Granger Causality in Expectiles: a M-vine copula test

Expectile-based Granger causality allows for a more comprehensive assessment of directional dependence, capturing heterogeneous causal relationships across the entire distribution, including tail regions associated with extreme risks or rare events. Furthermore, methods grounded in copula theory provide a powerful and model-free way to describe and estimate non-linear and asymmetric dependence between variables. Consequently, by integrating copula-based techniques into the expectile Granger causality framework, one can more accurately model the joint distributional dynamics and uncover causal relationships that are obscured under linear and gaussian assumptions. In this work, we introduce a model-free measure of Granger causality in expectiles that generalizes the mean-focused measure of Song and Taamouti (2018) to other parts of the distribution. Based on this measure, we propose a Granger causality in expectiles test for $k$-Markov stationary processes based on vine copulas, suitable for non-linear and non-gaussian dependence structures. By means of a simulation study, we show that our test has excellent statistical properties in terms of size and power for a wide arrange of data generating processes often used for time series modeling. Lastly, we illustrate the use our test in an empirical application with real data from financial returns.