Bootstrapping High-Frequency Jump Tests. Issue 526 (3rd April 2019)

• Record Type: Journal Article
• Authors: Dovonon, Prosper; Gonçalves, Sílvia; Hounyo, Ulrich; Meddahi, Nour
• Is Part Of: Journal of the American Statistical Association. Volume 114:Issue 526(2019)
• Page Start: 793
• Page End: 803
• Publication Date: 2019-04-03
• Subjects: Asymptotic refinements -- Bias correction -- Jump tests -- Thresholding volatility bootstrap; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2018.1447485
• Languages: English
• ISSNs: 0162-1459

Abstract

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.