E. J. McCoy, A. T. Walden and D. B. Percival (1998), `Multitaper Spectral Estimation of Power Law Processes,' IEEE Transactions on Signal Processing, 46, no. 3, pp. 655-68.
In many branches of science, particularly astronomy and geophysics, power spectra of the form f^beta (where beta is a negative power-law exponent) are common. This form of spectrum is characterized by a sharp increase in the spectral density as the frequency f decreases towards zero. A power spectrum analysis method which has proven very powerful wherever the spectrum of interest is detailed and/or varies rapidly with a large dynamic range is the multitaper method. With multitaper spectral estimation a set of orthogonal tapers are applied to the time series, and the resulting direct spectral estimators ("eigenspectra") are averaged, thus reducing the variance.
One class of processes with spectra of power-law type are fractionally differenced Gaussian white noise processes which are stationary and can model certain types of long range persistence. Spectral decay f^{-beta} can be modelled for 0 < beta < 1. Estimation of the spectral slope parameter by regression on multitaper spectral ordinates is examined for this class of processes. It is shown that multitapering, using sine or Slepian tapers, produces much better results than using the periodogram, and is attractive compared to other competitive methods. This technique is applied to a geophysical estimation problem.
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