Transport metrics for power spectra

We present a family of metrics for power spectra based on the Monge-Kantorivic transportation distances. These metrics are constructed so that distances reduce with additive and multiplicative noise, reflecting the intuition that noise typically reduces our ability to discriminate spectra. In addition, perturbations measured in these metrics are continuous with respect to the statistics of the underlying time series. A general framework for constructing such metrics is put forth and these are contrasted with an earlier Riemannian metric which is based on prediction theory and the relevant geometry of the underlying time-series.