Bootstrapping tests for jumps with an application to test averaging

We propose new bootstrap methods for the Barndorff-Nielsen and Shephard (2006) and Andersen et al. (2012) tests for jumps, as well as for the realized bipower variation and the median realized variation.1 Both the i.i.d. and the Wild bootstrap are considered. We prove CLT-type results for the couples: realized volatility-realized bipower variation and realized volatility-median realized variation. Based on these results, we build boot- strapped tests for jumps. We introduce a new jump-testing procedure that uses Fisher (1932)’s method to average p-values from one/ different tests applied at different sampling frequencies. The procedure is proven to be more efficient than applying the asymptotic tests, as we discard less data and extract information from multiple frequencies and/ or procedures. We use a double bootstrap procedure to control the overall size of the test.