Asymptotic Theory for Kernel Estimators under Moderate Deviations from a\n Unit Root, with an Application to the Asymptotic Size of Nonparametric Tests

2015/09/16 by James A. Duffy, Duffy, James A.
Mathematics · #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1509.05017

Abstract

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

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