Parameter estimation for rough differential equations

TL;DR

This paper introduces a new estimator for rough differential equations, proving its statistical properties and applying it to estimate parameters in models driven by fractional Brownian motion.

Contribution

It develops the expected signature matching estimator for rough differential equations, establishing its consistency and asymptotic normality, and demonstrates its application to fractional diffusion models.

Findings

Estimator is consistent and asymptotically normal.

Effective in estimating parameters of fractional diffusions.

Applicable to differential equations driven by rough paths.

Abstract

We construct the "expected signature matching" estimator for differential equations driven by rough paths and we prove its consistency and asymptotic normality. We use it to estimate parameters of a diffusion and a fractional diffusions, that is, a differential equation driven by fractional Brownian motion.