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

Yin-Wong Cheung and Francis Diebold

No 34, Discussion Paper / Institute for Empirical Macroeconomics from Federal Reserve Bank of Minneapolis

Abstract: There are two approaches to maximum likelihood (ML) estimation of the parameter of fractionally-integrated noise: approximate frequency-domain ML (Fox and Taqqwu, 1986) and exact time-domain ML (Solwell, 1990a). If the mean of the process is known, then a clear finite-sample mean-squared error (MSE) ranking of the estimators emerges: the exact time-domain estimator has smaller MSE. 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 result is unknown and instead 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.

Keywords: time; series; analysis (search for similar items in EconPapers)
Date: 1990
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean (1994)
Working Paper: On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean (1993)
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