  We study the dependence structure of market states by estimating empirical
pairwise copulas of daily stock returns. We consider both original returns,
which exhibit time-varying trends and volatilities, as well as locally
normalized ones, where the non-stationarity has been removed. The empirical
pairwise copula for each state is compared with a bivariate K-copula. This
copula arises from a recently introduced random matrix model, in which
non-stationary correlations between returns are modeled by an ensemble of
random matrices. The comparison reveals overall good agreement between
empirical and analytical copulas, especially for locally normalized returns.
Still, there are some deviations in the tails. Furthermore, we find an
asymmetry in the dependence structure of market states. The empirical pairwise
copulas exhibit a stronger lower tail dependence, particularly in times of
crisis.
