Related papers: Autoregressive Models for Matrix-Valued Time Serie…

While Internet of Things (IoT) devices and sensors create continuous streams of information, Big Data infrastructures are deemed to handle the influx of data in real-time. One type of such a continuous stream of information is time series…

Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroscedasticity at the same time. In the meanwhile, it is still lack of a time series model to accommodate…

Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems. Empirically, we commonly access these systems through time series measurements. Often such time series may consist of discrete random…

In economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. In some applications such complex systems can be associated with some underlying…

Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and…

Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…

High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix…

Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack of theory to support the…

The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed.…

Many time series are generated by a set of entities that interact with one another over time. This paper introduces a broad, flexible framework to learn from multiple inter-dependent time series generated by such entities. Our framework…

Despite the popularisation of machine learning models, more often than not, they still operate as black boxes with no insight into what is happening inside the model. There exist a few methods that allow to visualise and explain why a model…

We introduce a general approach for modeling the dynamic of multivariate time series when the data are of mixed type (binary/count/continuous). Our method is quite flexible and conditionally on past values, each coordinate at time $t$ can…

This paper presents a framework for binary autoregressive time series in which each observation is a Bernoulli variable whose success probability evolves with past outcomes and probabilities, in the spirit of GARCH-type dynamics,…

Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a…

Modeling human mobility is vital for extensive applications such as transportation planning and epidemic modeling. With the rise of the Artificial Intelligence Generated Content (AIGC) paradigm, recent works explore synthetic trajectory…

This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…

Generative modeling of high-dimensional data is a key problem in machine learning. Successful approaches include latent variable models and autoregressive models. The complementary strengths of these approaches, to model global and local…

There has been an enormous interest in analysing and modelling periodic time series. The research on periodically integrated autoregressive (PIAR) models which capture the periodic structure and the presence of unit roots is widely applied…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

Motivated by a dataset of burglaries in Chicago, USA, we introduce a novel framework to analyze time series of count data combining common multivariate time series models with latent position network models. This novel methodology allows us…