Robust Inferential Methodology for Multidimensional Diffusion Processes

TL;DR

This paper develops a robust estimation method for multivariate diffusion processes observed at high frequency, providing consistency, asymptotic normality, and improved stability over traditional approaches, especially under data contamination.

Contribution

It introduces the minimum density power divergence estimator (MDPDE) for diffusion processes, offering robustness and asymptotic properties, extending classical methods in high-frequency data analysis.

Findings

MDPDE is consistent and asymptotically normal for drift and diffusion parameters.

The drift estimator converges at the √(n h_n) rate, diffusion at √n.

Simulation shows MDPDE outperforms likelihood-based estimators in finite samples.

Abstract

We investigate robust parameter estimation and testing procedure for multivariate diffusion processes observed at high frequency via the minimum density power divergence estimator (MDPDE). Within a general diffusion framework and under standard regularity conditions, we establish consistency and asymptotic normality for the estimators of both drift and diffusion parameters. The drift estimator converges at the $\sqrt{n h_n}$ rate, whereas the diffusion estimator attains the standard $\sqrt{n}$ rate, and the two estimators are shown to be asymptotically independent. The proposed methodology constitutes a robust alternative to quasi-likelihood and ordinary least squares based approaches, offering resilience against outliers, local contamination, and mild model misspecification, while remaining asymptotically equivalent to classical methods in the absence of contamination. Simulation studies demonstrate that the MDPDE achieves reliable finite-sample performance and enhanced numerical stability relative to likelihood-based estimators. These results underscore the practical relevance of divergence-based estimation for high-frequency diffusion models and point to natural extensions to more complex continuous-time settings.