A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model With Time-Varying Correlations

TLDR

The article proposes a new multivariate GARCH model with time‑varying correlations. The model uses a vech representation where each conditional variance follows a univariate GARCH and the conditional correlation matrix follows an ARMA‑type process, and it is applied to real data sets. Monte Carlo simulations show that the model’s maximum‑likelihood estimates have finite‑sample distributions consistent with theory, and the model preserves the positive‑definite property while retaining univariate GARCH intuition.

Abstract

In this article we propose a new multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. Whereas each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analog. Our new model retains the intuition and interpretation of the univariate GARCH model and yet satisfies the positive-definite condition as found in the constant-correlation and Baba–Engle–Kraft–Kroner models. We report some Monte Carlo results on the finite-sample distributions of the maximum likelihood estimate of the varying-correlation MGARCH model. The new model is applied to some real data sets.