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.
"Parameter estimation for rough differential equations." Ann. Statist. 39 (4) 2047 - 2073, August 2011. https://doi.org/10.1214/11-AOS893