Open Access
October 2012 Nonparametric regression for locally stationary time series
Michael Vogt
Ann. Statist. 40(5): 2601-2633 (October 2012). DOI: 10.1214/12-AOS1043


In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We introduce a kernel-based method to estimate the time-varying regression function and provide asymptotic theory for our estimates. Moreover, we show that the main conditions of the theory are satisfied for a large class of nonlinear autoregressive processes with a time-varying regression function. Finally, we examine structured models where the regression function splits up into time-varying additive components. As will be seen, estimation in these models does not suffer from the curse of dimensionality.


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Michael Vogt. "Nonparametric regression for locally stationary time series." Ann. Statist. 40 (5) 2601 - 2633, October 2012.


Published: October 2012
First available in Project Euclid: 4 February 2013

zbMATH: 1373.62459
MathSciNet: MR3097614
Digital Object Identifier: 10.1214/12-AOS1043

Primary: 62G08 , 62M10
Secondary: 62G20

Keywords: local stationarity , Nonparametric regression , smooth backfitting

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 5 • October 2012
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