One-step prediction for Pn-weakly stationary processes

Volker Hösel, Rupert Lasser

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)199-212
Number of pages14
JournalMonatshefte fur Mathematik
Issue number3
StatePublished - Sep 1992
Externally publishedYes


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