Modelling time-varying volatility interactions

In this paper, we propose an additive time-varying (or partially time-varying) multivariate model of volatility, where a time-dependent component is added to the extended vector GARCH process for modelling the dynamics of volatility interactions. In our framework, co-dependence in volatility is allowed to change smoothly between two extreme states and second-moment interdependence is identified from these crisis-contingent strucural changes. The estimation of the new time-varying vector GARCH process is simplified using an equation-by-equation estimator for the volatility equations in the first step, and estimating the correlation matrix in the second step. A new Lagrange multiplier test is derived for testing the null hypothesis of constancy co-dependence volatility against a smoothly time-varying interdependence between financial markets. The test appears to be a useful statistical tool for evaluating the adequacy of GARCH equations by testing the presence of significant changes in cross-market volatility transmissions. Monte Carlo simulation experiments show that the test statistic has satisfactory empirical properties in finite samples. An application to sovereign bond yield returns illustrates the modelling strategy of the new specification.