  We define a random-matrix ensemble given by the infinite-time covariance
matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a
Gaussian symmetric matrix. The spectral properties of this ensemble are shown
to be in qualitative agreement with some stylized facts of financial markets.
Through the presented model formulas are given for the analysis of
heterogeneous time-series. Furthermore evidence for a localization transition
in eigenvectors related to small and large eigenvalues in cross-correlations
analysis of this model is found and a simple explanation of localization
phenomena in financial time-series is provided. Finally we identify both in our
model and in real financial data an inverted-bell effect in correlation between
localized components and their local temperature: high and low
temperature/volatility components are the most localized ones.
