Modeling high-frequency financial data by pure jump processes

TL;DR

This paper develops a simple and effective statistical test to determine whether high-frequency financial data can be adequately modeled using pure jump processes without a diffusion component.

Contribution

It introduces a novel statistical test for assessing the necessity of a diffusion component in high-frequency financial data models, supported by asymptotic analysis and empirical validation.

Findings

The test effectively distinguishes pure jump models from those requiring diffusion.

Simulation studies demonstrate the test's accuracy and robustness.

Real data examples confirm the practical applicability of the method.

Abstract

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.