
THE LEAST SQUARES ESTIMATOR FOR AN ORNSTEINUHLENBECK PROCESS DRIVEN BY A HERMITE PROCESS WITH A PERIODIC MEAN
Guangjun SHEN, Qian YU, Zheng TANG
Acta mathematica scientia,Series B. 2021, 41 (2):
517534.
DOI: 10.1007/s1047302102150
We consider the least square estimator for the parameters of OrnsteinUhlenbeck 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 OrnsteinUhlenbeck processes with periodic mean, our work can be regarded as its nonGaussian extension.
References 
Related Articles 
Metrics
