- Title Pages
- Dedication
- Epigraph
- Preface
- Acknowledgements
- Mathematical Symbols and Abbreviations
- 1 Sets and Numbers
- 2 Limits and Continuity
- 3 Measure
- 4 Integration
- 5 Metric Spaces
- 6 Topology
- 7 Probability Spaces
- 8 Random Variables
- 9 Expectations
- 10 Conditioning
- 11 Characteristic Functions
- 12 Stochastic Processes
- 13 Dependence
- 14 Mixing
- 15 Martingales
- 16 Mixingales
- 17 Near‐Epoch Dependence
- 18 Stochastic Convergence
- 19 Convergence in L <sub>p</sub> Norm
- 20 The Strong Law of Large Numbers
- 21 Uniform Stochastic Convergence
- 22 Weak Convergence of Distributions
- 23 The Classical Central Limit Theorem
- 24 CLTs for Dependent Processes
- 25 Some Extensions
- 26 Weak Convergence in Metric Spaces
- 27 Weak Convergence in a Function Space
- 28 Cadlag Functions
- 29 FCLTs for Dependent Variables
- 30 Weak Convergence to Stochastic Integrals
- References
- Index

# 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

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .

- Title Pages
- Dedication
- Epigraph
- Preface
- Acknowledgements
- Mathematical Symbols and Abbreviations
- 1 Sets and Numbers
- 2 Limits and Continuity
- 3 Measure
- 4 Integration
- 5 Metric Spaces
- 6 Topology
- 7 Probability Spaces
- 8 Random Variables
- 9 Expectations
- 10 Conditioning
- 11 Characteristic Functions
- 12 Stochastic Processes
- 13 Dependence
- 14 Mixing
- 15 Martingales
- 16 Mixingales
- 17 Near‐Epoch Dependence
- 18 Stochastic Convergence
- 19 Convergence in L <sub>p</sub> Norm
- 20 The Strong Law of Large Numbers
- 21 Uniform Stochastic Convergence
- 22 Weak Convergence of Distributions
- 23 The Classical Central Limit Theorem
- 24 CLTs for Dependent Processes
- 25 Some Extensions
- 26 Weak Convergence in Metric Spaces
- 27 Weak Convergence in a Function Space
- 28 Cadlag Functions
- 29 FCLTs for Dependent Variables
- 30 Weak Convergence to Stochastic Integrals
- References
- Index