Prediction of weakly stationary sequences on polynomial hypergroups

• 成果类型: Article
• 署名作者: Hösel, V; Lasser, R
• 署名单位: Helmholtz Association; Helmholtz-Center Munich - German Research Center for Environmental Health
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 93-114
• 关键词: orthogonal polynomials

摘要

We investigate random sequences (X(n))(nis an element ofN0) 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))(nis an element ofN0) being asymptotically deterministic.