Related papers: A Hawkes model with CARMA(p,q) intensity
The Hawkes process is a class of point processes whose future depends on their own history. Previous theoretical work on the Hawkes process is limited to a special case in which a past event can only increase the occurrence of future…
Interest in continuous-time processes has increased rapidly in recent years, largely because of high-frequency data available in many applications. We develop a method for estimating the kernel function $g$ of a second-order stationary…
This study explores the application of Hawkes processes to model high-frequency data in the context of limit order books. Two distinct Hawkes-based models are proposed and analyzed: one utilizing exponential kernels and the other employing…
Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which typeof events…
An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive…
We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with…
Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience, social networks,…
Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for…
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…
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…
We investigate the nonparametric estimation problem of the density $\pi$, representing the stationary distribution of a two-dimensional system $\left(Z_t\right)_{t \in[0, T]}=\left(X_t, \lambda_t\right)_{t \in[0, T]}$. In this system, $X$…
We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter…
Human behavior drives a range of complex social, urban, and economic systems, yet understanding its structure and dynamics at the individual level remains an open question. From credit card transactions to communications data, human…
In this paper, we introduce a new class of processes which are diffusions with jumps driven by a multivariate nonlinear Hawkes process. Our goal is to study their long-time behavior. In the case of exponential memory kernels for the…
We present a modified version of the non parametric Hawkes kernel estimation procedure studied in arXiv:1401.0903 that is adapted to slowly decreasing kernels. We show on numerical simulations involving a reasonable number of events that…
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…
In this paper we show how to approximate the transition density of a CARMA(p, q) model driven by means of a time changed Brownian Motion based on the Gauss-Laguerre quadrature. We then provide an analytical formula for option prices when…
Multivariate Hawkes processes are past-dependant point processes originally introduced to model excitation effects, later extended to a nonlinear framework to account for the opposite effect, known as inhibition. Motivated by applications…
Existence and stability properties are studied for Hawkes process, i.e. point process $S$ that has long-memory and intensity $r(t)=\lambda \big(g_0(t)+ \sum_{\tau<t, \tau \in S} h(t-\tau) \big)$. The approach to Hawkes process presented in…