Related papers: Hawkes and INAR($\infty$) processes

Due to its clustering and self-exciting properties, the Hawkes process has been used extensively in numerous fields ranging from sismology to finance. Since data is often aquired on regular time intervals, we propose a piece-wise constant…

This article introduces the GNAR package, which fits, predicts, and simulates from a powerful new class of generalised network autoregressive processes. Such processes consist of a multivariate time series along with a real, or inferred,…

In this paper we introduce a new model named CARMA(p,q)-Hawkes process as the Hawkes model with exponential kernel implies a strictly decreasing behaviour of the autocorrelation function and empirically evidences reject the monotonicity…

The marked Hawkes risk process is a compound point process for which the occurrence and amplitude of past events impact the future. Thanks to its autoregressive properties, it found applications in various fields such as neuosciences,…

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…

Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger causality structure of such processes is fully encoded in…

INAR (integer-valued autoregressive) and INGARCH (integer-valued GARCH) models are among the most commonly employed approaches for count time series modelling, but have been studied in largely distinct strands of literature. In this paper,…

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification.…

Asynchronous events sequences are widely distributed in the natural world and human activities, such as earthquakes records, users activities in social media and so on. How to distill the information from these seemingly disorganized data…

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…

We aim to explicitly model the delayed Granger causal effects based on multivariate Hawkes processes. The idea is inspired by the fact that a causal event usually takes some time to exert an effect. Studying this time lag itself is of…

In the last decade Hawkes processes have received much attention as models for functional connectivity in neural spiking networks and other dynamical systems with a cascade behavior. In this paper we establish a renewal approach for…

Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed…

In a discrete-time setting, we consider an arrival process $\left\{\xi_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots…

Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes --- Hawkes process. We…

We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for…

In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of this paper is to deal with an infinite number of components.…

We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that…

An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound…

We consider a sequence of Hawkes processes whose excitation measures may depend on the generation, and study its scaling limits in the near-unstable limiting regime. The limiting random measures, characterized via a nonlinear convolutional…