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UNIFORM CONSISTENCY OF NONSTATIONARY KERNEL-WEIGHTED SAMPLE COVARIANCES FOR NONPARAMETRIC REGRESSION

Published online by Cambridge University Press:  11 May 2015

Degui Li ,
Peter C. B. Phillips  and
Jiti Gao
Degui Li*
Affiliation:
University of York
Peter C. B. Phillips
Affiliation:
Yale University, University of Auckland, Southampton University, and Singapore Management University
Jiti Gao
Affiliation:
Monash University
*
*Address correspondence to Degui Li, University of York, YO10 5DD, United Kingdom; e-mail: degui.li@york.ac.uk.
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Abstract

We obtain uniform consistency results for kernel-weighted sample covariances in a nonstationary multiple regression framework that allows for both fixed design and random design coefficient variation. In the fixed design case these nonparametric sample covariances have different uniform asymptotic rates depending on direction, a result that differs fundamentally from the random design and stationary cases. The uniform asymptotic rates derived exceed the corresponding rates in the stationary case and confirm the existence of uniform super-consistency. The modelling framework and convergence rates allow for endogeneity and thus broaden the practical econometric import of these results. As a specific application, we establish uniform consistency of nonparametric kernel estimators of the coefficient functions in nonlinear cointegration models with time varying coefficients or functional coefficients, and provide sharp convergence rates. For the fixed design models, in particular, there are two uniform convergence rates that apply in two different directions, both rates exceeding the usual rate in the stationary case.

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Type
ARTICLES
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Econometric Theory , Volume 32 , Issue 3 , June 2016 , pp. 655 - 685
Copyright
Copyright © Cambridge University Press 2015 

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