We consider a cointegrated regressor model where the regressor is a fractional Brownian motion with self-similarity index H 1 ∈ (0, 1) and the errors are considered to be the increments of a Hermite process which is a long memory non Gaussian H 2 -self-similar process with stationary increments, where H 2 ∈ ( 1 2 , 1).We prove that the estimator of the regression function is consistent and asymptotically normal.