A note on the Gumbel convergence for the Lee and Mykland jump tests

Abstract

The Lee and Mykland (2008, 2012) nonparametric jump tests have been widely used in the literature but its critical region is stated with reference to the asymptotic distribution of the maximum of a set of standard normal variates. However, such reference would imply a typo (of a non-negligible order) for the norming constants adopted. By using the asymptotic distribution of the maximum of a set of folded normal random variables instead, this paper shows that there is no typo at all, thus preserving the validity of all the empirical findings based on these tests.