On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)301-316
Journal / PublicationJournal of Econometrics
Issue number2
Publication statusPublished - Jun 1994
Externally publishedYes


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. © 1994.

Research Area(s)

  • Fractional differencing, Frequency domain estimation, Maximum likelihood estimation, Simulation