Review of Statistical Approaches for Modeling High-Frequency Trading Data

Due to technological advancements over the last two decades, algorithmic trading strategies are now widely used in financial markets. In turn, these strategies have generated high-frequency (HF) data sets, which provide information at an extremely fine scale and are useful for understanding market behaviors, dynamics, and microstructures. In this paper, we discuss how information flow impacts the behavior of high-frequency (HF) traders and how certain high-frequency trading (HFT) strategies significantly impact market dynamics (e.g., asset prices). The paper also reviews several statistical modeling approaches for analyzing HFT data. We discuss four popular approaches for handling HFT data: (i) aggregating data into regularly spaced bins and then applying regular time series models, (ii) modeling jumps in price processes, (iii) point process approaches for modeling the occurrence of events of interest, and (iv) modeling sequences of inter-event durations. We discuss two methods for defining events, one based on the asset price, and the other based on both price and volume of the asset. We construct durations based on these two definitions, and apply models to tick-by-tick data for assets traded on the New York Stock Exchange (NYSE). We discuss some open challenges arising in HFT data analysis including some empirical analysis, and also review applications of HFT data in finance and economics, outlining several research directions.