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

Jakub Woźny, Piotr Jaworski, Damian Jelito, Marcin Pitera and Agnieszka Wyłomańska

Journal of Multivariate Analysis, 2025, vol. 206, issue C

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 exemplary commodity and equity market data.

Keywords: Correlation; Covariance; Default risk charge; Factor copula model; Gaussian copula; Incremental risk charge; Markowitz portfolio optimisation; Multivariate normality test; Normal copula; 20/60/20 rule (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.jmva.2024.105396

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