The envelope of spectral power for stochastic processes

It is well known that the maximum likelihood (ML) spectral estimate represents an envelope on spectral power which is consistent with estimated covariance lags. However, in computing the envelope, the ML method allows for spectra corresponding to complex-valued stochastic processes. We study the respective envelope for processes constrained to be real-valued at the outset. The resulting envelope is less conservative than the one provided by the ML method. A closed form expression exists for the new envelope