My PhD

In many scientific fields, such as medicine, sociology, finance, epidemiology, and environmental sciences, it is natural to have records of counts over an observed time horizon. Examples of such data include the daily number of transactions in a stock market, the monthly number of viral diseases, or utilisation counts for health-care services. Therefore, count time series methods are needed to address specific questions in these areas.

Furthermore, in most of these data analysis studies, it is common to have information on several variables that describe the phenomena. For instance, in finance, it is common to analyse transaction counts across different assets simultaneously, and in epidemiology, in addition to the record number of cases, information on other covariates, such as demographics or comorbidities of the studied population. That is the scenario where multivariate modelling of count time series arises.

Due to the nature of the data, continuous time series methods such as AR(p) models are inappropriate. Thus, models that best describe count data are needed. Current statistical methods in multivariate count time series present several limitations. For example, count time series methods are scarce for modelling contemporaneous dependence and the cross-correlation structure among the variables in the analysis. In addition, current methods are computationally unsuitable for high-dimensional applications due to the discrete nature of the data.

The project aims to develop novel models for multivariate count time series, combining rigorous theoretical development, computational and practical advances, and motivation from real applications. The proposed research direction is to explore generalisations of observation-driven models for multivariate count time series, with a focus on capturing the dependency structure. In parallel, we aim to address the problem and develop new methods for count time series using point process theory.