Prediction of weakly stationary sequences on polynomial hypergroups

Prediction of weakly stationary sequences on polynomial hypergroups

Volker Hösel and Rupert Lasser

Source: Ann. Probab. Volume 31, Number 1 (2003), 93-114.

Abstract

We investigate random sequences $(X_n)_{\nin_0}$ with spectral representation based on certain orthogonal polynomials, that is, random sequences that are weakly stationary with respect to polynomial hypergroups. We present various situations where one meets this kind of sequence. The main topic is on the one-step prediction. In particular, it is examined when the mean-squared error tends to zero. For many cases we present a complete solution for the problem of $(X_n)_{\nin_0}$ being asymptotically deterministic.

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Primary Subjects: 60G10, 60G25, 43A62

Keywords: Prediction; random sequences; orthogonal polynomials; hypergroups

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1046294305
Digital Object Identifier: doi:10.1214/aop/1046294305
Mathematical Reviews number (MathSciNet): MR1959787
Zentralblatt MATH identifier: 1014.60039

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