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Discrete Fourier Transforms of Fractional Processes with Econometric Applications

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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 parameter d ≥ 1 2: 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 parameter d

Suggested Citation

  • Peter C.B. Phillips, 2021. "Discrete Fourier Transforms of Fractional Processes with Econometric Applications," Cowles Foundation Discussion Papers 2303, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2303
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    More about this item

    Keywords

    Discrete Fourier transform; Fractional Brownian motion; Fractional integration; Log periodogram regression; Nonstationarity; Operator decomposition; 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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