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Least squares estimator for Ornstein-Uhlenbeck processes driven by [alpha]-stable motions

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  • Hu, Yaozhong
  • Long, Hongwei

Abstract

We study the problem of parameter estimation for generalized Ornstein-Uhlenbeck processes driven by [alpha]-stable noises, observed at discrete time instants. Least squares method is used to obtain an asymptotically consistent estimator. The strong consistency and the rate of convergence of the estimator have been studied. The estimator has a higher order of convergence in the general stable, non-Gaussian case than in the classical Gaussian case.

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  • Hu, Yaozhong & Long, Hongwei, 2009. "Least squares estimator for Ornstein-Uhlenbeck processes driven by [alpha]-stable motions," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2465-2480, August.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:8:p:2465-2480
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    References listed on IDEAS

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    1. Yasutaka Shimizu, 2006. "M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely Many Jumps," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 179-225, July.
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    3. Yasutaka Shimizu & Nakahiro Yoshida, 2006. "Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 227-277, October.
    4. Kallenberg, Olav, 1992. "Some time change representations of stable integrals, via predictable transformations of local martingales," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 199-223, March.
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    1. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    2. Ren, Panpan & Wu, Jiang-Lun, 2021. "Least squares estimation for path-distribution dependent stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Xuekang Zhang & Huisheng Shu & Haoran Yi, 2023. "Parameter Estimation for Ornstein–Uhlenbeck Driven by Ornstein–Uhlenbeck Processes with Small Lévy Noises," Journal of Theoretical Probability, Springer, vol. 36(1), pages 78-98, March.
    4. Shen, Leyi & Xia, Xiaoyu & Yan, Litan, 2022. "Least squares estimation for the linear self-repelling diffusion driven by α-stable motions," Statistics & Probability Letters, Elsevier, vol. 181(C).
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    6. Guangjun Shen & Qian Yu, 2019. "Least squares estimator for Ornstein–Uhlenbeck processes driven by fractional Lévy processes from discrete observations," Statistical Papers, Springer, vol. 60(6), pages 2253-2271, December.
    7. Long, Hongwei, 2009. "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2076-2085, October.
    8. Wang, Xiaolong & Feng, Jing & Liu, Qi & Li, Yongge & Xu, Yong, 2022. "Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    9. Kevin W. Lu, 2022. "Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 365-396, July.
    10. Fabian Mies & Ansgar Steland, 2019. "Nonparametric Gaussian inference for stable processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 525-555, October.
    11. Yiying Cheng & Yaozhong Hu & Hongwei Long, 2020. "Generalized moment estimators for $$\alpha $$α-stable Ornstein–Uhlenbeck motions from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 53-81, April.
    12. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    13. Zhao, Huiyan & Zhang, Chongqi, 2019. "Minimum distance parameter estimation for SDEs with small α-stable noises," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 301-311.
    14. Barczy, Mátyás & Basrak, Bojan & Kevei, Péter & Pap, Gyula & Planinić, Hrvoje, 2021. "Statistical inference of subcritical strongly stationary Galton–Watson processes with regularly varying immigration," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 33-75.

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