Impact of Nonstationarity on Estimating and Modeling Empirical Copulas of Daily Stock Returns

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. This paper studies empirical dependencies of daily stock returns by their pairwise copulas. We investigate in particular to which extent the nonstationarity of financial time series affects both the estimation and the modeling of empirical copulas. We estimate empirical copulas from the nonstationary, original return time series and stationary, locally normalized ones. Thereby, we are able to explore the empirical dependence structure on two different scales: globally and locally. Additionally, the asymmetry of the empirical copulas is emphasized as a fundamental characteristic. We compare our empirical findings with a single Gaussian copula, a correlation-weighted average of Gaussian copulas, the K-copula which directly addresses the nonstationarity of dependencies as a model parameter, and 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