On comparison of the estimators of the Hurst index and the diffusion coefficient of the fractional Gompertz diffusion process

TL;DR

This paper evaluates various estimators for the Hurst index and diffusion coefficient of the fractional Gompertz diffusion process, demonstrating their consistency and normality, and compares their asymptotic behaviors through simulations.

Contribution

It introduces and compares multiple estimators for key parameters of the fractional Gompertz diffusion process, establishing their statistical properties.

Findings

Estimators are strongly consistent.

Most estimators are asymptotically normal.

Simulation results compare estimator performances.

Abstract

We study some estimators of the Hurst index and the diffusion coefficient of the fractional Gompertz diffusion process and prove that they are strongly consistent and most of them are asymptotically normal. Moreover, we compare the asymptotic behavior of these estimators with the aid of computer simulations.