Negative Volatility Spillovers in the Unrestricted EDCC-GARCH Model and its Generalizations

Economics

Further details

This paper considers a formulation of the extended constant/dynamic conditional correlation (ECCC/EDCC) GARCH model which allows for a bidirectional feedback between the volatilities, which can be of either sign, positive or negative. The non-negativity constraints on the parameters of the model may be relaxed without giving up the requirement that the conditional covariance matrix is positive definite. Nelson and Cao (1992) derive sufficient conditions for the non-negativity of the conditional variance for a univariate GARCH(p; q) model with p > 2 and Tsai and Chan (2007) prove that these conditions are also necessary. We show that the methodologies used in these two papers can be applied to the unrestricted ECCC model with N variables. This is because each variance admits an infinite moving-average representation in terms of the N convolutions of the GARCH kernels and the corresponding squared errors. Hence, all the N conditional variances are always non-negative if all these N2 kernels are non-negative. For the bivariate case of order 1 we look into the consequences of adopting these less severe restrictions by comparing the autocorrelation function of squared observations under these two sets of constraints. These results are helpful to the model-builder who can consider the unrestricted formulation as a tool for testing various economic theories