## Abstract

The one-step prediction problem is studied in the context of P_{n}-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 P_{n}-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 P_{n}-deterministic. For Jacobi polynomials P_{n}(x) the problem of {Mathematical expression} being asymptotic P_{n}-deterministic is completely solved.

Original language | English |
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Pages (from-to) | 199-212 |

Number of pages | 14 |

Journal | Monatshefte fur Mathematik |

Volume | 113 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1992 |

Externally published | Yes |

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