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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

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File URL: http://cowles.econ.yale.edu/P/cd/d12b/d1265.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1265.

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Length: 54 pages
Date of creation: Jul 2000
Date of revision:
Handle: RePEc:cwl:cwldpp:1265

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Related research

Keywords: Discrete Fourier transform; fractional Brownian motion; fractional integration; long memory; nonstationarity; semiparametric estimation; Whittle likelihood;

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References

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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. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  3. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
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Cited by:
  1. 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.
  2. Gilles Dufrénot & Valérie Mignon & Théo Naccache, . "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.
  3. 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.
  4. Dominique Guegan & Zhiping Lu & BeiJia Zhu, 2012. "Comparaison of several estimation procedures for long term behavior," Documents de travail du Centre d'Economie de la Sorbonne 12008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. Arielle Beyaert, 2004. "Fractional Output Convergence, with an Application to Nine Developed Countries," Econometric Society 2004 Australasian Meetings 280, Econometric Society.
  6. John Galbraith & Victoria Zinde-Walsh, 2001. "Autoregression-Based Estimators for ARFIMA Models," CIRANO Working Papers 2001s-11, CIRANO.

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