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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/14788
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| Title: | BROADBAND SEMIPARAMETRIC ESTIMATION OF THE MEMORY PARAMETER OF A
LONG-MEMORY TIME SERIES USING FRACTIONAL EXPONENTIAL MODELS |
| Authors: | Hurvich, Clifford M.
Brodsky, Julia |
| Issue Date: | Oct-1998 |
| Publisher: | Stern School of Business, New York University |
| Series/Report no.: | SOR-2000-2 |
| Abstract: | We consider a fractional exponential, or FEXP estimator of the memory
parameter of a stationary Gaussian long-memory time series. The
estimator is constructed by fitting a FEXP model of slowly increasing
dimension to the log periodogram at all Fourier frequencies by ordinary
least squares, and retaining the corresponding estimated memory
parameter. We do not assume that the data were necessarily generated by
a FEXP model, or by any other finite-parameter model. We do, however,
impose a global differentiability assumption on the spectral density
except at the origin. Because of this, and its use of all Fourier
frequencies, we refer to the FEXP estimator as a broadband
semiparametric estimator. We demonstrate the consistency of the FEXP
estimator, and obtain expressions for its asymptotic bias and variance.
It the true spectral density is sufficiently smooth, the FEXP estimator
can strongly outperform existing semiparametric estimators, such as the
Geweke-Porter-Hudak (GPH) and Gaussian semiparametric estimators (GSE),
attaining an asymptotic mean squared error proportional to (log n)/n,
where n is the sample size. In a simulation study, we demonstrate the
merits of using a finite-sample correction to the asymptotic variance,
and we also explore the possibility of automatically selecting the
dimension of the exponential model using
Mallowsâ CL criterion. |
| URI: | http://hdl.handle.net/2451/14788 |
| Appears in Collections: | IOMS: Statistics Working Papers
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