Uniform Consistency of Nonstationary Kernel-Weighted Sample Covariances for Nonparametric Regression

Degui Li, Peter Phillips and Jiti Gao

No 1929, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 convergence rates depending on direction, a result that differs fundamentally from the random design and stationary cases. The uniform convergence rates derived are faster than 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 and provide sharp convergence rates in that case. 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 (search for similar items in EconPapers)
JEL-codes: C13 C14 C32 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2013-12
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Published in Econometric Theory (June 2016)

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Related works:
Journal Article: UNIFORM CONSISTENCY OF NONSTATIONARY KERNEL-WEIGHTED SAMPLE COVARIANCES FOR NONPARAMETRIC REGRESSION (2016)
Working Paper: Uniform Consistency of Nonstationary Kernel-Weighted Sample Covariances for Nonparametric Regression (2013)
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