主  題:Direct Likelihood Evaluation for the Renewal Hawkes Process

內(nèi)容簡介:An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley et al. (2016 CSDA), which has the potential to significantly widen the application domains of the self-exciting point processes. However, the authors 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 talk we present an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley et al. 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. This talk is based on joint work with Tom Stindl. The R package implementing the proposed methodology is available on the CRAN: 

報告人:陳鋒      副教授

時  間:2019-01-18    15:30

地  點:競慧東樓302

舉辦單位:統(tǒng)計與數(shù)學學院  統(tǒng)計與大數(shù)據(jù)研究院  科研部