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.
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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 05-89, Wharton School Rodney L. White Center for Financial Research.
- Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
- 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.).
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:62:y:1994:i:2:p:301-316. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.