  This article concerns the estimation of hitting time statistics for
potentially non-stationary processes. The main focus is exceedance times of
environmental processes.
  To this end we consider an empirical estimator based on ergodic theory under
the assumption that the considered process is a deterministic transformation of
some ergodic process. This estimator is empirically analysed and rigorous
convergence results, including a central limit theorem, are covered.
  Using our estimator, we compute confidence intervals for mean exceedance
times of empirical wind data. This serves as a baseline for assessing the
performance of several models in terms of predicted mean exceedance time.
Special attention is given to the model class known as Gaussian copula
processes, which models the environmental process as a deterministic, possibly
time-dependent, transformation of a stationary parent Gaussian process.
