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UNIFORM CONVERGENCE RATES OVER MAXIMAL DOMAINS IN STRUCTURAL NONPARAMETRIC COINTEGRATING REGRESSION

Published online by Cambridge University Press:  25 January 2017

James A. Duffy
James A. Duffy*
Affiliation:
University of Oxford
*
*Address correspondence to James A. Duffy, Institute for New Economic Thinking, Oxford Martin School; and Economics Department, University of Oxford, Oxford, UK; e-mail: james.duffy@economics.ox.ac.uk.
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Abstract

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This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than the domains that have been considered in the existing literature, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring it to satisfy only certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).

Information

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 6 , December 2017, pp. 1387 - 1417
Copyright
Copyright © Cambridge University Press 2017 

Footnotes

The author thanks Xiaohong Chen, Bent Nielsen and Peter Phillips for helpful comments on this paper, and the earlier work. The manuscript was prepared with LYX 2.1.3 and JabRef 2.7b.

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