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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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CLTs for Dependent Processes

CLTs for Dependent Processes

Chapter:
(p.380) 24 CLTs for Dependent Processes
Source:
Stochastic Limit Theory
Author(s):

James Davidson

Publisher:
Oxford University Press
DOI:10.1093/0198774036.003.0024

This chapter deals with the central limit theorem (CLT) for dependent processes. As with the law of large numbers, the focus is on near‐epoch dependent and mixing processes, and array versions of the results are given to allow heterogeneity. The cornerstone of these results is a general CLT due to McLeish, from which a result for martingales is obtained directly. A result for stationary ergodic mixingales is given, and the rest of the chapter is devoted to proving and interpreting a CLT for arrays that are near‐epoch dependent on a strong‐mixing process.

Keywords:   central limit theorem, martingale difference array, near‐epoch dependence, stationary ergodic mixingale, strong mixing

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