Fixed and Long Time Span Jump Tests: New Monte Carlo and Empirical Evidence

Abstract

Numerous tests designed to detect realized jumps over a fixed time span have been proposed and extensively studied in the financial econometrics literature. These tests differ from “long time span tests” that detect jumps by examining the magnitude of the jump intensity parameter in the data generating process, and which are consistent. In this paper, long span jump tests are compared and contrasted with a variety of fixed span jump tests in a series of Monte Carlo experiments. It is found that both the long time span tests of Corradi et al. (2018) and the fixed span tests of Aït-Sahalia and Jacod (2009) exhibit reasonably good finite sample properties, for time spans both short and long. Various other tests suffer from finite sample distortions, both under sequential testing and under long time spans. The latter finding is new, and confirms the “pitfall” discussed in Huang and Tauchen (2005), of using asymptotic approximations associated with finite time span tests in order to study long time spans of data. An empirical analysis is carried out to investigate the implications of these findings, and “time-span robust” tests indicate that the prevalence of jumps is not as universal as might be expected.