Related papers: Spectral estimation of Hawkes processes from count…
Penalised estimation methods for point processes usually rely on a large amount of independent repetitions for cross-validation purposes. However, in the case of a single realisation of the process, existing cross-validation methods may be…
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…
Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences.…
In this paper, we consider the Whittle estimator for the parameters of a stationary solution of a continuous-time linear state space model sampled at low frequencies. In our context the driving process is a L\'evy process which allows…
This paper introduces the Hawkes skeleton and the Hawkes graph. These objects summarize the branching structure of a multivariate Hawkes point process in a compact, yet meaningful way. We demonstrate how graph-theoretic vocabulary…
We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…
The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time…
Driven by the recent surge in neural-inspired modeling, point processes have gained significant traction in systems and control. While the Hawkes process is the standard model for characterizing random event sequences with memory,…
We develop a Bayesian nonparametric framework for inference in spatio-temporal Hawkes processes, extending existing theoretical results beyond the purely temporal setting. Our framework encompasses modelling both the background and…
Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the…
As a tool for capturing irregular temporal dependencies (rather than resorting to binning temporal observations to construct time series), Hawkes processes with exponential decay have seen widespread adoption across many application…
Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…
The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due…
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…
This paper proposes a new estimation technique for fitting parametric Gibbs point process models to a spatial point pattern dataset. The technique is a counterpart, for spatial point processes, of the variational estimators for Markov…
We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit…
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, $X$…