Related papers: A Hawkes model with CARMA(p,q) intensity
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…
A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical…
We provide probabilistic and computational results on Markovian multivariate Hawkes processes and induced population processes. By applying the Markov property, we characterize in closed form a joint transform, bijective to the probability…
Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…
We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the…
An extension of the Hawkes model where the productivity is variable is considered. In particular, the case is considered where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood…
Continuous-time autoregressive moving average (CARMA) process driven by simple semi-L\'evy process has periodically correlated property with many potential application in finance. In this paper, we study on the estimation of the parameters…
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…
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…
In this paper, we use the Hawkes process to model the sequence of failure, i.e., events of compressor station and conduct survival analysis on various failure events of the compressor station. However, until now, nearly all relevant…
Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where…
Multivariate Hawkes processes (MHP) are a class of point processes in which events at different coordinates interact through mutual excitation. The weighted adjacency matrix of the MHP encodes the strength of the relations, and shares its…
We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the…
This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with…
This paper addresses nonparametric estimation of nonlinear multivariate Hawkes processes, where the interaction functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). Motivated by applications in neuroscience, the model…
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…
We revisit the proof of the limiting free energy of the continuous random energy model (CREM) using the Hamilton--Jacobi approach for mean-field disordered systems. To achieve this, we introduce an enriched model that interpolates between…
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 consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists…
We consider the learning of multi-agent Hawkes processes, a model containing multiple Hawkes processes with shared endogenous impact functions and different exogenous intensities. In the framework of stochastic maximum likelihood…