Bootstrapping High-Frequency Jump Tests. Issue 526 (3rd April 2019) - Dovonon, Prosper; Gonçalves, Sílvia; Hounyo, Ulrich; Meddahi, Nour
ABSTRACT: The main contribution of this article is to propose a bootstrap test for jumps based on functions of realized volatility and bipower variation. Bootstrap intraday returns are randomly generated from a mean zero Gaussian distribution with a variance given by a local measure of integrated volatility (which we denote by { v ^ i n } ). We first discuss a set of high-level conditions on { v ^ i n } such that any bootstrap test of this form has the correct asymptotic size and is alternative-consistent. We then provide a set of primitive conditions that justify the choice of a thresholding-based estimator for { v ^ i n } . Our cumulant expansions show that the bootstrap is unable to mimic the higher-order bias of the test statistic. We propose a modification of the original bootstrap test which contains an appropriate bias correction term and for which second-order asymptotic refinements are obtained.