  Motivated by the pressing request of methods able to create prediction sets
in a general regression framework for a multivariate functional response and
pushed by new methodological advancements in non-parametric prediction for
functional data, we propose a set of conformal predictors that produce
finite-sample either valid or exact multivariate simultaneous prediction bands
under the mild assumption of exchangeable regression pairs. The fact that the
prediction bands can be built around any regression estimator and that can be
easily found in closed form yields a very widely usable method, which is fairly
straightforward to implement. In addition, we first introduce and then describe
a specific conformal predictor that guarantees an asymptotic result in terms of
efficiency and inducing prediction bands able to modulate their width based on
the local behavior and magnitude of the functional data. The method is
investigated and analyzed through a simulation study and a real-world
application in the field of urban mobility.
