The Annals of Statistics

Modeling high-frequency financial data by pure jump processes

Bing-Yi Jing, Xin-Bing Kong, and Zhi Liu

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It is generally accepted that the asset price processes contain jumps. In fact, pure jump models have been widely used to model asset prices and/or stochastic volatilities. The question is: is there any statistical evidence from the high-frequency financial data to support using pure jump models alone? The purpose of this paper is to develop such a statistical test against the necessity of a diffusion component. The test is very simple to use and yet effective. Asymptotic properties of the proposed test statistic will be studied. Simulation studies and some real-life examples are included to illustrate our results.

Article information

Ann. Statist., Volume 40, Number 2 (2012), 759-784.

First available in Project Euclid: 17 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M05: Markov processes: estimation 62G20: Asymptotic properties
Secondary: 60J75: Jump processes 60G20: Generalized stochastic processes

Diffusion pure jump process semi-martingales high-frequency data hypothesis testing


Jing, Bing-Yi; Kong, Xin-Bing; Liu, Zhi. Modeling high-frequency financial data by pure jump processes. Ann. Statist. 40 (2012), no. 2, 759--784. doi:10.1214/12-AOS977.

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