Related papers: Hawkes autoregressive processes: a new model for m…
AutoRegressive Conditional Heteroscedasticity (ARCH) models are standard for modeling time series exhibiting volatility, with a rich literature in univariate and multivariate settings. In recent years, these models have been extended to…
Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which,…
It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from…
Human behavior drives a range of complex social, urban, and economic systems, yet understanding its structure and dynamics at the individual level remains an open question. From credit card transactions to communications data, human…
In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic…
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…
The Hawkes process is a versatile stochastic model for point patterns that exhibit self-excitation, that is, the property that an event occurrence increases the rate of occurrence for some period of time in the future. We present a Bayesian…
A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], is…
We develop a theory of evolutionary spectra for heteroskedasticity and autocorrelation robust (HAR) inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic time series which may…
Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually…
Contemporary time series analysis has seen more and more tensor type data, from many fields. For example, stocks can be grouped according to Size, Book-to-Market ratio, and Operating Profitability, leading to a 3-way tensor observation at…
Hawkes process models are used in settings where past events increase the likelihood of future events occurring. Many applications record events as counts on a regular grid, yet discrete-time Hawkes models remain comparatively underused and…
The Hawkes process is a simple point process with wide applications in finance, social networks, criminology, seismology, and many other fields. The Hawkes process is defined for continuous-time setting. However, data is also recorded in a…
We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…
Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…
Hawkes Processes capture self-excitation and mutual-excitation between events when the arrival of an event makes future events more likely to happen. Identification of such temporal covariance can reveal the underlying structure to better…
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…
The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…
Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for…
We propose a novel probabilistic framework to model continuous-time interaction events data. Our goal is to infer the \emph{implicit} community structure underlying the temporal interactions among entities, and also to exploit how the…