Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations

A general method is proposed for the construction of valid simultaneous confidence sets in the context of stationary GARCH models. The proposed method proceeds by numerically inverting the conventional likelihood ratio test. In order to hedge against the risk of a spurious rejection, candidate points that are rejected by the conventional test undergo a finite-sample parametric bootstrap test. A projection technique is then exploited to produce conservative confidence sets for general functions of the parameters. A simulation study illustrates the performance of the conventional likelihood ratio test and the parametric bootstrap test in the context of a GARCH model with heavy-tailed and skewed innovations. That model is then used in an empirical application to construct simultaneous confidence intervals for multi-step ahead conditional volatility forecasts for the returns on a major stock market index.