Empirical Likelihood for GARCH Models

This paper develops an empirical likelihood approach for regular generalized auto-regressive conditional heteroskedasticity (GARCH) models and GARCH models with unit roots. For regular GARCH models, it is shown that the log empirical likelihood ratio statistic asymptotically follows a X-2 distribution. For GARCH models with unit roots, two versions of the empirical likelihood methods, the least squares score and the maximum likelihood score functions, are considered. For both cases, the limiting distributions of the log empirical likelihood ratio statistics are established. These two statistics can be used to test for unit roots under the GARCH framework. Finite-sample performances are assessed through simulations for GARCH models with unit roots