  Fractional Ornstein-Uhlenbeck process of the second kind $(\text{fOU}_{2})$
is solution of the Langevin equation $\mathrm{d}X_t = -\theta
X_t\,\mathrm{d}t+\mathrm{d}Y_t^{(1)}, \ \theta >0$ with driving noise $
Y_t^{(1)} := \int^t_0 e^{-s} \,\mathrm{d}B_{a_s}; \ a_t= H e^{\frac{t}{H}}$
where $B$ is a fractional Brownian motion with Hurst parameter $H \in (0,1)$.
In this article, in the case $H>1/2$, we prove that the least squares estimator
$\hat{\theta}_T$ introduced in [\cite{h-n}, Statist. Probab. Lett. 80, no.
11-12, 1030-1038], 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 $H \in(1/2,1)$.
