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MARTINGALE LIMIT THEOREM REVISITED AND NONLINEAR COINTEGRATING REGRESSION

Published online by Cambridge University Press:  29 November 2013

Qiying Wang
Qiying Wang*
Affiliation:
University of Sydney
*
*Address correspondence to Qiying Wang, School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia; e-mail: qiying@maths.usyd.edu.au.
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Abstract

For a certain class of martingales, convergence to a mixture of normal distributions is established under convergence in distribution for the conditional variance. This is less restrictive in comparison with the classical martingale limit theorem, where one generally requires convergence in probability. The extension partially removes a barrier in the applications of the classical martingale limit theorem to nonparametric estimation and inference with nonstationarity and enhances the effectiveness of the classical martingale limit theorem as one of the main tools to investigate asymptotics in statistics, econometrics, and other fields. The main result is applied to investigate limit behavior of the conventional kernel estimator in a nonlinear cointegrating regression model, which improves existing works in the literature.

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ARTICLES
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Econometric Theory , Volume 30 , Issue 3 , June 2014 , pp. 509 - 535
Copyright
Copyright © Cambridge University Press 2013 

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