[Paper Review] On Some Resampling Procedures with the Empirical Beta Copula

Anna Kiriliouk, Johan Segers+1 more|arXiv (Cornell University)|May 29, 2019

Financial Risk and Volatility Modeling14 references4 citations

TL;DR

This paper proposes and evaluates resampling procedures based on the empirical beta copula for improved accuracy in statistical inference on copula dependence structures. It demonstrates asymptotic equivalence between bootstrap methods using the empirical and empirical beta copulas, and via Monte Carlo simulations shows that the beta copula-based resampling yields more reliable confidence intervals and hypothesis tests for rank correlations and dependence parameters.

ABSTRACT

The empirical beta copula is a simple but effective smoother of the empirical copula. Because it is a genuine copula, from which, moreover, it is particularly easy to sample, it is reasonable to expect that resampling procedures based on the empirical beta copula are expedient and accurate. In this paper, after reviewing the literature on some bootstrap approximations for the empirical copula process, we first show the asymptotic equivalence of several bootstrapped processes related to the empirical copula and empirical beta copula. Then we investigate the finite-sample properties of resampling schemes based on the empirical (beta) copula by Monte Carlo simulation. More specifically, we consider interval estimation for some functionals such as rank correlation coefficients and dependence parameters of several well-known families of copulas, constructing confidence intervals by several methods and comparing their accuracy and efficiency. We also compute the actual size and power of symmetry tests based on several resampling schemes for the empirical copula and empirical beta copula.

Motivation & Objective

• To assess the finite-sample performance of resampling procedures based on the empirical beta copula for statistical inference on copula parameters.
• To compare the accuracy and efficiency of confidence interval construction methods for rank correlation coefficients and copula dependence parameters.
• To evaluate the actual size and power of symmetry tests using resampling from the empirical and empirical beta copulas.
• To establish asymptotic equivalence between bootstrapped processes based on the empirical copula and the empirical beta copula.

Proposed method

• The empirical beta copula is used as a smoothed version of the empirical copula, enabling easier and more stable resampling.
• Asymptotic equivalence between bootstrap processes based on the empirical copula and the empirical beta copula is formally established.
• Monte Carlo simulations are conducted to evaluate resampling schemes under various copula families and dependence scenarios.
• Confidence intervals for rank correlation coefficients and copula parameters are constructed using several resampling-based methods.
• Symmetry tests are performed using resampled p-values derived from both the empirical and empirical beta copulas.
• The performance of each resampling scheme is evaluated in terms of coverage probability, interval width, actual size, and power.

Experimental results

Research questions

• RQ1 Does resampling from the empirical beta copula yield more accurate confidence intervals than resampling from the empirical copula?
• RQ2 How do different resampling-based methods compare in terms of coverage probability and interval width for dependence parameters?
• RQ3 What is the actual size and power of symmetry tests when using resampling from the empirical versus the empirical beta copula?
• RQ4 Are the bootstrap processes based on the empirical copula and the empirical beta copula asymptotically equivalent?

Key findings

• The empirical beta copula-based resampling produces confidence intervals with better coverage probabilities and narrower widths compared to standard empirical copula resampling.
• The bootstrap processes based on the empirical copula and the empirical beta copula are asymptotically equivalent, justifying the use of the latter for inference.
• Resampling from the empirical beta copula leads to more accurate actual size and higher power in symmetry tests compared to the empirical copula-based approach.
• The proposed resampling schemes show improved efficiency and robustness in finite samples, especially under moderate to high dependence.