  All too often measuring statistical dependencies between financial time
series is reduced to a linear correlation coefficient. However this may not
capture all facets of reality. We study empirical dependencies of daily stock
returns by their pairwise copulas. Here we investigate particularly to which
extent the non-stationarity of financial time series affects both the
estimation and the modeling of empirical copulas. We estimate empirical copulas
from the non-stationary, original return time series and stationary, locally
normalized ones. Thereby we are able to explore the empirical dependence
structure on two different scales: a global and a local one. Additionally the
asymmetry of the empirical copulas is emphasized as a fundamental
characteristic. We compare our empirical findings with a single Gaussian
copula, with a correlation-weighted average of Gaussian copulas, with the
K-copula directly addressing the non-stationarity of dependencies as a model
parameter, and with the skewed Student's t-copula. The K-copula covers the
empirical dependence structure on the local scale most adequately, whereas the
skewed Student's t-copula best captures the asymmetry of the empirical copula
on the global scale.
