Integer-valued Matrix AutoRegressive Score models

Policymakers and governmental institutions rely every day on data to make important decisions that impact citizens’ quality of life. For instance, the availability of large amounts of time series data observed in many dimensions and levels of granularity requires the development of new techniques to model and draw conclusions from such complex systems. Multivariate time series data structures typically deal with time series and cross-sectional dimensions. Nowadays, much more complex data structures have appeared, requiring mathematical objects defined in higher dimensions and beyond continuous-valued measurements; e.g. time series of counts related to several types of crimes occurring in different cities. The final object is a three-dimensional data set of counts called a discrete tensor. This research proposal introduces new empirical, econometric models to describe and study such discrete tensor data. Although in social sciences many tensor data possess a discrete structure, the statistical theory for discrete tensors is still under development. These specific data cannot be accommodated by existing tensor models which are specifically tailored for continuous variables and are typically described by simple linear patterns. The goal of the project is to fill the existing gap in the literature by developing new models for discrete-valued tensor data that possess flexible cross-sectional and serial dependence structures. To this aim, we combine a multivariate copula framework for count data and non-linear score-driven models with the existing tensor literature; As a result, we obtain a new model class, called Integer-valued Matrix Autoregressive Score model (IMARS). We then successfully apply these new models to relevant empirical problems in key areas of interest to policymakers, like crime data, allowing to understand the distribution of different types of crimes across geographical areas, forecast their incidence and study spillover effects over a space-time grid.