Related papers: Discretization of Self-Exciting Peaks Over Thresho…
In the last decade, Hawkes processes have received a lot of attention as good models for functional connectivity in neural spiking networks. In this paper we consider a variant of this process, the Age Dependent Hawkes process, which…
Classic estimation methods for Hawkes processes rely on the assumption that observed event times are indeed a realisation of a Hawkes process, without considering any potential perturbation of the model. However, in practice, observations…
Generalized autoregressive conditionally heteroskedastic (GARCH) processes are widely used for modelling features commonly found in observed financial returns. The extremal properties of these processes are of considerable interest for…
This study examines the use of a recurrent neural network for estimating the parameters of a Hawkes model based on high-frequency financial data, and subsequently, for computing volatility. Neural networks have shown promising results in…
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…
We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics…
Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
A new integer--valued autoregressive process (INAR) with Generalised Lagrangian Katz (GLK) innovations is defined. This process family provides a flexible modelling framework for count data, allowing for under and over--dispersion,…
Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help…
A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical…
We study large time behavior of critical marked Hawkes processes and related branching particle systems. In case of marked Hawkes processes we assume that the kernel function has multiplicative form and the marks corresponding to the events…
A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history…
We revisit the task of computing the span of the top $r$ singular vectors $u_1, \ldots, u_r$ of a matrix under differential privacy. We show that a simple and efficient algorithm -- based on singular value decomposition and standard…
A point process is R-dependent, if it behaves independently beyond the minimum distance R. This work investigates uniform positive lower bounds on the avoidance functions of R-dependent simple point processes with a common intensity.…
This paper investigates the asymptotic behavior of suitably time-modulated Hawkes processes with heavy-tailed kernels in a nearly unstable regime. We show that, under appropriate scaling, both the intensity processes and the rescaled Hawkes…
Hawkes Processes are a type of point process for modeling self-excitation, i.e., when the occurrence of an event makes future events more likely to occur. The corresponding self-triggering function of this type of process may be inferred…
The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…
We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…
Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…