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Discussion Paper

Discrete Fourier Transforms of Fractional Processes

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.