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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 (2002a) 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 that the resulting feasible ELW estimator is consistent for d > −1/2 and has a N(0, 1/4)limit distribution for dE2 (−1/2, 2) (dE2 (−/12 , 7/4 ) when the data has 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 even in a small sample.

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  • Shimotsu, Katsumi, 2002. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Economics Discussion Papers 8844, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:8844
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    Cited by:

    1. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    2. Ibrahim Kane & Fadhilah Yusof, 2013. "Assessment of Risk of Rainfall Events with a Hybrid of ARFIMA-GARCH," Modern Applied Science, Canadian Center of Science and Education, vol. 7(12), pages 1-78, December.
    3. Manmohan S. Kumar & Tatsuyoshi Okimoto, 2007. "Dynamics of Persistence in International Inflation Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(6), pages 1457-1479, September.
    4. Dominique Guegan & Zhiping Lu & Beijia Zhu, 2012. "Comparaison of Several Estimation Procedures for Long Term Behavior," Post-Print halshs-00673934, HAL.
    5. Dominique Guegan & Zhiping Lu & Beijia Zhu, 2012. "Comparaison of Several Estimation Procedures for Long Term Behavior," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00673934, HAL.

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