相关论文: Discretization of Self-Exciting Peaks Over Thresho…

Point process models are widely used for continuous asynchronous event data, where each data point includes time and additional information called "marks", which can be locations, nodes, or event types. This paper presents a novel point…

We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In…

In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs, the intensity increases and we expect more jumps to come.…

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…

It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the…

The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its…

Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical…

The Hawkes model is a past-dependent point process, widely used in various fields for modeling temporal clustering of events. Extending this framework, the multidimensional marked Hawkes process incorporates multiple interacting event types…

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…

We study the behavior of a real-valued and unobservable process (Y_t) under an extreme event of a related process (X_t) that is observable. Our analysis is motivated by the well-known GARCH model which represents two such sequences, i.e.…

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…

We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self…

Over the past few decades, the Hawkes process has become a popular framework for modeling temporal events thanks to its flexibility to capture different dependency structures. The objective of this work is to model call sequences emitted by…

The Epps effect is key phenomenology relating to high frequency correlation dynamics in financial markets. We argue that it can be used to provide insight into whether tick data is best represented as samples from Brownian diffusions, or as…

We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval $[0,T]$ in the limit $T \rightarrow \infty$. We further exhibit the asymptotic behaviour of the…

The Hawkes process is a versatile stochastic model for point patterns that exhibit self-excitation, that is, the property that an event occurrence increases the rate of occurrence for some period of time in the future. We present a Bayesian…

A self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p,q)-Hawkes model, has recently been introduced. The model generalizes the Hawkes process by substituting the…

Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that…

We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given…