The Annals of Probability

On Series Representations for Linear Predictors

Peter Bloomfield

Full-text: Open access

Abstract

The series expressions for the linear predictors of a stationary process have been known for a long time, but necessary and sufficient conditions for the mean square convergence of these series are still not available. It is shown that an equivalent problem is to find necessary and sufficient conditions for the invertibility of the infinite moving average representation of the process. Two known sufficient conditions are discussed, and a more general condition that includes both as special cases is given. The process that arises from fractional differencing of a random walk is discussed as an example.

Article information

Source
Ann. Probab., Volume 13, Number 1 (1985), 226-233.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993077

Digital Object Identifier
doi:10.1214/aop/1176993077

Mathematical Reviews number (MathSciNet)
MR770639

Zentralblatt MATH identifier
0559.60040

JSTOR
links.jstor.org

Subjects
Primary: 60G25: Prediction theory [See also 62M20]
Secondary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series

Keywords
Linear prediction mean square convergence invertibility

Citation

Bloomfield, Peter. On Series Representations for Linear Predictors. Ann. Probab. 13 (1985), no. 1, 226--233. doi:10.1214/aop/1176993077. https://projecteuclid.org/euclid.aop/1176993077


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