  The ordinary spectrum is restricted in its applications, since it is based on
the second order moments (auto and cross-covariances). Alternative approaches
to spectrum analysis have been investigated based on other measures of
dependence. One such approach was developed for univariate time series by the
authors of this paper using the local Gaussian auto-spectrum based on the local
Gaussian auto-correlations. This makes it possible to detect local structures
in univariate time series that looks like white noise when investigated by the
ordinary auto-spectrum. In this paper the local Gaussian approach is extended
to a local Gaussian cross-spectrum for multivariate time series. The local
Gaussian cross-spectrum has the desirable property that it coincides with the
ordinary cross-spectrum for Gaussian time series, which implies that it can be
used to detect non-Gaussian traits in the time series under investigation. In
particular: If the ordinary spectrum is flat, then peaks and troughs of the
local Gaussian spectrum can indicate nonlinear traits, which potentially might
reveal local periodic phenomena that goes undetected in an ordinary spectral
analysis.
