Identifying the Underlying Components of High-Frequency Data : Pure vs Jump Diffusion Processes

Hizmeri, Rodrigo and Izzeldin, Marwan and Urga, Giovanni (2025) Identifying the Underlying Components of High-Frequency Data : Pure vs Jump Diffusion Processes. Journal of Empirical Finance, 81 (3): 101594. ISSN 0927-5398

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Abstract

In this paper, we examine the finite sample properties of test statistics designed to identify distinct underlying components of high-frequency financial data, specifically the Brownian component and infinite vs. finite activity jumps. We conduct a comprehensive set of Monte Carlo simulations to evaluate the tests under various types of microstructure noise, price staleness, and different levels of jump activity. We apply these tests to a dataset comprising 100 individual S&P 500 constituents from diverse business sectors and the SPY (S&P 500 ETF) to empirically assess the relative magnitude of these components. Our findings strongly support the presence of both Brownian and jump components. Furthermore, we investigate the time-varying nature of rejection rates and we find that periods with more jumps days are usually associated with an increase in infinite jumps and a decrease infinite jumps. This suggests a dynamic interplay between jump components over time.