高频数据的纯跳过程检验
Testing for pure-jump processes for high-frequency data
摘要：
纯跳过程在高频金融数据建模中越来越受欢迎，部分原因是其通用性和灵活性。同时，在文献中提出了一些统计检验，以检查使用纯跳跃模型的有效性。然而，这些测试有几个缺点，如需要相当严格的条件，并具有缓慢的收敛速度。在本文中，我们提出了一个不同的测试，以检查是否可以通过一个纯跳跃过程的高频数据的底层过程建模。新的测试是基于实现的特征函数，并享有一个更快的收敛速度的顺序$O(n^{1/2})$（其中$n$是样本量）与现有的测试通常可用的$o(n^{1/4})$，它适用于更普遍比以前的测试，例如，它是强大的跳跃无限变化和灵活的建模的扩散组件。模拟研究证明了我们的研究结果，并测试也适用于一些真正的高频金融数据。
英文摘要：
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.
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