On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean
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.
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- Diebold, Francis X & Husted, Steven & Rush, Mark, 1991.
"Real Exchange Rates under the Gold Standard,"
Journal of Political Economy,
University of Chicago Press, vol. 99(6), pages 1252-71, December.
- Francis X. Diebold & Steven Husted & Mark Rush, 1990. "Real exchange rates under the gold standard," Discussion Paper / Institute for Empirical Macroeconomics 32, Federal Reserve Bank of Minneapolis.
- Joseph G. Haubrich & Andrew W. Lo, .
"The Sources and Nature of Long-Term Memory in the Business Cycle,"
Rodney L. White Center for Financial Research Working Papers
05-89, Wharton School Rodney L. White Center for Financial Research.
- Joseph G. Haubrich & Andrew W. Lo, 1991. "The sources and nature of long-term memory in the business cycle," Working Paper 9116, Federal Reserve Bank of Cleveland.
- Joseph G. Haubrich & Andrew W. Lo, 1989. "The Sources and Nature of Long-term Memory in the Business Cycle," NBER Working Papers 2951, National Bureau of Economic Research, Inc.
- Joseph G. Haubrich & Andrew W. Lo, . "The Sources and Nature of Long-Term Memory in the Business Cycle," Rodney L. White Center for Financial Research Working Papers 5-89, Wharton School Rodney L. White Center for Financial Research.
- Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
- Diebold, Francis X & Rudebusch, Glenn D, 1991.
"Is Consumption Too Smooth? Long Memory and the Deaton Paradox,"
The Review of Economics and Statistics,
MIT Press, vol. 73(1), pages 1-9, February.
- Francis X. Diebold & Glenn D. Rudebusch, 1989. "Is consumption too smooth? Long memory and the Deaton paradox," Finance and Economics Discussion Series 57, Board of Governors of the Federal Reserve System (U.S.).
- Shea, Gary S, 1991. "Uncertainty and Implied Variance Bounds in Long-Memory Models of the Interest Rate Term Structure," Empirical Economics, Springer, vol. 16(3), pages 287-312.
- Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
- Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
- Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
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