Title: Regularized Spectral Dynamics for High-Dimensional Copulas
Abstract: We introduce spectral dynamics for high-dimensional, asymmetric, tail-dependent copulas in combination with non-linear shrinkage of the copula dependence matrix. Our new copula model is based on evolution and regularization equations for the eigenvalues of the copula correlation matrix in order to achieve a parsimonious dynamic structure combined with robust estimation in high dimensions. We compare the performance of our dynamic spectral copula model with recently proposed clustering-based dynamic factor copula models. In simulation studies, we find that our copula model is highly competitive when the cluster factor copula is the true model, and that it outperforms other copulas in more general situations. In our empirical application, we study the high-dimensional dynamics of the global financial market using 100 stocks from 10 different countries and 10 different industry sectors. In this heterogenous setting, restrictive group-based dependence structures perform sub-optimally, while the spectral method captures the primary geographic and industry related co-movements, leading to improved out-of-sample performance. The spectral dynamics also reveal that global financial markets undergo orthogonal contractions in times of financial crises, resulting in reduced diversification potential and increased global systemic risk.