Hawkes process model with a time-dependent background rate and its application to high-frequency financial data

Area of Science:

• Quantitative Finance
• Financial Econometrics
• Time Series Analysis

Background:

• High-frequency financial data analysis requires sophisticated models.
• Existing Hawkes models often assume constant or slowly varying background rates.
• Market dynamics are influenced by both endogenous and exogenous factors.

Purpose of the Study:

• To develop a Hawkes process model with a time-varying background rate for high-frequency financial data.
• To improve the accuracy of modeling intraday seasonality and rapid rate changes.
• To better estimate market endogeneity using the branching ratio.

Main Methods:

• Developed a Hawkes process model where the logarithm of the background rate is modeled using a linear model with variable-width basis functions.
• Employed a Bayesian method for parameter estimation.
• Analyzed tick data of the Nikkei 225 mini.

Main Results:

• The proposed model demonstrates superior fit compared to Hawkes models with constant or slowly varying background rates.
• Significant improvement in goodness-of-fit was observed during periods of high background rate fluctuation.
• The model is statistically consistent with the analyzed financial data.
• Estimated branching ratio of 0.41 indicates a greater influence of exogenous factors.

Conclusions:

• A time-varying background rate is crucial for accurately modeling high-frequency financial data.
• The developed model provides a more robust framework for analyzing market dynamics and endogeneity.
• Accurate modeling of the background rate is essential for reliable branching ratio estimation.