2020/04/10 by El Mehdi Haress, Haress, El Mehdi, Yaozhong Hu +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Fractional Differential Equations Solutions #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.2004.05096
arxiv created 2020/04/10 · openalex publication_date 2020/04/10 · arxiv updated 2020/04/13 · openalex created_date 2020/04/17 · openalex updated_date 2026/07/28
Let the Ornstein-Uhlenbeck process (Xt)t≥0 driven by a fractional Brownian motion BH , described by dXt = -θXt dt + σdBtH be observed at discrete time instants tk=kh, k=0, 1, 2, ⋯, 2n+2 . We propose ergodic type statistical estimators θn , Hn and σn to estimate all the parameters θ, H and σ in the above Ornstein-Uhlenbeck model simultaneously. We prove the strong consistence and the rate of convergence of the estimators. The step size h can be arbitrarily fixed and will not be forced to go zero, which is usually a reality. The tools to use are the generalized moment approach (via ergodic theorem) and the Malliavin calculus.