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

Rachid Belfadli (), Khalifa Es-Sebaiy () and Fatima-Ezzahra Farah
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Rachid Belfadli: Cadi Ayyad University
Khalifa Es-Sebaiy: Kuwait University
Fatima-Ezzahra Farah: Cadi Ayyad University

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 7, No 5, 885-911

Abstract: Abstract Consider a periodic, mean-reverting Ornstein–Uhlenbeck process $$X=\{X_t,t\ge 0\}$$ X = { X t , t ≥ 0 } of the form $$d X_{t}=\left( L(t)+\alpha X_{t}\right) d t+ dB^H_{t}, \quad t \ge 0$$ d X t = L ( t ) + α X t d t + d B t H , t ≥ 0 , where $$L(t)=\sum _{i=1}^{p}\mu _i\phi _i (t)$$ L ( t ) = ∑ i = 1 p μ i ϕ i ( t ) is a periodic parametric function, and $$\{B^H_t,t\ge 0\}$$ { B t H , t ≥ 0 } is a fractional Brownian motion of Hurst parameter $$\frac{1}{2}\le H 0$$ α > 0 , and for all $$\frac{1}{2}\le H

Keywords: Parameter estimation; Strong consistency; Joint asymptotic distribution; Fractional Ornstein–Uhlenbeck process; Periodic mean function; Young integral; 60G15; 60G22; 62F12; 62M09; 62M86 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00854-x

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