Maximum likelihood drift estimation for the mixing of two fractional Brownian motions

2015/06/15 by Yuliya Mishura, Mishura, Yuliya · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #stat.ME

paper · pdf · doi:10.48550/arxiv.1506.04731

arxiv created 2015/06/15 · openalex publication_date 2015/06/15 · arxiv updated 2015/06/16 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We construct the maximum likelihood estimator (MLE) of the unknown drift parameter θ∈ ℝ in the linear model X_t=θt+σB^H₁(t)+B^H₂(t), t∈[0,T], where B^H₁ and B^H₂ are two independent fractional Brownian motions with Hurst indices \frac12<H₁<H₂<1. The formula for MLE is based on the solution of the integral equation with weak polar kernel.

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