On the asymptotic properties of a feasible estimator of the continuous time long memory parameter

This article considers a fractional noise model in continuous time and examines the asymptotic properties of a feasible frequency domain maximum likelihood estimator of the long memory parameter. The feasible estimator is one that maximizes an approximation to the likelihood function (the approximation arises from the fact that the spectral density function involves the finite truncation of an infinite summation). It is of interest therefore to explore the conditions required of this approximation to ensure the consistency and asymptotic normality of this estimator.