The Annals of Statistics

Simultaneous nonparametric inference of time series

Weidong Liu and Wei Biao Wu

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 38, Number 4 (2010), 2388-2421.

Dates
First available in Project Euclid: 11 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aos/1278861252

Digital Object Identifier
doi:10.1214/09-AOS789

Mathematical Reviews number (MathSciNet)
MR2676893

Zentralblatt MATH identifier
1202.62048

Subjects
Primary: 62H15: Hypothesis testing
Secondary: 62G10: Hypothesis testing

Keywords
Gumbel distribution kernel density estimation linear process maximum deviation nonlinear time series nonparametric regression simultaneous confidence band stationary process treasury bill data

Citation

Liu, Weidong; Wu, Wei Biao. Simultaneous nonparametric inference of time series. Ann. Statist. 38 (2010), no. 4, 2388--2421. doi:10.1214/09-AOS789. https://projecteuclid.org/euclid.aos/1278861252


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