Moments method of estimation for diffusion processes with random effects driven by fractional Brownian motion with real application

In this paper, we propose a moment method for inferring the parameters of random effects in a stochastic differential equation driven by fractional Brownian motion, where the likelihood function is generally difficult to formulate explicitly. We obtain moment estimators for the random effects, and we study their consistency and asymptotic normality. We then derive parameter estimates for specific random effects distributions. The theoretical results are supported by numerical simulations and illustrated through an empirical study on Asian financial data.