Resampling techniques for a class of smooth, possibly data-adaptive empirical copulas

TL;DR

This paper evaluates two resampling methods for inference on smooth, data-adaptive empirical copulas, demonstrating their effectiveness in constructing confidence intervals and detecting change-points in multivariate time series.

Contribution

It introduces and validates two resampling techniques for smooth copula estimators, extending their application to dependent data and change-point analysis.

Findings

Smooth resampling methods outperform non-smooth counterparts in simulations.

The methods are applicable to time series dependence and change-point detection.

The study includes analysis of derivative estimators for copulas with potential regression applications.

Abstract

We investigate the validity of two resampling techniques when carrying out inference on the underlying unknown copula using a recently proposed class of smooth, possibly data-adaptive nonparametric estimators that contains empirical Bernstein copulas (and thus the empirical beta copula). Following \cite{KirSegTsu21}, the first resampling technique is based on drawing samples from the smooth estimator and can only can be used in the case of independent observations. The second technique is a smooth extension of the so-called sequential dependent multiplier bootstrap and can thus be used in a time series setting and, possibly, for change-point analysis. The two studied resampling schemes are applied to confidence interval construction and the offline detection of changes in the cross-sectional dependence of multivariate time series, respectively. Monte Carlo experiments confirm the possible advantages of such smooth inference procedures over their non-smooth counterparts. A by-product of this work is the study of the weak consistency and finite-sample performance of two classes of smooth estimators of the first-order partial derivatives of a copula which can have applications in mean and quantile regression.