Open Access
November 2018 Statistical inference for the doubly stochastic self-exciting process
Simon Clinet, Yoann Potiron
Bernoulli 24(4B): 3469-3493 (November 2018). DOI: 10.3150/17-BEJ966


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 $T^{-1}\int_{0}^{T}\theta_{t}^{*}\,dt$, where $\theta_{t}^{*}$ 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.


Download Citation

Simon Clinet. Yoann Potiron. "Statistical inference for the doubly stochastic self-exciting process." Bernoulli 24 (4B) 3469 - 3493, November 2018.


Received: 1 February 2017; Revised: 1 June 2017; Published: November 2018
First available in Project Euclid: 18 April 2018

zbMATH: 06869882
MathSciNet: MR3788179
Digital Object Identifier: 10.3150/17-BEJ966

Keywords: Hawkes process , high-frequency data , integrated parameter , self-exciting process , Stochastic , time-varying parameter

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 4B • November 2018
Back to Top