Abstract
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.
Keywords
MathematicsRange (aeronautics)Applied mathematicsSimple (philosophy)HomogeneousCentral limit theoremLimit (mathematics)Invariance principleAlgebraic numberSample (material)Calculus (dental)Mathematical analysisStatisticsCombinatorics
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Publication Info
- Year
- 1992
- Type
- article
- Volume
- 20
- Issue
- 2
- Citations
- 906
- Access
- Closed
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Cite This
Peter C.B. Phillips,
Victor Solo
(1992).
Asymptotics for Linear Processes.
The Annals of Statistics
, 20
(2)
.
https://doi.org/10.1214/aos/1176348666
Identifiers
- DOI
- 10.1214/aos/1176348666