## QML estimation for of a class of asymmetric GARCH models with covariates

par - publié le

Le Quyen Thieu
(Université Pierre et Marie Curie)

Modeling and forecasting volatility is one of the major current issues in contemporary finance. The GARCH models are among the essential tools for modeling volatility. In particular, the asymmetrical models are remarkably advanced for making GARCH conditional volatility as a function of the magnitude of past shocks and its sign. To improve the prediction of the volatility, we have inserted extra informations (under the form of exogenous covariates) to the volatility equation and have taken into account its probabilistic and statistical properties. The asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is obtained for a wide class of asymmetric GARCH models with exogenous covariates. The true value of the parameter is not restricted to belong to the interior of the parameter space, which allows us to derive tests for the significance of the parameters. In particular, the relevance of the exogenous variables can be assessed. The results are obtained without assuming that the innovations are independent, which allows conditioning on different information sets. Monte Carlo experiments and applications to financial series illustrate the asymptotic results. In particular, an empirical study demonstrates that the realized volatility can be an helpful covariate for predicting squared returns.