Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling

Abstract

Abstract The paper shows that the distribution of the normalized minimum contrast estimator of the drift parameter in the fractional Ornstein-Uhlenbeck process observed over [0, T] converges to the standard normal distribution with an uniform error rate of the order O(T −1/2) for the case H > 1/2 where H is the Hurst exponent of the fractional Brownian motion driving the Ornstein-Uhlenbeck process. Then based on discrete observations, it introduces several approximate minimum contrast estimators and studies their rate of of weak convergence to normal distribution.