Empirical Likelihood-Based Inference for Nonparametric Recurrent Diffusions
42 Pages Posted: 15 Jun 2008 Last revised: 18 Jan 2010
Date Written: May 2, 2009
Abstract
This paper provides a new approach to constructing confidence intervals for nonparametric drift and diffusion functions in the continuous-time diffusion model via empirical likelihood (EL). The log EL ratios are constructed through the estimating equations satisfied by the local linear estimators. Limit theories are developed by means of increasing time span and shrinking observational intervals. The results apply to both stationary and nonstationary recurrent diffusion processes. Simulations show that for both drift and diffusion functions, the new procedure performs remarkably well in finite samples and clearly dominates the conventional method in constructing confidence intervals based on asymptotic normality. An empirical example is provided to illustrate the usefulness of the proposed method.
Keywords: Confidence interval; continuous-time models; diffusion; drift; empirical likelihood; local linear smoothing; local time; nonparametric estimation; nonstationarity; stochastic differential equation.
JEL Classification: C12, C14, C22
Suggested Citation: Suggested Citation
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