🤖 AI Summary
This study addresses the challenge of modeling and forecasting inter-arrival times of limit order book events in high-frequency financial markets, which exhibit heavy-tailed distributions that are difficult to capture accurately. The authors propose a flexible residual point process model that integrates heavy-tailed inter-event time characteristics with a self-exciting decay structure, embedding empirical duration distributions within a self-exciting point process framework. Theoretical analysis establishes that, under suitable conditions, the model possesses desirable stochastic stability properties, including irreducibility, aperiodicity, positive Harris recurrence, and a unique stationary distribution. Empirical results based on ultra-high-frequency trading data demonstrate that the proposed approach significantly outperforms existing benchmark models in predicting event durations.
📝 Abstract
This paper presents a method for forecasting limit order book durations using a self-exciting flexible residual point process. High-frequency events in modern exchanges exhibit heavy-tailed interarrival times, posing a significant challenge for accurate prediction. The proposed approach incorporates the empirical distributional features of interarrival times while preserving the self-exciting and decay structure. This work also examines the stochastic stability of the process, which can be interpreted as a general state-space Markov chain. Under suitable conditions, the process is irreducible, aperiodic, positive Harris recurrent, and has a stationary distribution. An empirical study demonstrates that the model achieves strong predictive performance compared with several alternative approaches when forecasting durations in ultra-high-frequency trading data.