Oscillations of empirical distribution functions under dependence

Abstract

We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as the one obtained under independence. The dependence conditions are expressed in terms of physical dependence measures which are directly related to the data-generating mechanism of the underlying processes and thus are easy to work with.