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Original Articles

Partial self-exciting point processes and their parameter estimations

, &
Pages 2913-2935 | Received 23 Nov 2017, Accepted 13 Apr 2018, Published online: 04 Dec 2018

References

  • Bacry, E., I. Mastromatteo, and J. F. Muzy. 2015. Hawkes processes in finance. arXiv:1502.04592v1. Market Microstructure and Liquidity 01 (01):1550005.
  • Balderama, E., F. P. Schoenberg, E. Murray, and P. W. Rundel. 2012. Application of branching point process models to the study of invasive red banana plants in Costa Rica. Journal of the American Statistical Association 107 (498):467–476.
  • Cui, L., Hawkes, R. A. G. Yi. and H. 2017. A new method for moments of Hawkes processes. (submitted).
  • Cui, L. R., Z. L. Chen, and H. D. Gao. 2018. Reliability for systems with self-healing effect under shock models. Quality Technology and Quantitative Management, Online 1. 15 (5):551–567.
  • Dassios, A., and H. B. Zhao. 2011. A dynamic contagion process. Advances in Applied Probability 43 (3):814–846.
  • Davis, M. H. A. 1984. Piecewise-deterministic markov processes: a general class of nondiffusion stochastic models. Journal of the Royal Statistical Society: Series B 46:353–388.
  • Ertekin, S., C. Rudin, and T. H. McCormick. 2015. Reactive point processes: a new approach to predicting power failures in underground electrical systems. The Annals of Applied Statistics 9 (1):122–144.
  • Fox, E. W., M. B. Short, F. P. Schoenberg, K. D. Coronges, and A. L. Bertozzi. 2016. Modeling E-mail networks and inferring leadership using self-exciting point processes. Journal of the American Statistical Association 111 (514):564–584.
  • Halpin, P. F., and P. De Boeck. 2013. Modelling dyadic interaction with Hawkes processes. Psychometrika 78 (4):793–722.
  • Hawkes, A. G. 1971. Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 (1):83–90.
  • Hawkes, A. G. 1971b. Point spectra of some mutually exciting point processes. Journal of the Royal Statistical Society: Series B 33:438–443.
  • Hegemann, R., E. Lewis, and A. Bertozzi. 2013. An estimate & score algorithm for simultaneous parameter estimation and reconstruction of missing data on social networks. Security Informatics 2 (1):1–14.
  • Krumin, M., I. Reutsky, and S. Shoham. 2010. Correlation-based analysis and generation of multiple spike trains using hawkes models with an exogenous input. Frontiers in Computational Neuroscience 4:147.
  • Laub, P. J., T. Taimre and P. K. Pollett. 2015. Hawkes processes. arXiv 1507 :02822v1.
  • Lewis, E., G. Mohler, P. J. Brantingham, and A. L. Bertozzi. 2012. Self-exciting point process models of civilian deaths in Iraq. Security Journal 25 (3):244–264.
  • Lin, F.C. 2011. A random effects epidemic-type aftershock sequence model. Computational Statistics and Data Analysis 55 (4):1610–1616.
  • Mohler, G. O., M. B. Short, P. J. Brantingham, F. P. Schoenberg, and G. E. Tita. 2011. Self-exciting point process modeling of crime. Journal of the American Statistical Association 106 (493):100–108.
  • Musmeci, F., and D. Vere-Jones. 1992. A space-time clustering model for historical earthquakes. Annals of the Institute of Statistical Mathematics 44 (1):1–11.
  • Ogata, Y. 1988. Statistical method for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association 83 (401):9–27.
  • Ozaki, T. 1979. Maximum likelihood estimation of hawkes’ self-exciting point processes. Annals of the Institute of Statistical Mathematics 31 (1):145–55.
  • Reynaud-Bouret, P., and S. Schbath. 2010. Adaptive estimation for hawkes processes: application to genome analysis. The Annals of Statistics 38 (5):2781–2822.
  • Saichev, A., and D. Sornette. 2006. Renormalization of the ETAS branching model of triggered seismicity from total to observable seismicity. The European Physical Journal B 51 (3):443–459.
  • Sornette, D., and M. J. Werner. 2005. Constraints on the size of the smallest triggering earthquake from the ETAS model, baath's law, and observed aftershock sequences. Journal of Geophysical Research 110(B8):1–11.
  • Vere-Jones, D., and T. Ozaki. 1982. Some examples of statistical estimation applied to earthquake data. Annals of the Institute of Statistical Mathematics 34 (1):189–207.
  • Wang, T., M. Bebbington, and D. Harte. 2012. Markov-modulated hawkes process with stepwise decay. Annals of the Institute of Statistical Mathematics 64 (3):521–544.
  • Wheatley, S., V. Filimonov, and D. Sornette. 2016. The hawkes process with renewal immigration & its estimation with an EM algorithm. Computational Statistics and Data Analysis 94:120–35.
  • White, G., and M. D. Porter. 2014. GPU accelerated MCMC for modeling terrorist activity. Computational Statistics and Data Analysis 71:643–651.
  • Zhu, L. 2013. Nonlinear hawkes processes. USA: Ph.D. thesis, New York University.

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