Granger Causality in Expectiles: an M-vine copula test

TL;DR

This paper introduces a model-free, distribution-aware Granger causality measure based on expectiles, utilizing M-vine copula models to detect complex, non-linear, and non-Gaussian causal relationships in multivariate financial data.

Contribution

It develops a novel, non-parametric test for distributional Granger causality using expectiles and M-vine copulas, allowing for joint causality detection beyond pairwise analysis.

Findings

Accurate size control and increased power with larger samples.

Joint testing reveals causal links invisible to pairwise tests.

Applications demonstrate practical relevance in stock market indices.

Abstract

A model-free measure of Granger causality in expectiles is proposed, generalizing the traditional mean-based measure to arbitrary positions of the conditional distribution. Expectiles are the only law-invariant risk measures that are both coherent and elicitable, making them particularly well-suited for studying distributional Granger causality where risk quantification and forecast evaluation are both relevant. Based on this measure, a test is developed using M-vine copula models that accounts for multivariate Granger causality with $d+1$ series under non-linear and non-Gaussian dependence, without imposing parametric assumptions on the joint distribution. Strong consistency of the test statistic is established under some regularity conditions. In finite samples, simulations show accurate size control and power increasing with sample size. A key advantage is the joint testing capability: causal relationships invisible to pairwise tests can be detected, as demonstrated both theoretically and empirically. Two applications to international stock market indices at the global and Asian regional level illustrate the practical relevance of the proposed framework.