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 novel recursive-design residual block bootstrap procedure to accurately quantify the uncertainty around parameter estimates and volatility forecasts. A simulation study provides evidence for the validity of the recursive-design residual block bootstrap in the presence of dependent innovations. The resulting bootstrap confidence intervals are not only valid but also potentially narrower than the ones obtained from the inconsistent fixed design bootstrap, depending on the underlying data-generating process and the sample size. In an application to financial time series, we illustrate the empirical relevance of our proposed methods, showing evidence for the residual dependence and demonstrating notable differences between the confidence intervals obtained by the fixed- and the recursive-design bootstrap procedure.