  It is now widely accepted that volatility models have to incorporate the
so-called leverage effect in order to to model the dynamics of daily financial
returns.We suggest a new class of multivariate power transformed asymmetric
models. It includes several functional forms of multivariate GARCH models which
are of great interest in financial modeling and time series literature. We
provide an explicit necessary and sufficient condition to establish the strict
stationarity of the model. We derive the asymptotic properties of the
quasi-maximum likelihood estimator of the parameters. These properties are
established both when the power of the transformation is known or is unknown.
The asymptotic results are illustrated by Monte Carlo experiments. An
application to real financial data is also proposed.
