MULTITAPER SPECTRAL ESTIMATION OF POWER-LAW PROCESSES

In many branches of science, particularly astronomy and geophysics, po wer spectra of the form f(-beta), where beta is a positive, power-law exponent, are common, This form of spectrum is characterized by a shar p increase in the spectral density as the frequency f decreases toward zero, A power spectrum analysis method that has proven very powerful wherever the spectrum of interest is detailed and/or varies rapidly wi th a large dynamic range is the multitaper method, With multitaper spe ctral estimation, a set of orthogonal tapers are applied to the time s eries, and the resulting direct spectral estimators (''eigenspectra'') are averaged, thus, reducing the variance. One class of processes wit h spectra of the power-law type are fractionally differenced Gaussian processes that are stationary and can model certain types of long-rang e persistence, Spectral decay f(-beta) can be modeled for 0 < beta < 1 . Estimation of the spectral slope parameter by regression on multitap er spectral ordinates is examined for this class of processes, It is s hown that multitapering, or using sine or Slepian tapers, produces muc h better results than using the periodogram and is attractive compared with other competing methods, The technique is applied to a geophysic al estimation problem.