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Exact Local Whittle Estimation Of Fractional Integration With Unknown Mean And Time Trend

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  • Shimotsu, Katsumi

Abstract

Recently Shimotsu and Phillips (2002, Essex Discussion Paper 535) 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 have the same N(0, 1/4 ) limit distribution for all values of d. With economic applications in mind, we extend the ELW estimator so that it accommodates an unknown mean and a linear time trend. We show the resulting feasible ELW estimator is consistent for d > -1/2 and has a N(0, 1/4 ) limit distribution for d in (-1/2, 2) (d in (-1/2, 7/4) when the data have a linear trend) except for a few negligible intervals. A simulation study shows that the feasible ELW estimator inherits the desirable properties of the ELW estimator also in small samples.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 26 (2010)
Issue (Month): 02 (April)
Pages: 501-540

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Handle: RePEc:cup:etheor:v:26:y:2010:i:02:p:501-540_10

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  1. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
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  13. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation for Research in Economics, Yale University, revised Sep 2003.
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  16. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Cowles Foundation Discussion Papers 1367, Cowles Foundation for Research in Economics, Yale University, revised Jul 2004.
  17. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May.
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  21. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation for Research in Economics, Yale University.
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