  We construct and analyze symmetrized delay correlation matrices for empirical
data sets for atmopheric and financial data to derive information about
correlation between different entities of the time series over time. The
information about correlations is obtained by comparing the results for the
eigenvalue distribution with the analytical results for the independent,
identically distributed random data sets. For the atmospheric case we find long
term correlations between different entities of the multivariable time series.
For the financial time series we find little correlations between different
entities over a time delay beyond about two days. Most of the eigenvalues for
the symmetrized delay correlation matrices for the financial data are
symmetrically distributed about zero. The delay correlation results for the
financial data are similar to the analytical results for the random data sets.
However there are considerable deviations for the atmospheric data from the
random case.
