Open Access
February, 1985 On Series Representations for Linear Predictors
Peter Bloomfield
Ann. Probab. 13(1): 226-233 (February, 1985). DOI: 10.1214/aop/1176993077


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.


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Peter Bloomfield. "On Series Representations for Linear Predictors." Ann. Probab. 13 (1) 226 - 233, February, 1985.


Published: February, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0559.60040
MathSciNet: MR770639
Digital Object Identifier: 10.1214/aop/1176993077

Primary: 60G25
Secondary: 42A20

Keywords: invertibility , Linear prediction , mean square convergence

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 1 • February, 1985
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