Estimation of multivariate asymmetric power GARCH models
This work addresses the need for improved volatility models in financial time series analysis, though it appears incremental as it builds upon existing GARCH frameworks.
The authors tackled the problem of modeling daily financial returns by introducing a new class of multivariate power transformed asymmetric GARCH models that incorporate the leverage effect, providing conditions for strict stationarity and deriving asymptotic properties for parameter estimation, with results validated through Monte Carlo experiments and real data application.
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.