This supplement to Cavaliere and Georgiev (2020), CG hereafter, has four main sections. In Section S.2 we present the proofs of the results on weak convergence in distribution formulated in Appendix A of CG. In Sections S.3 and S.4 some derivations pertaining to the applications in Sections 2 and 4 of CG are given. Finally, Section S.5 provides a description of the Monte Carlo simulation design used in Section 2 of CG. For notation, see CG. Unless di¤erently speci ed, all references are to sections, equations and results in CG.