The Self-normalized Asymptotic Results for Linear Processes
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.
KeywordsCentral Limit Theorem Linear Process Stationary Time Series White Noise Process Short Memory
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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