  We first introduce a class of divergence measures between power spectral
density matrices. These are derived by comparing the suitability of different
models in the context of optimal prediction. Distances between "infinitesimally
close" power spectra are quadratic, and hence, they induce a
differential-geometric structure. We study the corresponding Riemannian metrics
and, for a particular case, provide explicit formulae for the corresponding
geodesics and geodesic distances. The close connection between the geometry of
power spectra and the geometry of the Fisher-Rao metric is noted.
