  In this paper, we develop a new and effective approach to nonparametric
quantile regression that accommodates ultrahigh-dimensional data arising from
spatio-temporal processes. This approach proves advantageous in staving off
computational challenges that constitute known hindrances to existing
nonparametric quantile regression methods when the number of predictors is much
larger than the available sample size. We investigate conditions under which
estimation is feasible and of good overall quality and obtain sharp
approximations that we employ to devising statistical inference methodology.
These include simultaneous confidence intervals and tests of hypotheses, whose
asymptotics is borne by a non-trivial functional central limit theorem tailored
to martingale differences. Additionally, we provide finite-sample results
through various simulations which, accompanied by an illustrative application
to real-worldesque data (on electricity demand), offer guarantees on the
performance of the proposed methodology.
