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EXACT LOCAL WHITTLE ESTIMATION OFFRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIMETREND

Published online by Cambridge University Press:  30 September 2009

Katsumi Shimotsu
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Abstract

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Recently, Shimotsu and Phillips (2005, Annalsof Statistics 33, 1890–1933) developed anew semiparametric estimator, the exact localWhittle (ELW) estimator, of the memory parameter(d) in fractionally integratedprocesses. The ELW estimator has been shown to beconsistent, and it has the same $N(0,{\textstyle{1 \over 4}})$ asymptoticdistribution for all values of d,if the optimization covers an interval of width lessthan 9/2 and the mean of the process is known. Withthe intent to provide a semiparametric estimatorsuitable for economic data, we extend the ELWestimator so that it accommodates an unknown meanand a polynomial time trend. We show that thetwo-step ELW estimator, which is based on a modifiedELW objective function using a tapered local Whittleestimator in the first stage, has an $N(0,{\textstyle{1 \over 4}})$ asymptoticdistribution for $d \in (- {\textstyle{1 \over 2}},2)$ (or$d \in (- {\textstyle{1 \over 2}},{\textstyle{7 \over 4}})$ when the datahave a polynomial trend). Our simulation studyillustrates that the two-step ELW estimator inheritsthe desirable properties of the ELW estimator.

Information

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 2 , April 2010, pp. 501 - 540
Copyright
Copyright © Cambridge University Press 2009

Footnotes

The author thanks the co-editor and threeanonymous referees for helpful and constructivecomments. The author thanks Peter C.B. Phillipsand Morten Ø. Nielsen for helpful comments and theCowles Foundation for hospitality during his stayfrom January 2002 to August 2003. This researchwas supported by ESRC under grant R000223629.

References

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