Abstract

For time series with strong temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a representation as functionals of the empirical process and therefore inherit its slow convergence. Inference based on the asymptotic distribution of those quantities becomes highly impacted by relatively small sample sizes. We assess the quality of higher order approximations of the empirical process by deriving the asymptotic distribution of the corresponding error terms.