THE VARIANCE OF MULTITAPER SPECTRUM ESTIMATES FOR REAL GAUSSIAN-PROCESSES

Multitaper spectral estimation has proven very powerful as a spectral analysis method wherever the spectrum of interest is detailed and/or v aries rapidly with a large dynamic range. In his original paper D. J. Thomson gave a simple approximation for the variance of a multitaper s pectral estimate which is generally adequate when the spectrum is slow ly varying over the taper bandwidth. We show that near zero or Nyquist frequency this approximation is poor even for white noise and derive the exact expression of the variance in the general case of a stationa ry real-valued time series. This expression is illustrated on an autor egressive time series and a convenient computational approach outlined . It is shown that this multitaper variance expression for real-valued processes is not derivable as a special case of the multitaper varian ce for complex-valued, circularly symmetric processes, as previously s uggested in the literature.