Bootstrapping GARCH models under dependent innovations

This study reflects on the inconsistency of the fixed-design residual bootstrap procedure for GARCH models under dependent innovations. We introduce a recursive- design residual block bootstrap procedure to accurately quantify the uncertainty around parameter estimates and the next period’s volatility. A simulation study provides evidence for the validity of the recursive-design residual block bootstrap under dependent innovations. The resulting confidence intervals are not only valid but also potentially narrower than those obtained by the inconsistent fixed-design bootstrap. In an empirical illustration, we demonstrate the practical relevance by showing residual dependence and differences in confidence intervals between the two bootstrap procedures.