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Hösel, V. ; Lasser, R.H.

One-step prediction for Pn-weakly stationary processes.

Monatsh. Math. 113, 199-212 (1992)
DOI
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The one-step prediction problem is studied in the context of Pn-weakly stationary stochastic processes {Mathematical expression}, where {Mathematical expression} is an orthogonal polynomial sequence defining a polynomial hypergroup on {Mathematical expression}. This kind of stochastic processes appears when estimating the mean of classical weakly stationary processes. In particular, it is investigated whether these processes are asymptotic Pn-deterministic, i.e. the prediction mean-squared error tends to zero. Sufficient conditions on the covariance function or the spectral measure are given for {Mathematical expression} being asymptotic Pn-deterministic. For Jacobi polynomials Pn(x) the problem of {Mathematical expression} being asymptotic Pn-deterministic is completely solved.
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Publication type Article: Journal article
Document type Scientific Article
Corresponding Author
ISSN (print) / ISBN 0026-9255
Journal Monatshefte für Mathematik
Quellenangaben Volume: 113, Issue: 3, Pages: 199-212 Article Number: , Supplement: ,
Publisher Universität Wien
Non-patent literature Publications
Reviewing status Peer reviewed