Robust estimation and inference for high-dimensional time series

点击翻译按钮获取中文摘要

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.