Local Asymptotic Normality for Mixed Fractional Brownian Motion with $0<H<3/4$
Chunhao Cai
TL;DR
This paper proves the Local Asymptotic Normality property for mixed fractional Brownian motion with Hurst index between 0 and 3/4, addressing estimation challenges in high-frequency data.
Contribution
It establishes the LAN property for mixed fractional Brownian motion in the specified Hurst index range, a novel theoretical result.
Findings
LAN property holds for H in (0, 3/4)
Estimation of volatility and Hurst index faces Fisher information degeneracy
Provides theoretical foundation for high-frequency inference on mixed fractional Brownian motion
Abstract
This paper establishes the Local Asymptotic Normality (LAN) property for the mixed fractional Brownian motion under high-frequency observations with Hurst index . The simultaneous estimation of the volatility and the Hurst index encounters a degeneracy problem in the Fisher information matrix.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Stochastic processes and financial applications · Random Matrices and Applications