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Modified Local Whittle Estimation of the Memory Parameter in the Nonstationary Case

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Abstract

Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an estimator of the memory parameter that covers a range of values of d commonly encountered in applied work with economic data. The new estimator is called the modified local Whittle estimator and employs a version of the Whittle likelihood based on frequencies adjacent to the origin and modified to take into account the form of the data generating mechanism in the frequency domain. The modified local Whittle estimator is shown to be consistent for 0

Suggested Citation

  • Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Modified Local Whittle Estimation of the Memory Parameter in the Nonstationary Case," Cowles Foundation Discussion Papers 1265, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1265
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    2. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    3. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Arielle Beyaert, 2004. "Fractional Output Convergence, with an Application to Nine Developed Countries," Econometric Society 2004 Australasian Meetings 280, Econometric Society.
    2. John W. Galbraith & Victoria Zinde-Walsh, 2001. "Autoregression-Based Estimators for ARFIMA Models," CIRANO Working Papers 2001s-11, CIRANO.
    3. Gilles Dufrénot & Valérie Mignon & Théo Naccache, 2009. "The slow convergence of per capita income between the developing countries: “growth resistance” and sometimes “growth tragedy”," Discussion Papers 09/03, University of Nottingham, CREDIT.
    4. Dominique Guegan & Zhiping Lu & Beijia Zhu, 2012. "Comparaison of Several Estimation Procedures for Long Term Behavior," Post-Print halshs-00673934, HAL.
    5. Han, Young Wook, 2005. "Long memory volatility dependency, temporal aggregation and the Korean currency crisis: the role of a high frequency Korean won (KRW)-US dollar ($) exchange rate," Japan and the World Economy, Elsevier, vol. 17(1), pages 97-109, January.
    6. 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.
    7. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, vol. 130(2), pages 209-233, February.

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    More about this item

    Keywords

    Discrete Fourier transform; fractional Brownian motion; fractional integration; long memory; nonstationarity; semiparametric estimation; Whittle likelihood;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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