Abstract :
This paper considers a formulation of the extended constant or time-varying conditional
correlation GARCH model that allows for volatility feedback of either the
positive or negative sign. In the previous literature, negative volatility spillovers were
ruled out by the assumption that all the parameters of the model are nonnegative,
which is a sufficient condition for ensuring the positive definiteness of the conditional
covariance matrix. In order to allow for negative feedback, we show that the
positive definiteness of the conditional covariance matrix can be guaranteed even if
some of the parameters are negative. Thus, we extend the results of Nelson and Cao
(1992) and Tsai and Chan (2008) to a multivariate setting. For the bivariate case of
order one, we look into the consequences of adopting these less severe restrictions
and find that the flexibility of the process is substantially increased. Our results are
helpful for the model-builder, who can consider the unrestricted formulation as a
tool for testing various economic theories.
