December 2013 Inference for a nonstationary self-exciting point process with an application in ultra-high frequency financial data modeling
Feng Chen, Peter Hall
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J. Appl. Probab. 50(4): 1006-1024 (December 2013). DOI: 10.1239/jap/1389370096


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.


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Feng Chen. Peter Hall. "Inference for a nonstationary self-exciting point process with an application in ultra-high frequency financial data modeling." J. Appl. Probab. 50 (4) 1006 - 1024, December 2013.


Published: December 2013
First available in Project Euclid: 10 January 2014

zbMATH: 06279824
MathSciNet: MR3161370
Digital Object Identifier: 10.1239/jap/1389370096

Primary: 60G55
Secondary: 60F05 , 62F12 , 62P20

Keywords: asymptotic normality , consistency , Hawkes process , intensity process , martingale central limit theorem , maximum likelihood estimator , nonstationary , point process , Self-exciting , ultra-high frequency

Rights: Copyright © 2013 Applied Probability Trust


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Vol.50 • No. 4 • December 2013
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