A Bias--Reduced Log--Periodogram Regression Estimator for the Long--Memory Parameter
In this paper, we propose a simple bias--reduced log--periodogram regression estimator, "ˆd-sub-r", of the long--memory parameter, "d", that eliminates the first-- and higher--order biases of the Geweke and Porter--Hudak (1983) (GPH) estimator. The bias--reduced estimator is the same as the GPH estimator except that one includes frequencies to the power 2"k" for "k"=1,…,"r", for some positive integer "r", as additional regressors in the pseudo--regression model that yields the GPH estimator. The reduction in bias is obtained using assumptions on the spectrum only in a neighborhood of the zero frequency.Following the work of Robinson (1995b) and Hurvich, Deo, and Brodsky (1998), we establish the asymptotic bias, variance, and mean--squared error (MSE) of "ˆd-sub-r", determine the asymptotic MSE optimal choice of the number of frequencies, "m", to include in the regression, and establish the asymptotic normality of "ˆd-sub-r". These results show that the bias of "ˆd-sub-r" goes to zero at a faster rate than that of the GPH estimator when the normalized spectrum at zero is sufficiently smooth, but that its variance only is increased by a multiplicative constant.We show that the bias--reduced estimator "ˆd-sub-r" attains the optimal rate of convergence for a class of spectral densities that includes those that are smooth of order "s"≥1 at zero when "r"≥("s" - 2)/2 and "m" is chosen appropriately. For "s">2, the GPH estimator does not attain this rate. The proof uses results of Giraitis, Robinson, and Samarov (1997).We specify a data--dependent plug--in method for selecting the number of frequencies "m" to minimize asymptotic MSE for a given value of "r".Some Monte Carlo simulation results for stationary Gaussian ARFIMA (1, "d", 1) and (2, "d", 0) models show that the bias--reduced estimators perform well relative to the standard log--periodogram regression estimator. Copyright The Econometric Society 2003.
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.
Volume (Year): 71 (2003)
Issue (Month): 2 (March)
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/
More information through EDIRC
|Order Information:|| Web: https://www.econometricsociety.org/publications/econometrica/access/ordering-back-issues Email: |
When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:71:y:2003:i:2:p:675-712. 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: (Wiley-Blackwell Digital Licensing)or (Christopher F. Baum)
If references are entirely missing, you can add them using this form.