In order to disentangle the internal dynamics from exogenous factors within the Autoregressive Conditional Duration (ACD) model, we present an effective measure of endogeneity. Inspired from the Hawkes model, this measure is defined as the average fraction of events that are triggered due to internal feedback mechanism…
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48 results for “Fractional Hawkes Process”
NeuroMem-FHP framework estimates FHP parameters efficiently.
problem Estimating parameters of fractional Hawkes process (FHP) with long-range dependence.
method Developed LSTM and Transformer neural architectures to estimate FHP parameters directly from inter-arrival times.
result Transformer achieves highest estimation accuracy (MSE = 0.1634) compared to classical MLE (MSE = 2.8032).
Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processesmath.PR
We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has norm close to one and power law tail of the form , with . We in particular prove that when , after suitable rescaling, their law converges to that of a kind of integr…
The study examines insurance demand under rough volatility and path-dependent shocks.
problem Optimal insurance and investment strategies under rough volatility and path-dependent shocks.
method Rough volatility model and Hawkes process with power kernel, Functional Ito formula extension.
result Individuals demand more catastrophe insurance when path-dependent effects are considered.
Calibrates Hawkes models for market events, revealing power-law feedback kernels.
problem Estimating the influence of past events and price changes on future market events.
method Proposes a calibration procedure for Quadratic Hawkes models, analyzing the kernel components.
result Empirically calibrated kernel components reveal power-law behavior, suggesting system near critical point.
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Br…
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.
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.
We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \cite{doetei:10}). We introduce in particular Volterra Wishart processes with fractional kernels and values in the con…
Study models market volatility with persistent and temporary impacts.
problem Microstructure of rough volatility models driven by Poisson measures.
method Existence and uniqueness of solutions for stochastic path-dependent Volterra equations.
result Volatility process converges to fractional Heston model with spikes.
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external perturbation to the system. In this paper we propose a novel procedure for the detection…
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 Processcs.LG
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.
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.
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 Processesmath.PR
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.
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…
Exact asymptotic solutions to nonlinear Hawkes processes: a systematic classification of the steady-state solutionscond-mat.stat-mech
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 , with as a function of parameters.
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 complexity.
Proposes a new jump-diffusion model for option pricing.
problem Capturing self-excitation and contagion effects in option pricing models.
method Combines Heston and Queue-Hawkes models with closed-form characteristic function.
result Reduces computational complexity and offers better volatility smile fitting.
In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Util…
Paper presents a method for estimating Hawkes process parameters.
problem Estimating parameters of Hawkes processes with self-excitation or inhibition.
method Maximum likelihood estimation for Hawkes processes with self-excitation or inhibition.
result The proposed estimator provides more accurate estimations in the inhibition context.
In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regards to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for seve…
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.
As a powerful tool of asynchronous event sequence analysis, point processes have been studied for a long time and achieved numerous successes in different fields. Among various point process models, Hawkes process and its variants attract many researchers in statistics and computer science these years because they capt…
New model prices options with complex market data structures.
problem Complex market data structures in option pricing.
method Compound CARMA(p,q)-Hawkes model.
result Model can replicate volatility smile in financial markets.
This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of age pyramid which evolves according to immigration and births. The virtue if t…
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 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.
Unified model explains market dynamics, linking order flow, volatility, and impact.
problem Understanding the dynamics of order flow, market impact, and volatility in financial markets.
method Proposes a microstructural model using Hawkes processes to distinguish core orders and reaction flow, and analyzes their scaling limits.
result Estimates the persistence parameter and finds it consistent with market impact and volatility properties.
Study shows how heavy-tailed Hawkes processes can model rough volatility in financial markets.
problem Modeling rough volatility in financial markets with heavy-tailed Hawkes processes.
method Established weak convergence of Hawkes process with power-law kernel, derived scaling limit for financial market model.
result Price-volatility process converges weakly to a rough Heston model after rescaling.
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.
This paper explores neural models to improve modeling of Hawkes process intensity functions.
problem Traditional Hawkes process intensity function's parametrized kernel function biases future event predictions.
method Uses neural models to model the kernel function of Hawkes process intensity function.
result Neural models can better capture future event characteristics using past events data.
Model detects market anomalies using a Hawkes process with hidden Markov chain.
problem Detecting high-frequency market manipulation in cryptocurrency trades.
method Developed a Markov-modulated Hawkes process with piecewise constant excitation kernels.
result Demonstrated the model's effectiveness in detecting suspicious trading activities.
This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point processes. We then introduce the Hawkes process, its event intensity function, as…
NNNH uses neural networks to model complex event patterns.
problem Analyzing multi-dimensional nonlinear Hawkes processes with mutual excitation and inhibition.
method NNNH employs feedforward neural networks to model individual kernels and base intensity, optimizing parameters via Stochastic Gradient Descent.
result NNNH accurately captures complexities of nonlinear Hawkes processes, as demonstrated by numerical experiments.
Researchers prove a new measure for a financial volatility model.
problem Modeling financial volatility with a Hawkes process.
method Prove existence of equivalent martingale measures for a Heston-Hawkes model.
result Existence of a family of equivalent martingale measures for the model.