Statistical analysis of the non-ergodic fractional Ornstein-Uhlenbeck process with periodic mean

2020/08/31 by Rachid Belfadli, Belfadli, Rachid, Khalifa Es-Sebaiy +3
Economics, Econometrics and Finance · Mathematics · #60G15 #60G22 #62F12 #62M09 #62M86 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.PR #math.ST #msc:60G15 #msc:60G22 #msc:62F12 #msc:62M09 #msc:62M86 #stat.TH

paper · pdf · doi:10.48550/arxiv.2009.00052

arxiv created 2020/08/31 · openalex publication_date 2020/08/31 · arxiv updated 2020/09/02 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Consider a periodic, mean-reverting Ornstein-Uhlenbeck process X=\X_t,t≥0\ of the form d X_t=(L(t)+αX_t) d t+ dB^H_t, t ≥ 0, where L(t)=∑_i=1^pμ_iϕ_i (t) is a periodic parametric function, and \B^H_t,t≥0\ is a fractional Brownian motion of Hurst parameter \frac12≤ H<1. In the "ergodic" case α<0, the parametric estimation of (μ₁,…,μ_p,α) based on continuous-time observation of X has been considered in Dehling et al. \citeDFK, and in Dehling et al. \citeDFW for H=\frac12, and \frac12<H<1, respectively. In this paper we consider the "non-ergodic" case α>0, and for all \frac12≤ H<1. We analyze the strong consistency and the asymptotic distribution for the estimator of (μ₁,…,μ_p,α) when the whole trajectory of X is observed.

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