Uniform convergence of the empirical spectral distribution function

Let X be a linear process having a finite fourth moment. Assume F is a class of square-integrable functions. We consider the empirical spectral distribution function J(n,X) based on X and indexed by F. If F is totally bounded then J(n,X) satisfies a uniform strong law of large numbers. If, in addition, a metric entropy condition holds, then J(n,X) obeys the uniform central limit theorem. (C) 1997 Elsevier Science B.V.