THE LEAST SQUARES ESTIMATOR FOR AN ORNSTEIN-UHLENBECK PROCESS DRIVEN BY A HERMITE PROCESS WITH A PERIODIC MEAN

doi:10.1007/s10473-021-0215-0

Abstract

Abstract: We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes $${\rm d}Y_s=\Big (\sum\limits_{j=1}^{k}\mu_j \phi_j (s)- \beta Y_s\Big){\rm d}s + {\rm d}Z_s^{q,H},$$ driven by the Hermite process $Z_s^{q,H}$ with order $q \geq 1$ and a Hurst index $H \in (\frac12,1)$, where the periodic functions $\phi_j(s), j=1,\ldots,k$ are bounded, and the real numbers $\mu_j, j=1,\ldots, k$ together with $\beta>0$ are unknown parameters. We establish the consistency of a least squares estimation and obtain the asymptotic behavior for the estimator. We also introduce alternative estimators, which can be looked upon as an application of the least squares estimator. In terms of the fractional Ornstein-Uhlenbeck processes with periodic mean, our work can be regarded as its non-Gaussian extension.

Key words: Least squares estimator, consistency, asymptotic distribution, Ornstein-Uhlenbeck processes, Hermite processes

CLC Number:

60G18

Guangjun SHEN, Qian YU, Zheng TANG. THE LEAST SQUARES ESTIMATOR FOR AN ORNSTEIN-UHLENBECK PROCESS DRIVEN BY A HERMITE PROCESS WITH A PERIODIC MEAN[J].Acta mathematica scientia,Series B, 2021, 41(2): 517-534.

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