Uniform Convergence Rate of the Nonparametric Estimator for Integrated Diffusion Processes

TL;DR

This paper establishes the first uniform convergence rates for Nadaraya-Watson estimators of integrated diffusion processes, enabling improved nonparametric inference in various scientific fields.

Contribution

It introduces uniform convergence rates for nonparametric estimators of diffusion coefficients, extending previous pointwise results to unbounded support under specific conditions.

Findings

Derived uniform convergence rates over unbounded support

Applicable to specification testing and semiparametric inference

Facilitates applications in finance, geology, and physics

Abstract

The nonparametric estimation of integrated diffusion processes has been extensively studied, with most existing research focusing on pointwise convergence. This paper is the first to establish uniform convergence rates for the Nadaraya-Watson estimators of their coefficients. We derive these rates over unbounded support under the assumptions of a vanishing observation interval and a long time horizon. Our findings serve as essential tools for specification testing and semiparametric inference in various diffusion models and time series, facilitating applications in finance, geology, and physics through nonparametric estimation methods.