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Least squares estimations for approximate fractional Vasicek model driven by a semimartingale

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  • Wang, Jixia
  • Xiao, Xiaofang
  • Li, Chao

Abstract

In this paper, our main objective is to obtain the least squares estimations of the drift parameters for the approximate fractional Vasicek process driven by a semimartingale. We first introduce an approximate approach to a fractional Vasicek model and simulate sample paths of this approximate fractional model. The solution of this approximate model converges to the solution of the original model in L2(Ω). Based on the approximate fractional Vasicek process and continuous observation, the estimations of the drift parameters are obtained by using the least squares method, and the strong consistency of the estimations proposed is established. Simulation studies show that the estimations are closer to the true values for different parameters, which indicates that the proposed estimations perform well in finite samples. Real data analysis is presented to illustrate the application of this model in practice.

Suggested Citation

  • Wang, Jixia & Xiao, Xiaofang & Li, Chao, 2023. "Least squares estimations for approximate fractional Vasicek model driven by a semimartingale," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 207-218.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:207-218
    DOI: 10.1016/j.matcom.2023.01.015
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    References listed on IDEAS

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    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    5. Khalifa Es-Sebaiy & Mohammed Es.Sebaiy, 2021. "Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 409-436, June.
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    9. Dai, Min & Duan, Jinqiao & Liao, Junjun & Wang, Xiangjun, 2021. "Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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