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Discrete Fourier Transforms of Fractional Processes August

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  • Phillips, Peter

Abstract

Discrete Fourier transforms (dft's) of fractional processes are studied and a 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 < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested.

Suggested Citation

  • Phillips, Peter, 1999. "Discrete Fourier Transforms of Fractional Processes August," Working Papers 149, Department of Economics, The University of Auckland.
  • Handle: RePEc:auc:wpaper:149
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    File URL: http://hdl.handle.net/2292/149
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    Cited by:

    1. Shi, Wendong & Sun, Jingwei, 2016. "Aggregation and long-memory: An analysis based on the discrete Fourier transform," Economic Modelling, Elsevier, vol. 53(C), pages 470-476.
    2. Bardet Jean-Marc & Dola Béchir, 2016. "Semiparametric Stationarity and Fractional Unit Roots Tests Based on Data-Driven Multidimensional Increment Ratio Statistics," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 115-153, July.
    3. Samet Günay, 2016. "Performance of the Multifractal Model of Asset Returns (MMAR): Evidence from Emerging Stock Markets," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 4(2), pages 1-17, May.
    4. Goodell, John W. & McGroarty, Frank & Urquhart, Andrew, 2015. "Political uncertainty and the 2012 US presidential election: A cointegration study of prediction markets, polls and a stand-out expert," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 162-171.
    5. Ewa M. Syczewska, 2006. "The Phillips Method of Fractional Integration Parameter Estimation and Aggregation of PLN Exchange Rates," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 7, pages 209-220.
    6. Bailey, Natalia & Giraitis, Liudas, 2016. "Spectral approach to parameter-free unit root testing," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 4-16.
    7. Leonardo Chaves Borges Cardoso & Maurício Vaz Lobo Bittencourt, 2016. "Price Volatility Transmission From Oil To Energy And Non-Energy Agricultural Commodities," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting] 181, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    8. repec:gam:jijfss:v:4:y:2016:i:2:p:11:d:70218 is not listed on IDEAS
    9. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.

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