The Extremal Index of Sub-Sampled Periodic Sequences with Strong Local Dependence

Abstract

Let X = {Xn}n≥1 be a T-periodic sequence. We define a family of local dependence conditions D (k) T (u), k ≥ 1, and calculate the extremal index θX from the distributions of k consecutive variables of X. For a periodic sub-sampled sequence Y = {Xg(n)}n≥1, where g generates blocks of I1 observations separated by J observations, we present results on local and long range dependence conditions and compute the extremal index θY.