Related papers: Hawkes autoregressive processes: a new model for m…

The Hawkes process is a self-exciting sample point process. It has wide applications in finance, social networks, criminology, seismology, and many other fields. With the development of storage technology, data-driven models are attracting…

A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…

The autoregressive Hilbertian model (ARH) was introduced in the early 90's by Denis Bosq. It was the subject of a vast literature and gave birth to numerous extensions. The model generalizes the classical multidimensional autoregressive…

Prediction of trajectories such as that of pedestrians is crucial to the performance of autonomous agents. While previous works have leveraged conditional generative models like GANs and VAEs for learning the likely future trajectories,…

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…

In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional…

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…

Autoregressive networks can achieve promising performance in many sequence modeling tasks with short-range dependence. However, when handling high-dimensional inputs and outputs, the huge amount of parameters in the network lead to…

Despite the impressive success of deep neural networks in many application areas, neural network models have so far not been widely adopted in the context of volatility forecasting. In this work, we aim to bridge the conceptual gap between…

The paper develops a general flexible framework for Network Autoregressive Processes (NAR), wherein the response of each node linearly depends on its past values, a prespecified linear combination of neighboring nodes and a set of…

In this paper, we study a discrete-time analogue of a Hawkes process, modelled as a Poisson autoregressive process whose parameters depend on the past of the trajectory. The model is characterized to allow these parameters to take negative…

Many economic variables feature changes in their conditional mean and volatility, and Time Varying Vector Autoregressive Models are often used to handle such complexity in the data. Unfortunately, when the number of series grows, they…

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…

Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes,…

A novel spatial autoregressive model for panel data is introduced, which incorporates multilayer networks and accounts for time-varying relationships. Moreover, the proposed approach allows the structural variance to evolve smoothly over…

We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it allows for both common drivers, parameters common to all the…

Recent work by Marino et al. (2020) showed improved performance in sequential density estimation by combining masked autoregressive flows with hierarchical latent variable models. We draw a connection between such autoregressive generative…

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…

Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…

The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…