Forecasting Duration in High‐Frequency Financial Data Using a Self‐Exciting Flexible Residual Point Process

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 ultrahigh‐frequency trading data.