We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to measure dependence and allow for additional time dependence. Our main result is a functional central limit theorem for locally stationary processes. Moreover, maximal inequalities for expectations of sums are developed. We show the applicability of our theory in some examples, for instance, we provide uniform convergence rates for nonparametric regression with locally stationary noise.
The authors would like to thank the associate editor and two anonymous referees for their helpful remarks which helped to provide a much more concise version of the paper.
"Empirical process theory for locally stationary processes." Bernoulli 28 (1) 453 - 480, February 2022. https://doi.org/10.3150/21-BEJ1351