Document Type
Discussion Paper
Publication Date
12-1-1999
CFDP Number
1243
CFDP Pages
59
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 < 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.
Recommended Citation
Phillips, Peter C.B., "Discrete Fourier Transforms of Fractional Processes" (1999). Cowles Foundation Discussion Papers. 1493.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/1493