Confidence bands in nonparametric time series regression

• 成果类型: Article
• 署名作者: Zhao, Zhibiao; Wul, Wei Biao
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS533
• 发表日期: 2008
• 页码: 1854-1878
• 关键词: variance; probabilities; deviations; bootstrap; inference

摘要

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear autoregressive processes. The results are applied to the S&P 500 Index data.