Vector-on-function quantile regression for stationary ergodic processes

This paper deals with quantile regression of a vector response (Y∈RqY∈Rq, q≥2q≥2) on a functional covariate XX that takes values in an infinite dimensional space. The main purpose is to introduce a kernel-type estimator of the conditional geometric quantiles whenever functional strictly stationary ergodic data are considered. We established the strong consistency with rate of the proposed estimator as well as the asymptotic distribution that leads to build a confidence region for the multivariate quantile regression. We gave also an application to joint horizon time series forecasting.