A DCC Mgarch Copula-Based Model for Measuring Dependence in Multivariate Inancial Time Series Data

Abstract

In the realm of financial time series, accurately modeling dependencies among macroe-conomic variables is crucial for enhancing parameter estimation and capturing nonlinear relationships, an inherent characteristic of financial time series data. This study proposes a DCC-MGARCH model integrated with copulas (Gumbel, Clayton, and t copulas) and a modified form of Kullback-Leibler (KL) divergence to improve dependency measurement and parameter estimation accuracy. The study employs a modified form of Kullback-Leibler divergence to quantify dependencies, enhancing both parameter estimation and predictive performance. The model was tested using both simulated and real-world fi-nancial data, with results indicating synchrony in volatility and covariance structures. However, the Gumbel copula did not conform well to the dependence structure, while the Clayton and t copulas provided better representations. The hybrid KL-based copula-DCC-MGARCH model outperformed the traditional DCC-MGARCH model. These findings highlight the effectiveness of KL divergence in optimizing copula selection, making the proposed model a robust tool for measuring nonlinear dependencies in multivariate fi-nancial time series.