Network Informed Methods for High Dimensional Time Series

High-dimensional panels of time series arise in many scientific disciplines such as neuroscience, finance, and macroeconomics. Often, co-movements within groups of the panel components occur. Extracting these groupings from the data provides a course-grained description of the complex system in question and can inform subsequent prediction tasks. In this project we develop a network time series model that posits a particular random graph called a stochastic blockmodel as the mechanism for network generation. The stochastic blockmodel is chosen because it yields networks that have a group structure, which, in our context, correspond to groups of time series that have high co-movement. The model marries literature on random graphs with vector autoregressive processes, a standard model for multivariate time series. As such, we call it the Network Informed Restricted Vector Autoregression (NIRVAR) model. We provide a novel estimation framework that is interpretable and outperforms competing network time series models on three applications to finance, macroeconomics, and transportation system.

There are two follow-on projects that are currently in progress. Firstly, we aim to prove consistency and asymptotic normality of the estimated NIRVAR groups with respect to their population counterparts. This is important as it would provide theoretical justification for the proposed estimation framework. Secondly, a natural extension is to incorporate a factor model into the NIRVAR framework. Factor models are well studied and many real-world datasets are known to exhibit factor-like behaviour. Currently, this is an applied project and the aim is to show that incorporating a factor model improves the predictive performance of NIRVAR. If progress is made on the theoretical project, then this theory could be extended to the "NIRVAR plus factors" model.

The primary CDT impact will be training 75 PhD graduates as the next generation of leaders in statistics and statistical machine learning. These graduates will lead in industry, government, health care, and academic research. They will bridge the gap between academia and industry, resulting in significant knowledge transfer to both established and start-up companies. Because this cohort will also learn to mentor other researchers, the CDT will ultimately address a UK-wide skills gap. The students will also be crucial in keeping the UK at the forefront of methodological research in statistics and machine learning.
After graduating, students will act as multipliers, educating others in advanced methodology throughout their career. There are a range of further impacts:
- The CDT has a large number of high calibre external partners in government, health care, industry and science. These partnerships will catalyse immediate knowledge transfer, bringing cutting edge methodology to a large number of areas. Knowledge transfer will also be achieved through internships/placements of our students with users of statistics and machine learning.
- Our Women in Mathematics and Statistics summer programme is aimed at students who could go on to apply for a PhD. This programme will inspire the next generation of statisticians and also provide excellent leadership training for the CDT students.
- The students will develop new methodology and theory in the domains of statistics and statistical machine learning. It will be relevant research, addressing the key questions behind real world problems. The research will be published in the best possible statistics journals and machine learning conferences and will be made available online. To maximize reproducibility and replicability, source code and replication files will be made available as open source software or, when relevant to an industrial collaboration, held as a patent or software copyright.