Methodologies used to iinfer the dynamics of high dimensional time-series data.

This project falls within the EPSRC Statistics and Applied Probability Research Area. My research focuses on methodologies used to infer the dynamics of high dimensional time-series data. Alongside Nikolaos Kantas and George Deligiannidis, we aim to perform model calibration on state space models with non-Markovian, potentially long-memory latent states. Current state-of-the-art approaches involve particle MCMC, where information on filtering density is stored in a finite set of particles. However, these methods suffer from the curse of dimensionality, path degeneracy, and scale poorly with the size of the dataset. To overcome these issues, I am investigating the application of diffusion models in time-series, initially with a look towards time-series synthesis of Fractional Brownian Motion. Our future aims include to investigate how well diffusion models can infer the drift and diffusion coefficients of SDE-driven time-series, and, ultimately, how they can be applied in particle filtering. On the other hand, alongside Mihai Cucuringu and Guy Nason, I am focusing on modelling the covariance structure of high dimensional time-series, with a specific focus on financial time-series and portfolio construction. Previous literature on covariance forecasting often focuses on M-GARCH models, which suffer from the curse of dimensionality. In recent years, a growing body of literature has applied network science methods for both modelling and forecasting. Building on previous research by both supervisors, I am investigating how to incorporate autoregressive and network effects in models for correlation and covariance structures, with flexibility in choosing the maximum autoregressive lag and the influence of the network at each lag. In the long-term, I aim to use these models to build better measures of cross-asset risk, and use graph clustering techniques to build portfolios that deliver better returns.

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.