Publication Type

Journal Article

Version

publishedVersion

Publication Date

6-2016

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.

Keywords

Cointegration, Functional coefficients, Kernel degeneracy, Nonparametric kernel smoothing, Random coordinate rotation, Super-consistency, Uniform convergence rates, Time varying coefficients

Discipline

Growth and Development

Research Areas

Econometrics

Publication

Econometric Theory

Volume

32

Issue

3

First Page

655

Last Page

685

ISSN

0266-4666

Identifier

10.1017/S0266466615000109

Publisher

Cambridge University Press

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1017/S0266466615000109

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