Discrete Fourier transforms of fractional processes with econometric applications
Discrete Fourier transforms of fractional processes with econometric applications
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. 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 modied versions of these procedures are suggested for nonstationary cases.
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Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Phillips, Peter Charles Bonest
(2023)
Discrete Fourier transforms of fractional processes with econometric applications.
Advances in Econometrics, 45A, .
(doi:10.1108/S0731-90532023000045A001).
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. 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 modied versions of these procedures are suggested for nonstationary cases.
Text
DFT_2021_August_A4_pcb
- Accepted Manuscript
More information
Accepted/In Press date: 17 September 2021
e-pub ahead of print date: 24 April 2023
Identifiers
Local EPrints ID: 451711
URI: http://eprints.soton.ac.uk/id/eprint/451711
ISSN: 0731-9053
PURE UUID: c18591ed-7d05-4dce-90b8-abb179445637
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Date deposited: 21 Oct 2021 16:31
Last modified: 17 Mar 2024 06:50
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