New method detects structural shifts in multivariate Hawkes processes.
problem Detecting changes in multivariate Hawkes processes.
method Using Fréchet statistics on overlapping windows of causal network.
result Accurately detects and characterizes changes in causal structure.
Proposes a new model for complex multivariate event data.
problem Modeling complex multivariate event data with spatio-temporal dynamics.
method Integrates spatial information into latent state evolution through learned temporal and spatial decay dynamics.
result Successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns.
The paper analyzes multivariate Hawkes processes and their induced population processes.
problem Analyzing the time-dependent joint probability distribution of multivariate Hawkes processes.
method Exact and asymptotic analysis of general multivariate Hawkes processes and their induced population processes.
result Full characterization of the time-dependent joint transform of the multivariate population process and its intensity process.
New MGCPP model for order flow in financial markets.
problem Modeling order flow dynamics in financial markets.
method Developed MGCPP, proved LLN and FCLTs, applied to real data.
result Validated MGCPP model with real trading data.
The paper develops Hawkes-based models for LOB and applies them to European, spread, and basket option pricing.
problem Developing accurate models for pricing options in the context of limit order books (LOB).
method Introduces multivariate Hawkes processes and their limit theorems, applies to European, spread, and basket options.
result Hawkes-based models provide more market forecast information than classical models.
We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional constraint variable, whose evo…
Given a collection of entities (or nodes) in a network and our intermittent observations of activities from each entity, an important problem is to learn the hidden edges depicting directional relationships among these entities. Here, we study causal relationships (excitations) that are realized by a multivariate Hawke…
The paper introduces new processes for modeling multivariate volatility.
problem Developing new stochastic processes for multivariate volatility modeling.
method Introducing Volterra Wishart and Volterra pure jump processes with fractional kernels.
result Affine covariance processes for multivariate volatility modeling.
The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced…
Model predicts depegging dynamics of stablecoins like Tether and Bitcoin.
problem Understanding depegging effects of stablecoins on cryptocurrencies.
method Multivariate Hawkes process model.
result Numerical example shows model's effectiveness.
Develops a framework for inferring causal relationships in networked data with uncertainty quantification.
problem Extracting reliable inference from complex Hawkes network data with uncertainty.
method Statistical inference framework based on maximum likelihood estimation and concentration inequalities of continuous-time martingales.
result Provides a non-asymptotic confidence set for uncertainty quantification.
Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes, the occurrence of an event in one process affects the probability of occurrence…
Develops quasi-likelihood analysis for marked point processes and applies it to Hawkes processes.
problem Analyzing multivariate marked point processes and their applications.
method Quasi-likelihood analysis for a general class of multivariate marked point processes, with focus on marked Hawkes processes.
result The quasi-likelihood analysis for marked Hawkes processes provides explicit conditions for ergodicity and Markovian transformation.
Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems. Given a calibrated Hawkes process, of concern is the statistical fit to empirical data, particularly for the accurate quantification of self- and mutual-exc…
New model predicts network events better than existing ones.
problem Existing models can't capture complex network structures.
method Proposed MULCH model using multivariate Hawkes processes.
result MULCH model outperforms other models in predictions and generation.
Extends QHawkes to MQHawkes for analyzing financial co-jumps.
problem Capturing endogenous co-jumps in financial markets.
method Develops MQHawkes process with quadratic kernels, investigates stationarity, and derives Yule-Walker equations.
result Volatility distribution exhibits power-law behavior with computable exponents.
A new metric space model for point process excitations uncovers hidden interactions.
problem Estimating pairwise interactions in multivariate Hawkes processes is often infeasible.
method Developed a Hidden Hawkes Geometry (HHG) model to embed event types in a metric space.
result Learning the embedding reveals salient interactions in various applications.
Estimates neuronal connectivity from spike times using flexible Hawkes processes.
problem Learning latent network structure from multivariate point process data.
method Proposes a new nonstationary Hawkes process and uses sparse least squares estimation.
result Establishes non-asymptotic error bounds and selection consistency for estimated parameters.
Modeling multiple Hawkes processes with shared dynamics using graphons.
problem Modeling multiple multivariate point processes with shared dynamics.
method Leverage graphons to model an uncountable event type space, learn graphon-based Hawkes process model by minimizing hierarchical optimal transport distance.
result Infer underlying relations and simulate event sequences with similar dynamics.
Extends Hawkes process for flexible residual modeling in point processes.
problem Modeling high-frequency financial data with complex residual distributions.
method Introduces self and mutually exciting point process with discretely Markovian dynamics.
result Flexible residual distributions improve intensity modeling and high-frequency data estimation.
In this paper we propose an overview of the recent academic literature devoted to the applications of Hawkes processes in finance. Hawkes processes constitute a particular class of multivariate point processes that has become very popular in empirical high frequency finance this last decade. After a reminder of the mai…
Study uses Hawkes processes to analyze stock market contagion in China.
problem Understanding contagion in Chinese stock market.
method Fitting Hawkes processes to daily returns and sector indices.
result Identifies long-term dependencies and trending patterns in sector indices.
Framework simulates market microstructure with stable Hawkes processes.
problem Reproduce realistic market order flow dynamics.
method Deterministic C++ LOB simulator with Hawkes-driven stochastic order flow.
result Derives stability and ergodicity proofs for Hawkes models.
We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation f…
Proposes online learning for Hawkes processes with network structure and event interaction.
problem Modeling complex interactions and latent structures in network events.
method Online learning approach for mixture of multivariate Hawkes processes.
result Efficacy demonstrated on synthetic and real-world data.
In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems both in the number of events in the observed history n and the number of event types d (i.e. dimensions). The proposed Low-Rank Hawkes Process (LRHP) framework introduces a low-rank approximation of the kernel m…
New model scales MHPs for analyzing large-scale diffusion processes.
problem Complex temporal dependencies in MHPs make them hard to scale.
method Exploits sparsity in diffusion processes to compute MHP likelihood and gradients efficiently.
result Improves runtime performance by multiple orders of magnitude on sparse event sequences.
A new parallel algorithm speeds up Hawkes process estimation.
problem Slow maximum likelihood estimation for Hawkes processes.
method Parallel prefix scan for sparse transition matrices.
result Massive speedup with O(N/P) complexity. New scalable variational Bayes methods for Hawkes processes.
problem Computational intractability of Bayesian estimation for generalised nonlinear Hawkes processes.
method Unified variational Bayes framework, adaptive mean-field approximation, sparsity-inducing procedure.
result Adaptive mean-field variational algorithm for sigmoid Hawkes processes is scalable and robust.
Deep RL controller outperforms market making benchmarks in a Hawkes process model.
problem Optimal market making in financial markets.
method Deep reinforcement learning on a Hawkes process-based simulator.
result Deep RL controller outperforms benchmarks in various risk-reward metrics.
Graph Hawkes Neural Network forecasts evolving graph sequences.
problem Modeling dynamic graph sequences with complex event types.
method Generalized Hawkes process to neural network, capturing complex event impacts.
result Effective at predicting future events in evolving graph sequences.
Proposes SAHP for better Hawkes process modeling.
problem Predicting occurrence patterns of event sequences.
method Leverages self-attention to modify Hawkes process intensity function.
result Demonstrates effectiveness on real-world datasets.
We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy (2015) can be successfully used to study complex interactions between the time of arrival of orders and their size, observed in a limit order book market. We apply this methodology to high-fre…
In this paper, we design a nonparametric online algorithm for estimating the triggering functions of multivariate Hawkes processes. Unlike parametric estimation, where evolutionary dynamics can be exploited for fast computation of the gradient, and unlike typical function learning, where representer theorem is readily …
New statistical inference method for high-dimensional Hawkes processes.
problem Uncertainty evaluation of network estimates in high-dimensional point process data.
method Develops a new statistical inference procedure using concentration inequalities and martingale central limit theory.
result Characterizes the convergence rate of test statistics for high-dimensional Hawkes processes.
Modeling high-frequency order book data with Hawkes-Markovian process.
problem Capturing the dynamics of high-frequency order book events.
method Hawkes process with Markovian baseline intensities, LASSO regularization, and Akaike Information Criteria.
result Effective modeling of order book dynamics with reduced parameter redundancy.
Modeling delayed Granger causality in Hawkes processes.
problem Capturing the time lag between causal events in multivariate Hawkes processes.
method Proposed a Hawkes process model with latent time lags, using Variational Auto-Encoder (VAE) for inference.
result Identified and inferred time lags with posterior distributions, improving event prediction and root cause analysis.
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequentl…
Paper uncovers causal structures in Hawkes processes with latent subprocesses.
problem Tackles latent subprocesses in Hawkes processes with complex event-driven interactions.
method Proposes a two-phase iterative algorithm that infers causal relationships and identifies latent subprocesses.
result Successfully recovers causal structures in datasets with latent subprocesses.
We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an …
New models explain multidimensional rough volatility from microscopic price dynamics.
problem Designing new rough stochastic volatility models for multi-asset scenarios.
method Using Hawkes processes to model microstructural interactions and investigate scaling limits.
result Multivariate rough volatility models arise naturally from microscopic price dynamics.
New algorithm optimizes Hawkes process models with short data.
problem Learning causal-interaction networks from short Hawkes process sequences.
method Variational Expectation-Maximization algorithm with extended hyper-parameters and posterior learning.
result Significantly outperforms state-of-the-art methods under short observation sequences.
We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, test…
There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work o…
New model for clustering dependent community Hawkes processes in temporal networks.
problem Modeling strong dependence and community structure in temporal networks.
method Dependent Community Hawkes (DCH) models combining stochastic block models and Hawkes processes.
result Spectral clustering error bound derived for DCH models.
Study optimizes investment strategies in markets with contagious price jumps.
problem Optimizing portfolios in financial markets with contagious price jumps.
method Applied stochastic maximum principle, backward stochastic differential equations, and linear-quadratic control techniques.
result Obtained efficient strategy and efficient frontier in semi-closed form.
The paper develops a new model for order book dynamics using Hawkes processes.
problem Capturing the dynamics of order flow and liquidity migration in financial markets.
method Develops a mesoscopic model using Hawkes processes to describe interactions between order arrivals, cancellations, and liquidity movement.
result Derives a diffusive limit for the order book dynamics, providing a unified framework for market microstructure.
Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of high frequency cojumps. We show that the dynamics of these jumps is described neither …