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Feng Chen: Direct Likelihood Evaluation for the Renewal Hawkes Process
time: Dec 26, 2019

Time: 14:30, December 27, 2019 (Friday)

Location: 1710, building B,Feicuihu Campusscience and education building

Speaker:FengChen, senior lecturer, doctoral supervisor

From:Department of statistics, University of New South Wales

Organizer:School of Mathematics

Lecturer introduce:In 2008,Feng Chenreceived a doctorate in statistics from the University of Hong Kong. Since 2008, he has worked in the Department of statistics of the University of New South Wales (UNSW Sydney), Australia. He is currently a senior lecturer and doctoral supervisor. Research fields include statistical theory and method, survival analysis, application probability, application statistics, statistical calculation, etc. more than 30 academic papers have been published in internationally renowned journals in related fields, and three graduate doctoral students have been trained, and another one is in training. Currently, he is a member of the editorial board and deputy editor of Journal of statistical planning and influence. For more information, see the homepage: https://web.matches.unsw.edu.au / ~ FengChen/.

Description:An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley, Filimonov, and Sornette, which has the potential to significantly widen the application domains of the self-exciting point processes. However, they claimed that computation of the likelihood of the RHawkes process requires exponential time and therefore is practically impossible. They proposed two expectation–maximization (EM) type algorithms to compute the maximum likelihood estimator (MLE) of the model parameters. Because of the fundamental role of likelihood in statistical inference, a practically feasible method for likelihood evaluation is highly desirable. In this article, we provide an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley, Filimonov, and Sornette. We demonstrate the superior performance of the resulting MLEs of the model relative to the EM estimators through simulations. We also present a computationally efficient procedure to calculate the Rosenblatt residuals of the process for goodness-of-fit assessment, and a simple yet efficient procedure for future event prediction. The proposed methodologies were applied on real data from seismology and finance.