Tests of independence and randomness for arbitrary data using copula-based covariances

2023/01/30 by Bouchra Nasri, Nasri, Bouchra R., Bruno Rémillard +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2301.13259

openalex publication_date 2023/01/30 · openalex created_date 2023/02/03 · openalex updated_date 2026/07/28

Abstract

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multivariate extensions using Möbius transforms. We find the asymptotic distributions of these statistics under the null hypothesis of independence or randomness, as well as under contiguous alternatives. This enables us to find out locally most powerful test statistics for some alternatives, whatever the margins. Numerical experiments are performed for Wald's type combinations of these statistics to assess the finite sample performance.

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