A1014
Title: Robust estimation and testing for GARCH models via exponentially tilted empirical likelihood
Authors: Yashuang Li - Yunnan University (China) [presenting]
Puying Zhao - Yunnan University (China)
Niansheng Tang - Yunnan University (China)
Abstract: The GARCH model has become one of the most powerful and widespread tools for dealing with time series heteroskedastic models. A commonly employed approach for inference on GARCH models is the quasi-maximum likelihood. However, unless the data are sampled regularly, the quasi-maximum likelihood estimator is inconsistent due to density misspecification or the presence of outliers. The main aim is to present a robust nonparametric likelihood analysis of GARCH models, including estimation of the coefficient parameters and model specification testing of the GARCH process. A set of identifying moment functions is specified by applying quantile regression models to the GARCH process. The moment restrictions allow the GARCH innovations to be generally distributed and are less sensitive to outliers. Exponentially tilted empirical likelihood (ETEL) is then explored to combine these quantile-related moment restrictions effectively. The ETEL framework allows for imposing over-identifying restrictions and offers implied probabilities for efficient and robust moment estimation and inference. Asymptotic properties of the resultant ETEL estimators and test statistics are investigated under mild conditions on the innovation distributions. The proposed strategies are illustrated and evaluated through numerical experiments on simulated and real datasets.
