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Uniform convergence of the empirical spectral distribution function

Let X be a linear process having a finite fourth moment. Assume is a class of square-integrable functions. We consider the empirical spectral distribution function Jn,X based on X and indexed by . If is totally bounded then Jn,X satisfies a uniform strong law of large numbers. If, in addition, a metric entropy condition holds, then Jn,X obeys the uniform central limit theorem.
Year of publication:
1997
Authors: Mikosch, T. ; Norvaisa, R.
Published in:
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 70.1997, 1, p. 85-114
Publisher: Elsevier
Keywords: Linear process Stationary sequence Spectral distribution function Empirical spectral distribution function Periodogram Uniform central limit theorem Uniform law of large numbers
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10008874143
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