Statistical inference for ergodic point processes and application to Limit Order Book

Simon Clinet, Nakahiro Yoshida

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We construct a general procedure for the Quasi Likelihood Analysis applied to a multivariate point process on the real half line in an ergodic framework. When a particular family of laws of large numbers applies to the parametrized stochastic intensity of the model, we establish the consistency, the asymptotic normality and the convergence of moments of both the Quasi Maximum Likelihood estimator and the Quasi Bayesian estimator. We finally illustrate our results by showing how they can be applied to various Limit Order Book models such as the fundamental cases of Markovian models and exponential Hawkes process-based models.

Original languageEnglish
Pages (from-to)1800-1839
Number of pages40
JournalStochastic Processes and their Applications
Volume127
Issue number6
DOIs
Publication statusPublished - 2017 Jun 1
Externally publishedYes

Keywords

  • Ergodicity
  • Hawkes process
  • Inferential statistics
  • Limit Order Book
  • Multivariate point process
  • Quasi Likelihood Analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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