Journal of Applied Probability

Inference for a nonstationary self-exciting point process with an application in ultra-high frequency financial data modeling

Feng Chen and Peter Hall

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Self-exciting point processes (SEPPs), or Hawkes processes, have found applications in a wide range of fields, such as epidemiology, seismology, neuroscience, engineering, and more recently financial econometrics and social interactions. In the traditional SEPP models, the baseline intensity is assumed to be a constant. This has restricted the application of SEPPs to situations where there is clearly a self-exciting phenomenon, but a constant baseline intensity is inappropriate. In this paper, to model point processes with varying baseline intensity, we introduce SEPP models with time-varying background intensities (SEPPVB, for short). We show that SEPPVB models are competitive with autoregressive conditional SEPP models (Engle and Russell 1998) for modeling ultra-high frequency data. We also develop asymptotic theory for maximum likelihood estimation based inference of parametric SEPP models, including SEPPVB. We illustrate applications to ultra-high frequency financial data analysis, and we compare performance with the autoregressive conditional duration models.

Article information

J. Appl. Probab., Volume 50, Number 4 (2013), 1006-1024.

First available in Project Euclid: 10 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 60F05: Central limit and other weak theorems 62F12: Asymptotic properties of estimators 62P20: Applications to economics [See also 91Bxx]

Asymptotic normality consistency Hawkes process intensity process martingale central limit theorem maximum likelihood estimator nonstationary point process self-exciting ultra-high frequency


Chen, Feng; Hall, Peter. Inference for a nonstationary self-exciting point process with an application in ultra-high frequency financial data modeling. J. Appl. Probab. 50 (2013), no. 4, 1006--1024. doi:10.1239/jap/1389370096.

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