Related papers: A Multidimensional Fractional Hawkes Process for M…
Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events.…
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…
Hawkes process models are used in settings where past events increase the likelihood of future events occurring. Many applications record events as counts on a regular grid, yet discrete-time Hawkes models remain comparatively underused and…
The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…
We consider oscillatory systems of interacting Hawkes processes introduced in Ditlevsen and Loecherbach (2017) to model multi-class systems of interacting neurons together with the diffusion approximations of their intensity processes. This…
The Hawkes process has become a standard method for modeling self-exciting event sequences with different event types. A recent work has generalized the Hawkes process to a neurally self-modulating multivariate point process, which enables…
We present a new method of data clustering applied to earthquake catalogs, with the goal of reconstructing the seismically active part of fault networks. We first use an original method to separate clustered events from uncorrelated…
Earthquake aftershock identification is closely related to the question "Are aftershocks different from the rest of earthquakes?" We give a positive answer to this question and introduce a general statistical procedure for clustering…
Many point process models have been proposed for describing and forecasting earthquake occurrences in seismically active zones such as California, but the problem of how best to compare and evaluate the goodness of fit of such models…
Declustering aims to divide earthquake catalogs into independent events (mainshocks), and dependent (clustered) events, and is an integral component of many seismicity studies, including seismic hazard assessment. We assess the effect of…
We propose a new method to test the effectiveness of a spatial point process forecast based on a log-likelihood score for predicted point density and the information gain for events that actually occurred in the test period. The method…
Analysis of gun violence in the United States has utilized various models based on spatiotemporal point processes. Previous studies have identified a contagion effect in gun violence, characterized by bursts of diffusion across urban…
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.…
We propose two methods to calibrate the parameters of the epidemic-type aftershock sequence (ETAS) model based on expectation maximization (EM) while accounting for temporal variation of catalog completeness. The first method allows for…
The spatio-temporal Epidemic Type Aftershock Sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we…
The existence of magnitude dependence in earthquake triggering has been reported. Such a correlation is linked to the issue of seismic predictability and remains under intense debate whether it is physical or is caused by incomplete data…
Temporal networks observed continuously over time through timestamped relational events data are commonly encountered in application settings including online social media communications, financial transactions, and international relations.…
We modify ETAS models by replacing the Pareto-like kernel proposed by Ogata with a Mittag-Leffler type kernel. Provided that the kernel decays as a power law with exponent $\beta + 1 \in (1,2]$, this replacement has the advantage that the…
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…
We consider the stochastic volatility model obtained by adding a compound Hawkes process to the volatility of the well-known Heston model. A Hawkes process is a self-exciting counting process with many applications in mathematical finance,…