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Short Range and Long Range Dependence

  • Murray RosenblattEmail author
Chapter
Part of the Fields Institute Communications book series (FIC, volume 76)

Abstract

A discussion of the evolution of a notion of strong mixing as a measure of short range dependence and with additional restrictions a sufficient condition for a central limit theorem, is given. A characterization of strong mixing for stationary Gaussian sequences is noted. Examples of long range dependence leading to limit theorems with nonnormal limiting distributions are specified. Open questions concerning limit theorems for finite Fourier transforms are remarked on. There are also related queries on the use of Fourier methods for a class of nonstationary sequences.

Keywords

Spectral Density Central Limit Theorem Gaussian Process Asymptotic Normality Gaussian Stationary Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I thank Professor Rafal Kulik for his help in putting this paper into coherent form.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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