Related papers: Hawkes Processes with Variable Length Memory: Exis…
The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these…
A temporal point process is a stochastic process that predicts which type of events is likely to happen and when the event will occur given a history of a sequence of events. There are various examples of occurrence dynamics in the daily…
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…
In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show…
In a discrete-time setting, we consider an arrival process $\left\{\xi_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots…
Previous work has shown that popular trending events are important external factors which pose significant influence on user search behavior and also provided a way to computationally model this influence. However, their problem formulation…
Learning causal structure among event types on multi-type event sequences is an important but challenging task. Existing methods, such as the Multivariate Hawkes processes, mostly assumed that each sequence is independent and identically…
Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…
Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…
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…
Hawkes processes are point processes with self-exciting and clustering properties that are popular in applications. In recent years, renewal Hawkes processes have gained attention, due to their versatility such as the capability of…
Modeling event dynamics is central to many disciplines. Patterns in observed event arrival times are commonly modeled using point processes. Such event arrival data often exhibits self-exciting, heterogeneous and sporadic trends, which is…
Hawkes processes are a class of simple point processes whose intensity depends on the past history, and is in general non-Markovian. Limit theorems for Hawkes processes in various asymptotic regimes have been studied in the literature. In…
We propose a novel modeling framework for time-evolving networks allowing for long-term dependence in network features that update in continuous time. Dynamic network growth is functionally parameterized via the conditional intensity of a…
Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been…
The superposition of temporal point processes has been studied for many years, although the usefulness of such models for practical applications has not be fully developed. We investigate superposed Hawkes process as an important class of…
We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each…
Temporal networks allow representing connections between objects while incorporating the temporal dimension. While static network models can capture unchanging topological regularities, they often fail to model the effects associated with…
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 introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with…