Related papers: A Multidimensional Fractional Hawkes Process for M…
We develop flexible multivariate spatio-temporal Hawkes process models to analyze patterns of terrorism. Previous applications of point process methods to political violence data mainly utilize temporal Hawkes process models, neglecting…
Hawkes process (HP) is a point process with a conditionally dependent intensity function. This paper defines the tempered fractional Hawkes process (TFHP) by time-changing the HP with an inverse tempered stable subordinator. We obtained…
The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
This study examine the theoretical and empirical perspectives of the symmetric Hawkes model of the price tick structure. Combined with the maximum likelihood estimation, the model provides a proper method of volatility estimation…
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…
Foundational marked temporal point process (MTPP) models, such as the Hawkes process, often use inexpressive model families in order to offer interpretable parameterizations of event data. On the other hand, neural MTPPs models forego this…
We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…
The Hawkes process (HP) is commonly used to model event sequences with self-reinforcing dynamics, including electronic health records (EHRs). Traditional HPs capture self-reinforcement via parametric impact functions that can be inspected…
Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…
We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which…
We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic…
We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution…
Across a wide variety of applications, the self-exciting Hawkes process has been used to model phenomena in which the history of events influences future occurrences. However, there may be many situations in which the past events only…
Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous…
Earthquakes and aftershock sequences follow several empirical scaling laws: One of these laws is Bath's law for the magnitude of the largest aftershock. In this work, Modified Form of Bath's Law and its application to KOERI data have been…
Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences.…
This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit…
We present a stability study of the class of multivariate self-excited Hawkes point processes, that can model natural and social systems, including earthquakes, epileptic seizures and the dynamics of neuron assemblies, bursts of exchanges…
The Himalayan region, including Nepal, is prone to frequent and large earthquakes. Accurate forecasting of these earthquakes is crucial for minimizing loss of life and damage to infrastructure. In this study, we propose various time-scaled…