A dynamic conditional score model for the log correlation matrix

This paper proposes a new model for the dynamics of correlation matrices, where are driven by likelihood score with respect to matrix logarithm matrix. In analogy exponential GARCH volatility, this transformation ensures that matrices remain positive definite, even in high dimensions. For conditional distribution returns, we assume student-t copula explain dependence structure and univariate marginals potentially different degrees freedom. The separation into volatility parts allows two-step estimation, which facilitates estimation We derive theory one-step estimation. an application set six asset indices including financial alternative assets show performs well terms diagnostics, specification tests, out-of-sample forecasting.