Uniform and Lp Convergences for Nonparametric Continuous Time Regressions with Semiparametric Applications

Bu, Ruijun ORCID: 0000-0002-3947-3038, Kim, Jihyun and Wang, Bin (2023) Uniform and Lp Convergences for Nonparametric Continuous Time Regressions with Semiparametric Applications Journal of Econometrics, 235 (2). pp. 1934-1954. ISSN 0304-4076, 1872-6895

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Abstract

We obtain uniform and L<inf>p</inf> convergence rates of kernel type nonparametric estimators for the instantaneous conditional mean and variance functions of continuous time regressions, where the regressor is assumed to be a general recurrent diffusion. Our asymptotics are developed under a general set-up, with a shrinking sampling interval and an increasing time span, and without the stationarity assumption. Based on our convergence results, we develop a semiparametric inferential procedure for continuous time predictive regressions. In particular, a robust semiparametric likelihood ratio test for linear predictability is proposed, with its limit distribution established. We also apply our convergence results to obtain the asymptotics of a semiparametric maximum likelihood estimator of the drift of recurrent diffusions. In our simulation study, we examine the finite sample performance of our robust test against several existing tests in the literature. An empirical illustration is presented to test the predictability of the excess returns of two major stock indices using the commonly used dividend–price ratio and earnings–price ratio as the predictor.

Item Type:	Article
Uncontrolled Keywords:	Recurrent diffusion, Kernel estimation, Uniform convergence, Non, semiparametric model, Predictability, Robust inference
Divisions:	Faculty of Humanities & Social Sciences > School of Management
Depositing User:	Symplectic Admin
Date Deposited:	11 Apr 2023 09:17
Last Modified:	28 Feb 2026 02:03
DOI:	10.1016/j.jeconom.2023.02.006
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3169510
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