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August 2010 Simultaneous nonparametric inference of time series
Weidong Liu, Wei Biao Wu
Ann. Statist. 38(4): 2388-2421 (August 2010). DOI: 10.1214/09-AOS789

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.

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Weidong Liu. Wei Biao Wu. "Simultaneous nonparametric inference of time series." Ann. Statist. 38 (4) 2388 - 2421, August 2010. https://doi.org/10.1214/09-AOS789

Information

Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1202.62048
MathSciNet: MR2676893
Digital Object Identifier: 10.1214/09-AOS789

Subjects:
Primary: 62H15
Secondary: 62G10

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

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 4 • August 2010
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