Prediction of weakly stationary sequences on polynomial hypergroups

Volker Hösel; Rupert Lasser

doi:10.1214/aop/1046294305

Prediction of weakly stationary sequences on polynomial hypergroups

Volker Hösel, Rupert Lasser

Helmholtz Zentrum München German Research Center for Environmental Health

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We investigate random sequences (X_n)_n∈ℕ0 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)_n∈ℕ0 being asymptotically deterministic.

Original language	English
Pages (from-to)	93-114
Number of pages	22
Journal	Annals of Probability
Volume	31
Issue number	1
DOIs	https://doi.org/10.1214/aop/1046294305
State	Published - Jan 2003
Externally published	Yes

Keywords

Hypergroups
Orthogonal polynomials
Prediction
Random sequences

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10.1214/aop/1046294305

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abstract = "We investigate random sequences (Xn)n∈ℕ0 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 (Xn)n∈ℕ0 being asymptotically deterministic.",

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AB - We investigate random sequences (Xn)n∈ℕ0 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 (Xn)n∈ℕ0 being asymptotically deterministic.

KW - Hypergroups

KW - Orthogonal polynomials

KW - Prediction

KW - Random sequences

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Prediction of weakly stationary sequences on polynomial hypergroups

Abstract

Keywords

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