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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

Katsumi Shimotsu
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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
Econometric Theory , Volume 26 , Issue 2 , April 2010 , pp. 501 - 540
Copyright
Copyright © Cambridge University Press 2009

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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.

References

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