Prediction of weakly stationary sequences on polynomial hypergroups

• Volker Hösel ^[1] ; Rupert Lasser ^[1]
  1. [1] GSF-National Research Center for Environment and Health
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 1, 2003, págs. 93-114
• Idioma: inglés
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• Resumen

  • We investigate random sequences (Xn)\nin0 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)\nin0 being asymptotically deterministic.