Combined and Comparative Time-Series Spectrum Analysis

It is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might have been. One might also wish to estimate the significance of a particular peak that shows up in two or more power spectra. Visual comparison can be revealing, but it can also be misleading. This leads one to look for one or more ways of forming statistics, which lend themselves to significance estimation, from two or more power spectra. We here propose two such statistics, one that is most useful for the combined study of two or more similar time series, and another that is more useful for the study of dissimilar time series.