On the spectral coherence of nonstationary processes

It is shown that for a single path of a nonstationary process, reliable (i.e., low-variance) measurements of the degree of coherence between two spectral bands with substantial separation must be smaller than 1/2 unless the nonstationarity is of a special type. That is, the nonstationarity must be either of a known form (prior to measurement) or of a periodic nature, which is known as cyclostationarity. It is concluded that spectral correlation measurements on single time series are of highly questionable value for detection and characterization of nonstationarity, except in the special cases of cyclostationarity