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陳峰: Direct Likelihood Evaluation for the Renewal Hawkes Process

時間:2019-12-24來源:

報告時間2019年12月27日(星期五)14:30

報告地點:翡翠科教樓B座1710

:陳峰 高級講師, 博士生導師

工作單位:新南威爾士大學統計系

舉辦單位:數學學院

報告人簡介

2008年獲香港大學統計學博士學位,自2008年至今供職于澳大利亞新南威爾士大學(UNSW Sydney)統計系,現職高級講師,博士生導師。研究領域包括統計理論與方法、生存分析、應用概率、應用統計、統計計算等,已在相關領域的國際知名期刊發表學術論文30余篇,并培養畢業博士生三名,另有一名在培?,F為國際知名統計學期刊Journal of Statistical Planning and Inference編委會成員及副主編。更多信息見個人主頁:https://web.maths.unsw.edu.au/~fengchen/  。

報告簡介

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.

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