@article{10b62ce5e26648e8954164d4962a3de4, title = "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean", abstract = "There are two approaches to maximum likelihood (ML) estimation of the parameter of fractionally- integrated noise: approximate frequency-domain ML [Fox and Taqqu (1986)] and exact time- domain ML [Sowell (1992b)]. If the mean of the process is known, then a clear finite-sample mean-squared error ranking of the estimators emerges: the exact time-domain estimator is superior. We show in this paper, however, that the finite-sample efficiency of approximate frequency-domain ML relative to exact time-domain ML rises dramatically when the mean is unknown and so must be estimated. The intuition for our result is straightforward: the frequency-domain ML estimator is invariant to the true but unknown mean of the process, while the time-domain ML estimator is not. Feasible time-domain estimation must therefore be based upon de-meaned data, but the long memory associated with fractional integration makes precise estimation of the mean difficult. We conclude that the frequency-domain estimator is an attractive and efficient alternative for situations in which large sample sizes render time-domain estimation impractical. {\textcopyright} 1994.", keywords = "Fractional differencing, Frequency domain estimation, Maximum likelihood estimation, Simulation", author = "Yin-Wong Cheung and Diebold, {Francis X.}", year = "1994", month = jun, doi = "10.1016/0304-4076(94)90026-4", language = "English", volume = "62", pages = "301--316", journal = "Journal of Econometrics", issn = "0304-4076", publisher = "Elsevier BV", number = "2", }