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http://hdl.handle.net/2451/14773
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| Title: | PLUG-IN SELECTION OF THE NUMBER OF FREQUENCIES IN REGRESSION ESTIMATES
OF THE MEMORY PARAMETER OF A LONG-MEMORY TIME SERIES |
| Authors: | Hurvich, Clifford M.
Deo, Rohit S. |
| Keywords: | Periodogram
bandwith |
| Issue Date: | Jul-1998 |
| Publisher: | Stern School of Business, New York University |
| Series/Report no.: | SOR-97-7 |
| Abstract: | We consider the problem of selecting the number of frequencies, m, in a
log-periodogram regression estimator of the memory parameter d of a
Gaussian long-memory time series. It is known that under certain
conditions the optimal m, minimizing the mean squared error of the
corresponding estimator of d, is given by m(opt) = Cn4/5, where n is the
sample size and C is a constant. In practice, C would be unknown since
it depends on the properties of the spectral density near zero
frequency. In this paper, we propose an estimator of C based again on a
log-periodogram regression and derive its consistency. We also derive
an asymptotically valid confidence interval for d when the number of
frequencies used in the regression is deterministic and proportional to
n4/5. In this case, squared bias cannot be neglected since it is of the
same order as the variance. In a Monte Carlo study, we examine the
performance of the plug-in estimator of d, in which m is obtained by
using the estimator of C in the formula for m(opt) above. We also study
the performance of a bias-corrected version of the plug-in estimator of
d. Comparisons with the choice m = ný
frequencies, as originally suggested by Geweke and Porter-Hudak. |
| URI: | http://hdl.handle.net/2451/14773 |
| Appears in Collections: | IOMS: Statistics Working Papers
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