Abstract: The paper considers empirical distribution functions of stationary causal processes. Weak convergence of normalized empirical distribution functions to Gaussian processes is established and sample path properties are discussed. The Chibisov-O'Reilly Theorem is generalized to dependent random variables. The proposed dependence structure is related to the sensitivity measure, a quantity appearing in the prediction theory of stochastic processes.
Key words and phrases: Empirical process, Gaussian process, Hardy inequality, linear process, martingale, maximal inequality, nonlinear time series, prediction, short-range dependence, tightness, weak convergence.