Methodology for estimating marked Hawkes processes with neural networks.
problem Estimating conditional intensity of marked Hawkes processes.
method Proposes two models: Shallow Neural Hawkes with marks and Neural Network for Non-Linear Hawkes with Marks.
result Validation on synthetic datasets and real-world cryptocurrency order book data.
We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and a…
Study applies Hawkes volatility to mid-price process for real-time risk management.
problem Lack of studies on Hawkes volatility for tick-level price dynamics.
method Derived variance formula for unmarked and marked Hawkes models, applied to mid-price process.
result Reliable results and high predictive power of intraday Hawkes volatility.
We develop a quasi-likelihood analysis procedure for a general class of multivariate marked point processes. As a by-product of the general method, we establish under stability and ergodicity conditions the local asymptotic normality of the quasi-log likelihood, along with the convergence of moments of quasi-likelihood…
Exact asymptotic solutions found for nonlinear Hawkes processes.
problem Analytical solutions for nonlinear Hawkes processes with positive and negative feedbacks.
method Field master equation approach to classify steady-state solutions.
result Explicit power law formulas for steady-state intensity distributions Pss(λ)∝λ−1−a, with a as a function of parameters. A simple Hawkes model have been developed for the price tick structure dynamics incorporating market microstructure noise and trade clustering. In this paper, the model is extended with random mark to deal with more realistic price tick structures of equities. We examine the impact of jump in price dynamics to the futu…
Modeling intraday electricity prices with a Hawkes process.
problem Capturing the dynamics of intraday electricity prices, especially microstructure noise.
method 2D marked Hawkes process with increasing baseline intensity, providing analytic moments and signature plot.
result The model fits German intraday electricity data well and converges to a Brownian motion with increasing volatility.
Framework handles both exchangeable and non-exchangeable event sequences without tuning.
problem Handling both exchangeable and non-exchangeable event sequences efficiently.
method Parametric Hawkes-process-inspired conditional probability mass function with variational inference.
result Competitive computational and predictive performance against state-of-the-art methods.
New MTPP model offers interpretable predictions with state-of-the-art performance.
problem Inexpressive models lack interpretability, while neural models sacrifice interpretability for performance.
method Extends Hawkes process to a hypernetwork with a latent space, making it flexible and interpretable.
result Achieves state-of-the-art performance across various tasks and metrics.
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.
UNHaP removes noise from physiological events using Hawkes processes.
problem Challenges in identifying true events from spurious ones in physiological signal analysis.
method UNHaP uses marked Hawkes processes to distinguish and unmix true events from noise.
result UNHaP significantly reduces false detection rates and enhances event understanding.
Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-e…
Paper improves neural interaction modeling using nonlinear Hawkes processes.
problem Inability of classic Hawkes process to model inhibitory interactions.
method Augmented auxiliary latent variables and EM algorithm for efficient inference.
result Demonstrates accurate and efficient estimation of neural interaction dynamics.
New mechanism found for power laws including Zipf's law.
problem Understanding the ubiquity of power law distributions.
method Introduced nonlinear self-excited Hawkes processes with fast-accelerating intensities.
result Wide class of nonlinear Hawkes processes have power law intensity PDFs.
In this paper, we consider the sigmoid Gaussian Hawkes process model: the baseline intensity and triggering kernel of Hawkes process are both modeled as the sigmoid transformation of random trajectories drawn from Gaussian processes (GP). By introducing auxiliary latent random variables (branching structure, Pólya-Gamm…
We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying intensities. We demonstrate that inter-arrival times can be decomposed into simpler…
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…
This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline intensity, a state-dependent component specific to each process, and a state-dependent …
Neural Hawkes method estimates cryptocurrency market microstructure and causality.
problem Estimating non-parametric Hawkes processes in high dimensions.
method Physics-informed neural networks for solving integral equations.
result Robust estimation of Hawkes processes in high dimensions.
Paper introduces a neural network-based non-stationary influence kernel for complex event data.
problem Modeling complex, non-stationary, and dependent discrete event data.
method Neural Spectral Marked Point Processes (NSMPP) with a versatile non-stationary influence kernel.
result NSMPP outperforms state-of-the-art models on synthetic and real data.
It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence o…
S2P2 model improves predictive likelihoods for MTPPs.
problem Modeling irregular time intervals in event sequences.
method State-space point process model using deep state-space techniques.
result Empirically, S2P2 achieves state-of-the-art predictive likelihoods.
Understanding the diffusion in social network is an important task. However, this task is challenging since (1) the network structure is usually hidden with only observations of events like "post" or "repost" associated with each node, and (2) the interactions between nodes encompass multiple distinct patterns which in…
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 …
Modeling coating degradation with fewer data points.
problem Efficiently forecasting material degradation from high-frequency sensor data.
method Discrete degradation events using Hawkes processes.
result Forecasting future coating failure with superior performance.
New model uses variance-Hawkes process to fit energy market returns.
problem Modeling clustering effects in financial markets.
method Defining and fitting a variance-Hawkes process to energy market returns.
result Demonstrated that variance-Hawkes process can capture clustering effects.
Study optimal liquidation strategies under partial information in high-frequency trading.
problem Optimal liquidation strategies in high-frequency trading with incomplete information.
method Modeling price formation through Hawkes processes, incorporating liquidity as a hidden Markov process, and formulating as an impulse control problem.
result Development of an algorithm to approximate optimal liquidation strategies.
Crimes emerge out of complex interactions of human behaviors and situations. Linkages between crime incidents are highly complex. Detecting crime linkage given a set of incidents is a highly challenging task since we only have limited information, including text descriptions, incident times, and locations. In practice,…
Modeling social network activity through user and topic interaction.
problem Understanding complex dynamics of opinion formation in social networks.
method Mixture of Interacting Cascades (MIC) model of marked multidimensional Hawkes processes.
result MIC achieves superior performance in modeling information cascade spread.
The study examines Hawkes processes and their long-term behavior.
problem Understanding the long-term behavior of Hawkes processes.
method Proving functional limit theorems under various conditions on the dispersion of child events.
result Functional limit theorems hold for Hawkes processes with different levels of child event dispersion.
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…
Mamba Hawkes Process improves modeling of event sequences with long-term dependencies.
problem Modeling mutual inhibition and nonlinearity in asynchronous event sequences.
method Introduces Mamba Hawkes Process using Mamba state space architecture.
result MHP outperforms existing models across various datasets.
Flexible nonlinear Hawkes processes for time-varying systems.
problem Limited expressive ability of classic Hawkes processes.
method Flexible state-switching Hawkes processes with latent variable augmentation for Bayesian inference.
result Superior performance compared to state-of-the-art competitors.
Proposes first privacy-preserving method for estimating Hawkes processes.
problem Estimating point process models with sensitive personal data raises privacy concerns.
method Proposes differential privacy for event stream data and two optimization algorithms.
result Efficiently estimates Hawkes process models with privacy and utility guarantees.
New method detects market liquidity changes using order book data.
problem Detecting changes in market liquidity.
method Marked Hawkes processes and minimax quickest detection problem for doubly-stochastic Poisson process.
result Optimal stopping rule for detecting intensity changes in market liquidity.
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.
Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where the baseline intensity is time-dependent, the exciting function is a general funct…
New findings allow infinite mean intensity Hawkes processes to be stable.
problem Stability condition for Hawkes processes with infinite mean intensity.
method Analysis of Quadratic Hawkes processes with infinite mean intensity.
result Quadratic Hawkes processes are always stationary with infinite mean intensity when total endogeneity ratio exceeds unity.
New Hawkes processes model spatiotemporal events with triggering and clustering.
problem Modeling self-excitatory behavior in spatiotemporal data.
method Developed a new class of spatiotemporal Hawkes processes with efficient inference method.
result Efficiently modeled and inferred spatiotemporal events with triggering and clustering.
Paper proposes a neural network for non-parametric Hawkes process kernel estimation.
problem Estimating non-parametric Hawkes process kernels efficiently and interpretably.
method Single hidden layer neural network for unbiased log-likelihood estimation of Hawkes processes.
result Proposed neural network achieves comparable or better performance than existing methods.
The paper studies Hawkes processes under mean-field limits and criticality conditions.
problem Analyzing nearly unstable Hawkes processes in a mean-field regime.
method Extending the method by Jaisson and Rosenbaum, establishing scaling limits and propagation of chaos.
result Scaling limits of Hawkes processes are stochastic Volterra diffusions of affine type, with three distinct limiting regimes.
Hawkes processes are a particularly interesting class of stochastic process that have been applied in diverse areas, from earthquake modelling to financial analysis. They are point processes whose defining characteristic is that they 'self-excite', meaning that each arrival increases the rate of future arrivals for som…
Study differentially private methods for learning Hawkes processes.
problem Lack of thorough analysis on sample complexity for learning Hawkes processes parameters and releasing differentially private versions.
method Developed non-private and differentially private estimators for Hawkes processes parameters.
result Obtained sample complexity results for both private and non-private settings.
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they are affected by jumps. To this end, we introduce Neural Jump Stochastic Different…
We propose a novel fused Gromov-Wasserstein alignment method to jointly learn the Hawkes processes in different event spaces, and align their event types. Given two Hawkes processes, we use fused Gromov-Wasserstein discrepancy to measure their dissimilarity, which considers both the Wasserstein discrepancy based on the…
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.
Introduces a new Hawkes model with CARMA(p,q) intensity to better model dependence structures.
problem Modeling dependence structures in time series data with realistic autocorrelation functions.
method Develops a Hawkes process with CARMA(p,q) intensity to capture more complex dependencies.
result The CARMA(p,q)-Hawkes model can reproduce more realistic dependence structures and is stationary and positive.
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.