{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T06:21:47Z","timestamp":1682662907623},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1017\/s0021900200013760","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:50:03Z","timestamp":1459263003000},"page":"1006-1024","source":"Crossref","is-referenced-by-count":2,"title":["Inference for a Nonstationary Self-Exciting Point Process with an Application in Ultra-High Frequency Financial Data Modeling"],"prefix":"10.1017","volume":"50","author":[{"given":"Feng","family":"Chen","sequence":"first","affiliation":[]},{"given":"Peter","family":"Hall","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"key":"S0021900200013760_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/0378-3758(95)00070-4"},{"key":"S0021900200013760_ref23","volume-title":"Continuous Martingales and Brownian Motion","year":"1999"},{"key":"S0021900200013760_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/BF02480216"},{"key":"S0021900200013760_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(01)00063-X"},{"key":"S0021900200013760_ref19","volume-title":"The econometrics of randomly spaced financial data: a survey","year":"2009"},{"key":"S0021900200013760_ref18","volume-title":"Analytical and Numerical Methods for Volterra Equations","year":"1985"},{"key":"S0021900200013760_ref17","first-page":"171","volume":"13","year":"1977","journal-title":"Ann. 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