Multivariate Quantile-on-Quantile Granger Causality

Implements bivariate and Multivariate Quantile-on-Quantile Granger causality tests building on the Quantile-on-Quantile regression framework of Sim and Zhou (2015) and the quantile Granger causality test of Troster (2018) . The bivariate test estimates the local-linear slope in the quantile regression of y_t on lagged x_t with lagged y_t as control, using Gaussian kernel weights, and tests it against zero by paired bootstrap. The multivariate (conditional) test additionally conditions on a set of moderators Z and optional x times Z interaction terms, in the spirit of Sinha, Ghosh, Hussain, Nguyen and Das (2023) . A Sup-Wald summary across the quantile grid is also provided. Heatmaps and 3D surfaces default to the 'MATLAB' 'Parula' colour map.