Discrete Fourier Transforms of Fractional Processes with Econometric Applications*

Peter Phillips

A chapter in Essays in Honor of Joon Y. Park: Econometric Theory, 2023, vol. 45A, pp 3-71 from Emerald Group Publishing Limited

Abstract: The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameterd≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameterd

Keywords: Discrete Fourier transform; fractional Brownian motion; fractional integration; log periodogram regression; nonstationarity; operator decomposition; semiparametric estimation; Whittle likelihood; C22 (search for similar items in EconPapers)
Date: 2023
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Working Paper: Discrete Fourier Transforms of Fractional Processes with Econometric Applications (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-90532023000045a001

DOI: 10.1108/S0731-90532023000045A001

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