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ASYMPTOTIC THEORY FOR KERNEL ESTIMATORS UNDER MODERATE DEVIATIONS FROM A UNIT ROOT, WITH AN APPLICATION TO THE ASYMPTOTIC SIZE OF NONPARAMETRIC TESTS

  • James A. Duffy (a1)

Abstract

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. These results have applications to nonparametric predictive regression models. In particular, we show that the null rejection probability of a nonparametric t test is controlled uniformly in the degree of persistence of the regressor. This provides a rigorous justification for the validity of the usual nonparametric inferential procedures, even in cases where regressors may be highly persistent.

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Address correspondence to James A. Duffy, Corpus Christi College and Department of Economics, University of Oxford, Oxford, UK; e-mail: james.duffy@economics.ox.ac.uk.

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I thank V. Berenguer-Rico, S. Mavroeidis, B. Nielsen, and participants at seminars at Cambridge, Princeton, Vienna and UCL for comments on an earlier version of this article. The manuscript was prepared with LYX 2.3.1 and JabRef 3.8.2.

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ASYMPTOTIC THEORY FOR KERNEL ESTIMATORS UNDER MODERATE DEVIATIONS FROM A UNIT ROOT, WITH AN APPLICATION TO THE ASYMPTOTIC SIZE OF NONPARAMETRIC TESTS

  • James A. Duffy (a1)

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