The Annals of Statistics

Confidence bands in nonparametric time series regression

Zhibiao Zhao and Wei Biao Wu

Full-text: Open access

Abstract

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 auto-regressive processes. The results are applied to the S&P 500 Index data.

Article information

Source
Ann. Statist., Volume 36, Number 4 (2008), 1854-1878.

Dates
First available in Project Euclid: 16 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1216237302

Digital Object Identifier
doi:10.1214/07-AOS533

Mathematical Reviews number (MathSciNet)
MR2435458

Zentralblatt MATH identifier
1142.62346

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G15: Tolerance and confidence regions

Keywords
Long-range dependence model validation moderate deviation nonlinear time series nonparametric regression short-range dependence

Citation

Zhao, Zhibiao; Wu, Wei Biao. Confidence bands in nonparametric time series regression. Ann. Statist. 36 (2008), no. 4, 1854--1878. doi:10.1214/07-AOS533. https://projecteuclid.org/euclid.aos/1216237302


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