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.

翻译：提出了一种无模型的期望值格兰杰因果关系度量方法，将传统基于均值的度量推广到条件分布的任意位置。期望值是唯一兼具一致性和可激励性的法律不变风险度量，因此在风险量化与预测评估并重的分布性格兰杰因果关系研究中具有独特优势。基于该度量，利用M-vine copula模型开发了一种检验方法，该模型可处理具有$d+1$个序列的非线性和非高斯依赖下的多元格兰杰因果关系，无需对联合分布施加参数假设。在一定的正则条件下，建立了检验统计量的强相合性。有限样本仿真表明，该检验能准确控制检验水平，且检验功效随样本量增大而提高。一个关键优势在于其联合检验能力：理论和实证均证明，该方法能够检测到成对检验无法发现的因果关系。在全球和亚洲区域两个层面的国际股票市场指数应用案例，进一步展示了所提出框架的实际价值。