Regularised Estimators for Fractional Gaussian Noise

There is significant interest in long-range dependent processes since they occur in a wide range of phenomena across different areas of study. Based on the available models capable of describing long-range dependence, various parameter estimation methods have been developed. This paper revisits the maximum likelihood estimator and its computationally efficient approximations: the Whittle Estimator and the Circulant Embedding estimator. Based on the properties of these, a regularisation method for datasets largely contaminated with errors is introduced.