Parameter Estimation for the Linear Self-Attracting Diffusion Processes

In this paper, we investigate parameter estimation for a class of linear self-attracting diffusion processes. Specifically, we consider processes with a drift coefficient given by −θ∫0t(Xt−Xu)du. Employing both maximum likelihood estimation and least squares estimation, we show that the resulting estimators coincide. We establish the consistency and asymptotic normality of θ^N for high-frequency data, and assess its numerical performance through simulation studies.