The Annals of Statistics

Asymptotics for Linear Processes

Peter C. B. Phillips and Victor Solo

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A method of deriving asymptotics for linear processes is introduced which uses an explicit algebraic decomposition of the linear filter. The technique is closely related to Gordin's method but has some advantages over it, especially in terms of its range of application. The method offers a simple unified approach to strong laws, central limit theory and invariance principles for linear processes. Sample means and sample covariances are covered. The results accommodate both homogeneous and heterogeneous innovations as well as innovations with undefined means and variances.

Article information

Ann. Statist., Volume 20, Number 2 (1992), 971-1001.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles 60F15: Strong theorems

BN decomposition central limit theory functional limit laws infinite variance errors law of iterated logarithm linear process stable process strong laws


Phillips, Peter C. B.; Solo, Victor. Asymptotics for Linear Processes. Ann. Statist. 20 (1992), no. 2, 971--1001. doi:10.1214/aos/1176348666.

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