Testing for pure-jump processes for high-frequency data

Abstract

Pure-jump processes have been increasingly popular in modeling high-frequency\nfinancial data, partially due to their versatility and flexibility. In the\nmeantime, several statistical tests have been proposed in the literature to\ncheck the validity of using pure-jump models. However, these tests suffer from\nseveral drawbacks, such as requiring rather stringent conditions and having\nslow rates of convergence. In this paper, we propose a different test to check\nwhether the underlying process of high-frequency data can be modeled by a\npure-jump process. The new test is based on the realized characteristic\nfunction, and enjoys a much faster convergence rate of order $O(n^{1/2})$\n(where $n$ is the sample size) versus the usual $o(n^{1/4})$ available for\nexisting tests; it is applicable much more generally than previous tests; for\nexample, it is robust to jumps of infinite variation and flexible modeling of\nthe diffusion component. Simulation studies justify our findings and the test\nis also applied to some real high-frequency financial data.\n