An improvement of the mixing rates in a counter-example to the weak invariance principle

Abstract

In [1], the authors gave an example of absolutely regular strictly stationary process that satisfies the central limit theorem, but not the weak invariance principle. For each q</1/2, the process can be constructed with mixing rates of order N−q. The goal of this note is to show that actually the same construction can give mixing rates of order N−q for a given q<1.