SIMULTANEOUS NONPARAMETRIC INFERENCE OF TIME SERIES

• 成果类型: Article
• 署名作者: Liu, Weidong; Wu, Wei Biao
• 署名单位: University of Pennsylvania; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS789
• 发表日期: 2010
• 页码: 2388-2421
• 关键词: CONFIDENCE BANDS; term structure; DENSITY-ESTIMATION; weak dependence; partial sums; regression; approximation; models; probabilities; convolutions

摘要

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and regression estimates are asymptotically Gumbel. Our results substantially generalize earlier ones which were obtained under independence or beta mixing assumptions. The asymptotic results can be applied to assess patterns of marginal densities or regression functions via the construction of simultaneous confidence bands for which one can perform goodness-of-fit tests. As an application, we construct simultaneous confidence bands for drift and volatility functions in a dynamic short-term rate model for the U.S. Treasury yield curve rates data.