LAN property for stochastic differential equations with additive fractional noise and continuous time observation

2015/08/31 by Yanghui Liu, Liu, Yanghui, Eulàlia Nualart +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1509.00003

Abstract

We consider a stochastic differential equation with additive fractional noise with Hurst parameter H>1/2, and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric model with rate √τ as τ→ ∞, when the solution is observed continuously on the time interval [0,τ]. The proof uses ergodic properties of the equation and a Girsanov-type transform. We analyse the particular case of the fractional Ornstein-Uhlenbeck process and show that the Maximum Likelihood Estimator is asymptotically efficient in the sense of the Minimax Theorem.

Citations

• Fractional Brownian Motions, Fractional Noises and Applications

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