An improvement of the GPH estimator

In this paper three semi-parametric estimators of long memory are considered. These are the commonly used estimator of Geweke and Porter-Hudak [J. Time Series Anal. 4 (1983) 221], a modification of it and a frequency domain maximum likelihood (FDML) estimator, originally proposed by Künsch [Proceedings of the First World Congress 1 (1987) 67] and later thoroughly investigated by Robinson [Ann. Stat. 23(5) (1995) 1630]. The results show that the modified GPH estimator and the FDML estimator both have MSEs smaller than the original GPH estimator, with the FDML’s estimator being the smallest.