Inference in generalized exponential O–U processes

In this paper, we consider an inference problem in generalized exponential Ornstein–Uhlenbeck processes. Salient features of this paper consists in the fact that, first, we generalized the classical exponential Ornstein–Uhlenbeck processes to the case where the drift coefficient is driven by a period function of time. Second, as opposed to the results in recent literature, the dimension of the drift parameter is considered as unknown. Third, we weaken some assumptions, in recent literature, underlying the asymptotic optimality of some estimators of the drift parameter. We propose the unrestricted maximum likelihood estimator, the restricted maximum likelihood estimator and some shrinkage estimators for the drift parameters. We also derive asymptotic distributional risk of the proposed estimators as well as their relative efficiency. Finally, we present the simulation results which corroborate the theoretical findings.