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Discrete Fourier Transforms of Fractional Processes

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Abstract

Discrete Fourier transforms (dft's) of fractional processes are studied and an exact representation of the dft is given in terms of the component data. The new representation gives the frequency domain form of the model for a fractional process, and is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d >= 1/2. Various asymptotic approximations are suggested. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d

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File URL: http://cowles.econ.yale.edu/P/cd/d12a/d1243.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 1243.

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Length: 59 pages
Date of creation: Dec 1999
Date of revision:
Handle: RePEc:cwl:cwldpp:1243

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Discrete Fourier transform; fractional Brownian motion; fractional integration; nonstationarity; operator decomposition; semiparametric estimation; Whittle likelihood;

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References

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  1. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May.
  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. Gourieroux Christian & Akonom, J., 1988. "Functional limit theorem for fractional processes (a)," CEPREMAP Working Papers (Couverture Orange) 8801, CEPREMAP.
  4. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
  5. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  6. Peter C.B. Phillips, 1985. "Fractional Matrix Calculus and the Distribution of Multivariate Tests," Cowles Foundation Discussion Papers 767, Cowles Foundation for Research in Economics, Yale University.
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