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

Author

Listed:
  • Rachid Belfadli

    (Cadi Ayyad University)

  • Khalifa Es-Sebaiy

    (Kuwait University)

  • Fatima-Ezzahra Farah

    (Cadi Ayyad University)

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

Suggested Citation

  • Rachid Belfadli & Khalifa Es-Sebaiy & Fatima-Ezzahra Farah, 2022. "Statistical analysis of the non-ergodic fractional Ornstein–Uhlenbeck process with periodic mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 885-911, October.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:7:d:10.1007_s00184-021-00854-x
    DOI: 10.1007/s00184-021-00854-x
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    References listed on IDEAS

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    1. Es-Sebaiy, Khalifa & Viens, Frederi G., 2019. "Optimal rates for parameter estimation of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3018-3054.
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