Convergence of exceedance point processes of normal sequences with a seasonal component and its applications

Abstract

In this paper, we prove that, under some mild conditions, a time-normalized point process of exceedances by a nonstationary and strongly dependent normal sequence with a seasonal component converges in distribution to the in plane Cox process. As an application of the convergence result, we deduce two important joint limit distributions for the order statistics.MSC: 60F05; 62E20; 62F12; 62M10