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This paper proposes a simple and parsimonious discrete-time simulation model to describe the endogenous formation and periodic collapse of financial bubbles. While existing literature has extensively explored the statistical properties of…
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…
The Hawkes model is a past-dependent point process, widely used in various fields for modeling temporal clustering of events. Extending this framework, the multidimensional marked Hawkes process incorporates multiple interacting event types…
Hawkes processes have recently risen to the forefront of tools when it comes to modeling and generating sequential events data. Multidimensional Hawkes processes model both the self and cross-excitation between different types of events and…
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external…
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…
We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes…
The high-frequency cross-correlation existing between pairs of stocks traded in a financial market are investigated in a set of 100 stocks traded in US equity markets. A hierarchical organization of the investigated stocks is obtained by…
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta…
We provide some theoretical extensions and a calibration protocol for our former dynamic optimal execution model. The Hawkes parameters and the propagator are estimated independently on financial data from stocks of the CAC40.…
Animal acoustic communication often exhibits temporal dependence, with calls triggering or suppressing subsequent calls within and across call types, individuals, or species. While Hawkes processes provide a natural framework for modeling…
Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as $O(N^2)$ in the number of events. The canonical linear exponential Hawkes process admits a faster…
Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for five human…
A characteristic feature of complex systems in general is a tight coupling between their constituent parts. In complex socio-economic systems this kind of behavior leads to self-organization, which may be both desirable (e.g. social…
We introduce the Hyperedge-triggered Hawkes (HTH) process for inferring higher-order interaction structure in multi-cellular systems from asynchronous event-time data. Beyond standard pairwise excitation, the HTH intensity includes a term…
We introduce a new non parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this…
Scale invariance, collective behaviours and structural reorganization are crucial for portfolio management (portfolio composition, hedging, alternative definition of risk, etc.). This lack of any characteristic scale and such elaborated…
Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that…
Online boards offer a platform for sharing and discussing content, where discussion emerges as a cascade of comments in response to a post. Branching point process models offer a practical approach to modelling these cascades; however,…
We introduce matrix H theory, a framework for analyzing collective behavior arising from multivariate stochastic processes with hierarchical structure. The theory models the joint distribution of the multiple variables (the measured signal)…