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Generalized moment estimators for $$\alpha $$α-stable Ornstein–Uhlenbeck motions from discrete observations

Author

Listed:
  • Yiying Cheng

    (The University of Kansas)

  • Yaozhong Hu

    (University of Alberta)

  • Hongwei Long

    (Florida Atlantic University)

Abstract

We study the parameter estimation problem for discretely observed Ornstein–Uhlenbeck processes driven by $$\alpha $$α-stable Lévy motions. A method of moments via ergodic theory and via sample characteristic functions is proposed to estimate all the parameters involved in the Ornstein–Uhlenbeck processes. We obtain the strong consistency and asymptotic normality of the proposed joint estimators when the sample size $$n \rightarrow \infty $$n→∞ while the sampling time step h remains arbitrarily fixed. We also design a procedure to select the grid points in the characteristic functions in certain optimal way for the proposed estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:1:d:10.1007_s11203-019-09201-4
    DOI: 10.1007/s11203-019-09201-4
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