Related papers: Graphical Modeling for Multivariate Hawkes Process…

In this paper, we introduce different concepts of Granger causality and contemporaneous correlation for multivariate stationary continuous-time processes to model different dependencies between the component processes. Several equivalent…

When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based…

The neural Hawkes process (Mei & Eisner, 2017) is a generative model of irregularly spaced sequences of discrete events. To handle complex domains with many event types, Mei et al. (2020a) further consider a setting in which each event in…

Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. In this paper, we obtain a functional…

Marked Temporal Point Processes (MTPPs) arise naturally in medical, social, commercial, and financial domains. However, existing Transformer-based methods mostly inject temporal information only via positional encodings, relying on shared…

In this paper we propose an overview of the recent academic literature devoted to the applications of Hawkes processes in finance. Hawkes processes constitute a particular class of multivariate point processes that has become very popular…

We introduce a point process regression model that is applicable to price models and limit order book models. Hawkes type autoregression in the intensity process is generalized to a stochastic regression to covariate processes. We establish…

We adopt the interpretability offered by a parametric, Hawkes-process-inspired conditional probability mass function for the marks and apply variational inference techniques to derive a general and scalable inferential framework for marked…

Causal discovery from time-series data has been a central task in machine learning. Recently, Granger causality inference is gaining momentum due to its good explainability and high compatibility with emerging deep neural networks. However,…

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…

The dependencies of the lagged (Pearson) correlation function on the coefficients of multivariate autoregressive models are interpreted in the framework of time series graphs. Time series graphs are related to the concept of Granger…

Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high-dimensional…

We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by…

We consider a nonlinear multivariate Hawkes process having a variable length memory which allows to describe the activity of a neuronal network by its membrane potential. We propose a graphical construction of the process and we construct,…

We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying…

A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process…

In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to…

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…

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…

In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the…