This paper investigates the behavior of the GPH estimator of the fractional difference parameter suggested by Geweke and Porter-Hudak (1983), through Monte Carlo simulations. The simulation results indicate that when considering a stationary AR(1) generating process the GPH estimator of the fractional difference parameter has serious bias which increases with the value of the autoregressive parameter, even for relatively large samples. The results suggest that tests and point estimates based on this procedure can be seriously misleading with hypothesis ests yielding incorrect inferences and thus must be used with great care.