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

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 intensity parameter in the data generating process, and which are consistent. In this paper, long span tests, including the tests of Corradi et al. (2018) (called CSS tests), are compared and contrasted with a variety of fixed span tests, including the ASJ test of A¨ıt-Sahalia and Jacod (2009), the BNS test of Barndorff-Nielsen and Shephard (2006), and the PZ test of Podolskij and Ziggel (2010), in an extensive series of Monte Carlo experiments. The long span tests that we examine are consistent against the null hypothesis of zero jump intensity, while the fixed span tests are not designed to detect jumps in the data generating process, and instead detect realized jumps over a fixed time span. It is found that both the ASJ and CSS tests exhibit reasonably good finite sample properties, for time spans both short and long. The other tests suffer from finite sample distortions, both under sequential testing (as is well known) 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 extensive empirical analysis is carried out to investigate the implications of these findings. In particular, when applied to stock price and stock index data, “time-span robust” tests indicate that the prevalence of jumps is not as universal as might be expected. Various sector ETFs and individual stocks, for example, appear to exhibit no jumping behavior during a number of quarterly and annual periods