Paper: arXiv 2604.00346

Authors: Kyungsub Lee

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically rigorous point process model, proving state-space Markov chain properties like Harris recurrence alongside theoretical stability. It supports these theoretical contributions with robust empirical applications to ultra-high-frequency limit order book data, outperforming standard baseline models.

Research Flowchart

  flowchart TD
    A[Research Goal: Forecast Heavy-Tailed LOB Durations] --> B[Input: Ultra-High-Frequency Equity Trading Data]
    B --> C[Model Design: Self-Exciting Flexible Residual Point Process]
    C --> D[Theoretical Analysis: Prove Markov Chain Stochastic Stability]
    C --> E[Empirical Analysis: Parameter Estimation & Forecasting]
    D & E --> F[Outcomes: Strong Predictive Performance & Guaranteed Process Stability]

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2 of 50 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.