Parameter estimation for rough differential equations

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.

Published in at http://dx.doi.org/10.1214/11-AOS893 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Statistical aspects of the fractional stochastic calculus
• Monte Carlo maximum likelihood estimation for discretely observed diffusion processes
• A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion
• Stochastic calculus for fractional Brownian motion with Hurst exponent $H>1/4$: A rough path method by analytic extension
• Expectation of Stratonovich iterated integrals of Wiener processes

Cited by in corpus (5)

• Nonparametric inference for fractional diffusion
• Signature Cumulants, Ordered Partitions, and Independence of Stochastic Processes
• Pathwise stability of likelihood estimators for diffusions via rough paths
• Feature Engineering with Regularity Structures
• Lévy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory