Robust estimation and inference for high-dimensional time series

Time series data are collected in a wide range of areas such as finance, economics, medicine and social sciences.

Examples of datasets include, stock price data in finance, and EEG data in Neuroscience, which records electrical activity of the brain. For time series data, modelling techniques exist which provide ways to explain the behaviour of the process, make inferential statements about the observed data, and to forecast future observations. Furthermore, multivariate time series analysis methods make use of the possible interdependences between time series by analysing several time series jointly. In addition to the prevalence of time series datasets, modern datasets often include a large number of variables relative to the number of observations. Therefore, there is a demand for multivariate time series methods that work for high-dimensional data.

My project aims to robustify existing methodology for modelling high-dimensional time series data, ensuring the performance of model estimators under relaxed assumptions. In particular, we will be looking to utilise heavy-tailed robust covariance estimators within the estimation of vector autoregressive (VAR) models. With the aim that this will then provide theoretical guarantees for regularised methods for fitting sparse VAR models under weaker assumptions, in contrast to the Gaussian assumptions typically applied to the data. The robust estimation procedure could then be used within downstream methods which require estimation of coefficients of a VAR process.

Under the framework of VAR models further questions about the data can be asked, for example, detecting group structures in the data, or change points in the data. Next steps in the project could entail developing techniques that help solve these questions, with theoretical guarantees under assumptions that allow for heavy-tailedness in the data.

The potential impact of this research is that the performance of current tools will be improved, and work with a broader range of datasets. This could then lead to improvements in forecasting and ability to understanding the stochastic structure of time series data. These techniques could be used in the fields listed previously.

This project is developing statistical methodology, and therefore naturally falls under the EPSRC Statistics and applied probability research area.

The COMPASS Centre for Doctoral Training will have the following impact.

Doctoral Students Impact.

I1. Recruit and train over 55 students and provide them with a broad and comprehensive education in contemporary Computational Statistics & Data Science, leading to the award of a PhD. The training environment will be built around a set of multilevel cohorts: a variety of group sizes, within and across year cohort activities, within and across disciplinary boundaries with internal and external partners, where statistics and computation are the common focus, but remaining sensitive to disciplinary needs. Our novel doctoral training environment will powerfully impact on students, opening their eyes to not only a range of modern technical benefits and opportunities, but on the power of team-working with people from a range of backgrounds to solve the most important problems of the day. They will learn to apply their skills to achieve impact by collaborative working with internal and external partners, such as via our Rapid Response Teams, Policy Workshops & Statistical Clinics.

I2. As well as advanced training in computational statistics and data science, our students will be impacted by exposure to, and training in, important cognate topics such as ethics, responsible innovation, equality, diversity and inclusion, policy, effective communication and dissemination, enterprise, impact and consultancy skills. It is vital for our students to understand that their training will enable them to have a powerful impact on the wider world, so, e.g., AI algorithms they develop should not be discriminatory, and statistical methodologies should be reproducible, and statistical results accurately and comprehensibly communicated to the general public and policymakers.

I3. The students will gain experience via collaborations with academic partners within the University in cognate disciplines, and a wide range of external industrial & government partners. The students will be impacted by the structured training programmes of the UK Academy of Postgraduate Training in Statistics, the Bristol Doctoral College, the Jean Golding Institute, the Alan Turing Institute and the Heilbronn Institute for Mathematical Sciences, which will be integrated into our programme.

I4. Having received an excellent training, the students will then impact powerfully on the world in their future fruitful careers, spreading excellence.

Impact on our Partners & ourselves.

I5. Direct impacts will be achieved by students engaging with, and working on projects with, our academic partners, with discipline-specific problems arising in engineering, education, medicine, economics, earth sciences, life sciences and geographical sciences, and our external partners Adarga, the Atomic Weapons Establishment, CheckRisk, EDF, GCHQ, GSK, the Office for National Statistics, Sciex, Shell UK, Trainline and the UK Space Agency. The students will demonstrate a wide range of innovation with these partners, will attract engagement from new partners, and often provide attractive future employment matches for students and partners alike.

Wider Societal Impact

I6. COMPASS will greatly benefit the UK by providing over 55 highly trained PhD graduates in an area that is known to be suffering from extreme, well-known, shortages in the people pipeline nationally. COMPASS CDT graduates will be equipped for jobs in sectors of high economic value and national priority, including data science, analytics, pharmaceuticals, security, energy, communications, government, and indeed all research labs that deal with data. Through their training, they will enable these organisations to make well-informed and statistically principled decisions that will allow them to maximise their international competitiveness and contribution to societal well-being. COMPASS will also impact positively on the wider student community, both now and sustainably into the future.