Parameter estimation and long-range dependence of the fractional binomial process

TL;DR

This paper investigates the long-range dependence and parameter estimation of the fractional binomial process, extending classical binomial process theory with fractional calculus and providing simulation algorithms.

Contribution

It introduces second-order property analysis, long-range dependence study, and parameter estimation methods for the fractional binomial process, along with simulation algorithms.

Findings

Long-range dependence identified in the fractional binomial process

Method of moments effectively estimates process parameters

Simulation algorithms for sample paths are developed

Abstract

In 1990, Jakeman (see \cite{jakeman1990statistics}) defined the binomial process as a special case of the classical birth-death process, where the probability of birth is proportional to the difference between a fixed number and the number of individuals present. Later, a fractional generalization of the binomial process was studied by Cahoy and Polito (2012) (see \cite{cahoy2012fractional}) and called it as fractional binomial process (FBP). In this paper, we study second-order properties of the FBP and the long-range behavior of the FBP and its noise process. We also estimate the parameters of the FBP using the method of moments procedure. Finally, we present the simulated sample paths and its algorithm for the FBP.