Parameter estimation of a process driven by fractional Brownian motion: An estimating function approach

by Inderdeep Kaur, T. V. Ramanathan and U. V. Naik-Nimbalkar.

Abstract: Statistical inference problems related to self similar processes and processes driven by the fractional Brownian motion have been studied extensively by various researchers, when the process is observed continuously. However, there were not enough attempts to investigate the inference problems of these processes, when the observational scheme is discrete in nature. Here we address this problem using the ideas of estimating functions. Optimal estimating function has been proposed for the estimation of the parameters of a process driven by fractional Brownian motion. Simulation studies indicate that the computational time can be substantially reduced, if the proposed methods are used as opposed to approximations to the integrals that appears in the maximum likelihood estimator, under continuous observational scheme. We discuss the parameter estimation of fractional versions of Gompertzian and Vasicek models, using the proposed procedure.

Key Words: Discretely observed processes, Estimating equations, Fractional Brownian motions, Fractional Ornstein-Uhlenbeck type process, Self-similar processes

Authors:
Inderdeep Kaur, k.inderdeep@gmail.com
T. V. Ramanathan, ram@stats.unipune.ac.in
U. V. Naik-Nimbalkar, uvnaik@stats.unipune.ac.in

Editor: Shelton Peiris, shelton.peiris@sydney.edu.au

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