Statistical inference for ergodic point processes and application to Limit Order Book
Statistical inference for ergodic point processes and application to Limit Order Book
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DOI：
10.1016/j.spa.2016.09.014
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发表时间：
2017-06-01
影响因子：
1.4
通讯作者：
Yoshida, Nakahiro
中科院分区：
文献类型：
--
作者：
Clinet, Simon;Yoshida, Nakahiro
本文在遍历框架下构造了拟似然分析应用于真实的半直线上的多元点过程的一般过程。当一个特殊的大数定律族应用于模型的参数化随机强度时，我们建立了拟极大似然估计和拟贝叶斯估计的相合性、渐近正态性和矩的收敛性。最后，我们说明我们的结果，显示他们如何可以应用到各种极限订单簿模型，如马尔可夫模型和指数霍克斯过程为基础的模型的基本情况。(C)2016爱思唯尔B.V.保留所有权利。
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. (C) 2016 Elsevier B.V. All rights reserved.