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This paper considers functional central limit theorems for stationaryabsolutely regular mixing processes. Bounds for the entropy with bracketing arederived using recent results in Nickl and P\"otscher (2007). More specifically,their bracketing metric entropy bounds are extended to a norm defined inDoukhan, Massart and Rio (1995, henceforth DMR) that depends both on themarginal distribution of the process and on the mixing coefficients. Usingthese bounds, and based on a result in DMR, it is shown that for the class ofweighted Besov spaces polynomially decaying tail behavior of the function classis sufficient to obtain a functional central limit theorem under minimalconditions. A second class of functions that allow for a functional centrallimit theorem under minimal conditions are smooth functions defined on boundedsets. Similarly, a functional CLT for polynomially explosive tail behavior isobtained under additional moment conditions that are easy to check. Anapplication to a Hausman specification test illustrates the theory.

Invariance Principles for Dependent Processes Indexed by Besov Classes with an Application to a Hausman Test for Linearity