Statistical inference for models driven by $n$-th order fractional Brownian motion

We consider the following stochastic integral equation $X(t)=\mu t + \sigma \int _0^t \varphi (s) dB_H^n(s)$, $t\geq 0$, where $\varphi$ is a known function and $B^n_H$ is the $n$-th order fractional Brownian motion. We provide explicit maximum likelihood estimators for both $\mu$ and $\sigma ^2$, then we formulate explicitly a least squares estimator for $\mu$ and an estimator for $\sigma ^2$ by using power variations method. The consistency and asymptotic normality are established for those estimators when the number of observations or the time horizon is sufficiently large.