Asymptotic properties of the volatility estimator from high frequency data modeled by mixed fractional Brownian motion

TL;DR

This paper introduces a new volatility estimator for models driven by mixed fractional Brownian motion and demonstrates its desirable asymptotic properties, advancing statistical methods for high-frequency financial data analysis.

Contribution

It proposes a novel volatility estimator for mixed fractional Brownian motion models and establishes its asymptotic properties, filling a gap in high-frequency data analysis.

Findings

Estimator has desirable asymptotic properties

Provides a new tool for volatility estimation in MFBM models

Enhances understanding of high-frequency data modeling

Abstract

Properties of mixed fractional Brownian motion has been discussed by Cheridito (2001) and Zili (2006). We have proposed an estimator of volatility parameter for a model driven by MFBM. In our article we have shown that the estimator has some desirable asymptotic properties.