Gaussian dependence structure pairwise goodness-of-fit testing based on conditional covariance and the 20/60/20 rule

TL;DR

This paper introduces a new statistical testing framework for assessing Gaussian dependence structures using a 20/60/20 data clustering rule and conditional covariance estimates, demonstrating superior performance over existing methods.

Contribution

The paper proposes a novel, data-driven goodness-of-fit test for Gaussian dependence that leverages the 20/60/20 rule and conditional covariance, with proven statistical properties and practical effectiveness.

Findings

Outperforms benchmark tests in power simulations.

Provides a practical and interpretable test statistic.

Successfully applied to commodities market data.

Abstract

We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test clusters the data according to the 20/60/20 rule and confronts conditional covariance (or correlation) estimates on the obtained subsets. The corresponding test statistic has a natural practical interpretation, desirable statistical properties, and asymptotic pivotal distribution under the multivariate normality assumption. We illustrate the usefulness of the introduced framework using extensive power simulation studies and show that our approach outperforms popular benchmark alternatives. Also, we apply the proposed methodology to commodities market data.