The Annals of Statistics
- Ann. Statist.
- Volume 20, Number 2 (1992), 971-1001.
Asymptotics for Linear Processes
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.
Ann. Statist., Volume 20, Number 2 (1992), 971-1001.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
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
Phillips, Peter C. B.; Solo, Victor. Asymptotics for Linear Processes. Ann. Statist. 20 (1992), no. 2, 971--1001. doi:10.1214/aos/1176348666. https://projecteuclid.org/euclid.aos/1176348666