Comparison of the LS-based estimators and the MLE for the fractional Ornstein–Uhlenbeck process

Abstract

We deal with the fractional Ornstein–Uhlenbeck (fO–U) process driven by the fractional Brownian motion (fBm), where the drift parameter $$\alpha $$ of the fO–U process is any unknown real number, whereas the Hurst index H of the fBm belongs to (0, 1) and is assumed to be known. Under this setting we consider the least squares (LS)-based estimators and the maximum likelihood estimator (MLE) of $$\alpha $$ , and examine the efficiencies of the LS-based estimators relative to the MLE, paying attention to the effect of the sign of $$\alpha $$ and the value of H. It is found that the MLE is more efficient than the LSE when $$\alpha \ne 0$$ , but the LSE is more efficient when $$\alpha =0$$ .