Open Access
April 2015 Testing for pure-jump processes for high-frequency data
Xin-Bing Kong, Zhi Liu, Bing-Yi Jing
Ann. Statist. 43(2): 847-877 (April 2015). DOI: 10.1214/14-AOS1298


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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Xin-Bing Kong. Zhi Liu. Bing-Yi Jing. "Testing for pure-jump processes for high-frequency data." Ann. Statist. 43 (2) 847 - 877, April 2015.


Published: April 2015
First available in Project Euclid: 23 March 2015

zbMATH: 1312.62101
MathSciNet: MR3325712
Digital Object Identifier: 10.1214/14-AOS1298

Primary: 62G20 , 62M05
Secondary: 60G20 , 60J75

Keywords: integrated volatility , Itô semimartingale , pure-jump process , realized characteristic function

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 2 • April 2015
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