Parzen [4] and others have noted the similarity between probability densities, spectral densities, and their sample estimates. In the familiarx2goodness-of-fit test one seeks to determine whether an observed sample distribution could reasonably have resulted from sampling some specified probability distribution. One could ask a similar question concerning the spectral density of a process. That is, could the estimated spectral density ĝ(ω) of some sampled process have reasonably resulted from a process whose true spectrum isf(ω)? Durbin [l] considers a problem of this type in testing for randomness.