Weak convergence of the sequential empirical copula processes under long-range dependence

TL;DR

This paper investigates the asymptotic behavior of sequential empirical copula processes in multivariate stationary time series with long-range dependence, revealing distinct limit processes compared to i.i.d. cases.

Contribution

It establishes new limit theorems for empirical processes and copula processes under long-range dependence with Gaussian subordination.

Findings

Limit theorems for marginal and quantile empirical processes.

Asymptotic behavior of copula processes under long-memory.

Distinct limiting processes from i.i.d. scenarios.

Abstract

We consider multivariate copula-based stationary time-series under Gaussian subordination. Observed time series are subordinated to long-range dependent Gaussian processes and characterized by arbitrary marginal copula distributions. First of all, we establish limit theorems for the marginal and quantile marginal empirical processes of multivariate stationary long-range dependent sequences under Gaussian subordination. Furthermore, we establish the asymptotic behavior of sequential empirical copula processes under non-restrictive smoothness assumptions. The limiting processes in the case of long-memory sequences are quite different from the cases of of i.i.d. and weakly dependent observations.