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EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND
Published online by Cambridge University Press: 30 September 2009
Abstract
Recently, Shimotsu and Phillips (2005, Annals
of Statistics 33, 1890–1933) developed a
new semiparametric estimator, the exact local
Whittle (ELW) estimator, of the memory parameter
(d) in fractionally integrated
processes. The ELW estimator has been shown to be
consistent, and it has the same asymptotic
distribution for all values of d,
if the optimization covers an interval of width less
than 9/2 and the mean of the process is known. With
the intent to provide a semiparametric estimator
suitable for economic data, we extend the ELW
estimator so that it accommodates an unknown mean
and a polynomial time trend. We show that the
two-step ELW estimator, which is based on a modified
ELW objective function using a tapered local Whittle
estimator in the first stage, has an
asymptotic
distribution for
(or
when the data
have a polynomial trend). Our simulation study
illustrates that the two-step ELW estimator inherits
the desirable properties of the ELW estimator.
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 2009
Footnotes
The author thanks the co-editor and three anonymous referees for helpful and constructive comments. The author thanks Peter C.B. Phillips and Morten Ø. Nielsen for helpful comments and the Cowles Foundation for hospitality during his stay from January 2002 to August 2003. This research was supported by ESRC under grant R000223629.
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