The Annals of Probability
- Ann. Probab.
- Volume 13, Number 1 (1985), 226-233.
On Series Representations for Linear Predictors
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.
Ann. Probab., Volume 13, Number 1 (1985), 226-233.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G25: Prediction theory [See also 62M20]
Secondary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series
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