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The Self-normalized Asymptotic Results for Linear Processes

  • Magda Peligrad
  • Hailin SangEmail author
Part of the Fields Institute Communications book series (FIC, volume 76)

Abstract

The linear process is a tool for studying stationary time series. One can have a better understanding of many important time series by studying the corresponding linear processes. The strength of dependence and the tail properties of time series built upon linear processes can be expressed in terms of the linear process itself through the innovations and their weights. In this paper we survey recent developments on some asymptotics of linear processes. These asymptotics include central limit theorem, functional central limit theorem and their self-normalized forms.

Keywords

Central Limit Theorem Linear Process Stationary Time Series White Noise Process Short Memory 
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

We thank Rafal Kulik and the referees for helpful comments. Magda Peligrad was supported in part by a Charles Phelps Taft Memorial Fund grant, the NSA grant H98230-11-1-0135, and the NSF grant DMS-1208237.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Department of MathematicsUniversity of MississippiUniversityUSA

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