  This paper considers functional central limit theorems for stationary
absolutely regular mixing processes. Bounds for the entropy with bracketing are
derived using recent results in Nickl and P\"otscher (2007). More specifically,
their bracketing metric entropy bounds are extended to a norm defined in
Doukhan, Massart and Rio (1995, henceforth DMR) that depends both on the
marginal distribution of the process and on the mixing coefficients. Using
these bounds, and based on a result in DMR, it is shown that for the class of
weighted Besov spaces polynomially decaying tail behavior of the function class
is sufficient to obtain a functional central limit theorem under minimal
conditions. A second class of functions that allow for a functional central
limit theorem under minimal conditions are smooth functions defined on bounded
sets. Similarly, a functional CLT for polynomially explosive tail behavior is
obtained under additional moment conditions that are easy to check. An
application to a Hausman specification test illustrates the theory.
