Hypothesis testing of the drift parameter sign for fractional   Ornstein-Uhlenbeck process
  We consider the fractional Ornstein-Uhlenbeck process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary to the previous works, our approach is applicable for all $H\in(0,1)$. We also study the estimators for drift parameter for continuous and discrete observations and prove their strong consistency for all $H\in(0,1)$. 
Alexander Kukush, Yuliya Mishura, Kostiantyn Ralchenko
math.PR