Extended Multivariate EGARCH Model: A Model for Zero-Return and Negative Spillovers

This paper introduces an extended multivariate EGARCH model that overcomes the zero-return problem and allows for negative news and volatility spillover effects, making it an attractive tool for multivariate volatility modeling. Despite limitations, such as noninvertibility and unclear asymptotic properties of the QML estimator, our Monte Carlo simulations indicate that the standard QML estimator is consistent and asymptotically normal for larger sample sizes (i.e., $T\ge 2500$). Two empirical examples demonstrate the model's superior performance compared to multivariate GJR-GARCH and Log-GARCH models in volatility modeling. The first example analyzes the daily returns of three stocks from the DJ30 index, while the second example investigates volatility spillover effects among the bond, stock, crude oil, and gold markets. Overall, this extended multivariate EGARCH model offers a flexible and comprehensive framework for analyzing multivariate volatility and spillover effects in empirical finance research.