Theory of Probability and Mathematical Statistics
Statistical inference for models driven by n-th order fractional Brownian motion
Hicham Chaouch, Hamid El Maroufy and Mohamed El Omari
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Abstract: We consider the following stochastic integral equation X(t)=μt+σ∫0tφ(s)dBHn(s), t≥0, where φ is a known function and BHn is the n-th order fractional Brownian motion. We provide explicit maximum likelihood estimators for both μ and σ2, then we formulate explicitly a least squares estimator for μ and an estimator for σ2 by using power variations method. The consistency and asymptotic normality are established for those estimators when the number of observations or the time horizon is sufficiently large.
Keywords: n-th order fractional Brownian motion, maximum likelihood estimator, least squares estimator, consistency, asymptotic normality
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