 (Q n ? EQ n) does not converge to a Gaussian distribution. We provide conditions on the c j 's and on b for the quadratic form Q n , adequately normalized and randomly centered, to converge to a stable law of index , 1 < < 2, as n tends to innnity.