Statistical inference for the doubly stochastic self-exciting process

Simon Clinet, Yoann Potiron

研究成果: Article査読

5 被引用数 (Scopus)

抄録

We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter T −10T θt dt, where θt is the time-varying parameter, and we consider the high-frequency asymptotics. To estimate it naïvely, we chop the data into several blocks, compute the maximum likelihood estimator (MLE) on each block, and take the average of the local estimates. The asymptotic bias explodes asymptotically, thus we provide a non-naïve estimator which is constructed as the naïve one when applying a first-order bias reduction to the local MLE. We show the associated central limit theorem. Monte Carlo simulations show the importance of the bias correction and that the method performs well in finite sample, whereas the empirical study discusses the implementation in practice and documents the stochastic behavior of the parameters.

本文言語English
ページ(範囲)3469-3493
ページ数25
ジャーナルBernoulli
24
4B
DOI
出版ステータスPublished - 2018 11

ASJC Scopus subject areas

  • Statistics and Probability

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