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Rates of convergence for the empirical distribution function and the empirical characteristic function of a broad class of linear processes

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  • Hesse, C. H.

Abstract

This paper deals with uniform rates of convergence for the empirical distribution function and the empirical characteristic function for a broad class of stationary linear processes. In particular, the class X(n) = [Sigma]i=0[infinity] [delta](i) z(n-1) is considered under the conditions that (a) the disturbances z(n) are independent and identically distributed with a finite first absolute moment, (b) the distribution function F of X(n) has bounded density, and (c) the parameters [delta](i) are bounded in absolute value by some function g which satisfies [Sigma]i=1[infinity] ig(i)

Suggested Citation

  • Hesse, C. H., 1990. "Rates of convergence for the empirical distribution function and the empirical characteristic function of a broad class of linear processes," Journal of Multivariate Analysis, Elsevier, vol. 35(2), pages 186-202, November.
    • Handle: RePEc:eee:jmvana:v:35:y:1990:i:2:p:186-202
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    Cited by:

    1. Rosadi, Dedi, 2009. "Testing for independence in heavy-tailed time series using the codifference function," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4516-4529, October.
    2. Christian Hesse, 1995. "Deconvolving a density from contaminated dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 645-663, December.

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