Statistical inference for ergodic point processes and application to limit order book

DOI10.1016/j.spa.2016.09.014zbMath1373.60086arXiv1512.01899OpenAlexW2524671997MaRDI QIDQ2359704

Nakahiro Yoshida, Simon Clinet

Publication date: 22 June 2017

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.01899

zbMATH Keywords

ergodicityHawkes processlimit order bookmultivariate point processinferential statisticsquasi likelihood analysis

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Applications of statistics to actuarial sciences and financial mathematics (62P05) Statistical methods; risk measures (91G70) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (19)

Penalized least squares approximation methods and their applications to stochastic processes ⋮ Quasi-likelihood analysis and its applications ⋮ Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes ⋮ On the nonparametric inference of coefficients of self-exciting jump-diffusion ⋮ State-dependent Hawkes processes and their application to limit order book modelling ⋮ Marked point processes and intensity ratios for limit order book modeling ⋮ Stability for Hawkes processes with inhibition ⋮ Multivariate self-exciting jump processes with applications to financial data ⋮ Alternative asymptotic inference theory for a nonstationary Hawkes process ⋮ Bootstrap inference for Hawkes and general point processes ⋮ Sparse estimation for generalized exponential marked Hawkes process ⋮ Asymptotic distribution of the score test for detecting marks in Hawkes processes ⋮ Statistical inference for the doubly stochastic self-exciting process ⋮ Hawkes process and Edgeworth expansion with application to maximum likelihood estimator ⋮ Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise ⋮ Confidence interval for correlation estimator between latent processes ⋮ Exponential ergodicity for diffusions with jumps driven by a Hawkes process ⋮ Regenerative properties of the linear Hawkes process with unbounded memory ⋮ Partial quasi-likelihood analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximum likelihood estimation of Hawkes' self-exciting point processes
• Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations
• Markov chains and stochastic stability
• The asymptotic behaviour of maximum likelihood estimators for stationary point processes
• Estimation of the spectral parameters of a stationary point process
• Stability of nonlinear Hawkes processes
• A MATHEMATICAL APPROACH TO ORDER BOOK MODELING
• Price Dynamics in a Markovian Limit Order Market
• Modelling Bid and Ask Prices Using Constrained Hawkes Processes: Ergodicity and Scaling Limit
• A Stochastic Model for Order Book Dynamics
• Stability of Markovian processes II: continuous-time processes and sampled chains
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• Long-Time Behavior of a Hawkes Process--Based Limit Order Book
• Maximum likelihood estimation for stationary point processes
• The Markovian self-exciting process
• Ergodicity and Diffusivity of Markovian Order Book Models: A General Framework
• Statistical theory of the continuous double auction
• The order book as a queueing system: average depth and influence of the size of limit orders
• Simulating and Analyzing Order Book Data: The Queue-Reactive Model
• STATIONARY DISTRIBUTION OF THE VOLUME AT THE BEST QUOTE IN A POISSON ORDER BOOK MODEL
• Modelling microstructure noise with mutually exciting point processes
• Information criteria in model selection for mixing processes

This page was built for publication: Statistical inference for ergodic point processes and application to limit order book