Second-order expansions for maxima of dynamic bivariate normal copulas

TL;DR

This paper derives second-order distributional expansions for the maxima of independent bivariate normal copulas with monotone correlation functions, aiding in understanding convergence rates to their limiting distributions.

Contribution

It introduces second-order expansions for maxima of normal copulas with monotone correlations, providing insights into convergence rates beyond first-order asymptotics.

Findings

Derived second-order distributional expansions for maxima

Quantified convergence rates to limiting distributions

Applicable to normal copulas with monotone correlations

Abstract

In this paper, we establish the second-order distributional expansions of normalized maxima of n independent observations, where the ith observation follows from a normal copula with its correlation coefficient being a monotone continuous function. These expansions can be used to deduce the convergence rates of distributions of normalized maxima to their limits.