Self and mutually exciting point process embedding flexible residuals and intensity with discretely Markovian dynamics

ArXiv ID: 2401.13890 “View on arXiv”

Authors: Unknown

Abstract

This work introduces a self and mutually exciting point process that embeds flexible residuals and intensity with discretely Markovian dynamics. By allowing the integration of diverse residual distributions, this model serves as an extension of the Hawkes process, facilitating intensity modeling. This model’s nature enables a filtered historical simulation that more accurately incorporates the properties of the original time series. Furthermore, the process extends to multivariate models with manageable estimation and simulation implementations. We investigate the impact of a flexible residual distribution on the estimation of high-frequency financial data, comparing it with the Hawkes process.

Keywords: Hawkes process, self-exciting point process, filtered historical simulation, high-frequency financial data, discretely Markovian dynamics, General Financial Markets (High-Frequency)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts such as stochastic point processes, Markov properties, and recursive definitions with significant LaTeX/derivations, indicating high math complexity. It also demonstrates empirical rigor by testing the model on high-frequency financial data, comparing it with established baselines like the Hawkes process, and discussing implementation aspects such as filtered historical simulations.

  flowchart TD
    A["Research Goal"] --> B["Data & Inputs"]
    B --> C["Methodology"]
    C --> D["Computational Processes"]
    D --> E["Key Findings"]

    A["Research Goal<br>Develop flexible self/mutually exciting point process<br>extending Hawkes with discretely Markovian dynamics"]

    B["Data & Inputs<br>High-Frequency Financial Data<br>General Financial Markets"]

    C["Methodology<br>1. Integrate diverse residual distributions<br>2. Model discretely Markovian dynamics<br>3. Extend to multivariate models"]

    D["Computational Processes<br>Filtered Historical Simulation<br>Estimation & Simulation<br>High-frequency data integration"]

    E["Key Findings<br>1. Enhanced intensity modeling accuracy<br>2. Better property incorporation<br>3. Manageable multivariate estimation<br>4. Superior performance vs. Hawkes process"]