Bardwell, Lawrence and Fearnhead, Paul and Eckley, Idris (2018) Efficient search methods for high dimensional time-series. PhD thesis, Lancaster University.
2018_LawrenceBardwell_PhD.pdf - Published Version
Available under License Creative Commons Attribution-NoDerivs.
Download (1MB)
Abstract
This thesis looks at developing efficient methodology for analysing high dimensional time-series, with an aim of detecting structural changes in the properties of the time series that may affect only a subset of dimensions. Firstly, we develop a Bayesian approach to analysing multiple time-series with the aim of detecting abnormal regions. These are regions where the properties of the data change from some normal or baseline behaviour. We allow for the possibility that such changes will only be present in a, potentially small, subset of the time-series. A motivating application for this problem comes from detecting copy number variation (CNVs) in genetics, using data from multiple individuals. Secondly, we present a novel approach to detect sets of most recent changepoints in panel data which aims to pool information across time-series, so that we preferentially infer a most recent change at the same time point in multiple series. Lastly, an approach to fit a sequence of piece-wise linear segments to a univariate time series is considered. Two additional constraints on the resulting segmentation are imposed which are practically useful: (i) we require that the segmentation is robust to the presence of outliers; (ii) that there is an enforcement of continuity between the linear segments at the changepoint locations. These constraints add significantly to the computational complexity of the resulting recursive solution. Several steps are investigated to reduce the computational burden.