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February 2014 Uniform convergence rates for a class of martingales with application in non-linear cointegrating regression
Qiying Wang, Nigel Chan
Bernoulli 20(1): 207-230 (February 2014). DOI: 10.3150/12-BEJ482

Abstract

For a class of martingales, this paper provides a framework on the uniform consistency with broad applicability. The main condition imposed is only related to the conditional variance of the martingale, which holds true for stationary mixing time series, stationary iterated random function, Harris recurrent Markov chains and $I(1)$ processes with innovations being a linear process. Using the established results, this paper investigates the uniform convergence of the Nadaraya–Watson estimator in a non-linear cointegrating regression model. Our results not only provide sharp convergence rate, but also the optimal range for the uniform convergence to be held. This paper also considers the uniform upper and lower bound estimates for a functional of Harris recurrent Markov chain, which are of independent interests.

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Qiying Wang. Nigel Chan. "Uniform convergence rates for a class of martingales with application in non-linear cointegrating regression." Bernoulli 20 (1) 207 - 230, February 2014. https://doi.org/10.3150/12-BEJ482

Information

Published: February 2014
First available in Project Euclid: 22 January 2014

zbMATH: 06282548
MathSciNet: MR3160579
Digital Object Identifier: 10.3150/12-BEJ482

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 1 • February 2014
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