Abstract. Fractional Ornstein-Uhlenbeck process of the second kind (fOU2) is solution of the Langevin equation dXt = −θXt dt+dY , we prove that the least squares estimator θT introduced in [[7], Statist. Probab. Lett. 80, no. 11-12, 1030Lett. 80, no. 11-12, -1038, provides a consistent estimator. Moreover, using central limit theorem for multiple Wiener integrals, we prove asymptotic normality of the estimator valid for the whole range H ∈ ( 1 2 , 1).
We construct a new process using a fractional Brownian motion and a fractional Ornstein-Uhlenbeck process of the Second Kind as building blocks. We consider the increments of the new process in discrete time and, as a result, we obtain a more parsimonious process with similar autocovariance structure to that of a FARIMA. In practice, variance of the new increment process is a closed-form expression easier to compute than that of FARIMA.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.