  This paper introduces the novel class of modulated cyclostationary processes,
a class of non-stationary processes exhibiting frequency coupling, and proposes
a method of their estimation from repeated trials. Cyclostationary processes
also exhibit frequency correlation but have Loeve spectra whose support lies
only on parallel lines in the dual-frequency plane. Such extremely sparse
structure does not adequately represent many biological processes. Thus, we
propose a model that, in the time domain, modulates the covariance of
cyclostationary processes and consequently broadens their frequency support in
the dual-frequency plane. The spectra and the cross-coherence of the proposed
modulated cyclostationary process are first estimated using multitaper methods.
A shrinkage procedure is then applied to each trial-specific estimate to reduce
the estimation risk.
  Multiple trials of each series are observed. When combining information
across trials, we carefully take into account the bias that may be introduced
by phase misalignment and the fact that the Loeve spectra and cross-coherence
across replicates may only be "similar" - but not necessarily identical -
across replicates. The application of the inference methods developed for the
modulated cyclostationary model to EEG data also demonstrates that the proposed
model captures statistically significant cross-frequency interactions, that
ought to be further examined by neuroscientists.
