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