Chapter

CLTs for Dependent Processes

James Davidson

in Stochastic Limit Theory

Published in print October 1994 | ISBN: 9780198774037
Published online November 2003 | e-ISBN: 9780191596117 | DOI: http://dx.doi.org/10.1093/0198774036.003.0024

Series: Advanced Texts in Econometrics

 CLTs for Dependent Processes

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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

Chapter.  10973 words.  Illustrated.

Subjects: Econometrics and Mathematical Economics

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