Related papers: Multivariate Quadratic Hawkes Processes -- Part I:…
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the…
The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time…
Hawkes processes are a class of self-exciting point processes that are used to model complex phenomena. While most applications of Hawkes processes assume that event data occurs in continuous-time, the less-studied discrete-time version of…
We model the arrival of mid-price changes in the E-Mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to -1.15 at short…
We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by…
Cascades of events and extreme occurrences have garnered significant attention across diverse domains such as financial markets, seismology, and social physics. Such events can stem either from the internal dynamics inherent to the system…
This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First rates are derived for L1-metrics for stochastic intensities of the…
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 multivariate Hawkes process enables self- and cross-excitations through a triggering matrix that behaves like an asymmetrical covariance structure, characterizing pairwise interactions between the event types. Full-rank estimation of all…
We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…
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.…
We investigate the computational issues related to the memory size in the estimation of quadratic covariation, taking into account the specifics of financial ultra-high-frequency data. In multivariate price processes, we consider both…
This paper is devoted to establishing the full scaling limit theorems for multivariate Hawkes processes. Under some mild conditions on the exciting kernels, we develop a new way to prove that after a suitable time-spatial scaling, the…
Hawkes processes are a self-exciting stochastic process used to describe phenomena whereby past events increase the probability of the occurrence of future events. This work presents a flexible approach for modelling a variant of these,…
We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical results can be…
Many self-exciting systems change because endogenous amplification, as opposed to exogenous forcing, varies. We study a Hawkes process with fixed background rate and kernel, but piecewise time-varying productivity. For exponential kernels…
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…
We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In…
This paper considers population processes in which general, not necessarily Markovian, multivariate Hawkes processes dictate the stochastic arrivals. We establish results to determine the corresponding time-dependent joint probability…
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…