Change-point detection in time series with hydrological applications.
Masters thesis, UCL (University College London).
Water pollution is a global problem that is more serious in developing countries. This work was motivated by the need to understand water pollution and quality in Nigeria and specifically in the city of Ibadan. Initially, data were obtained consisting of multivariate monthly water chemistry measurements between 2003 and 2007 from two reservoirs in the city, and admissions to three nearby hospitals for several water-borne diseases between 1997 and 2008. Also used are monthly rainfall data over a fifteen-year period from a nearby weather station. An initial analysis revealed that the quality of the water chemistry data was poor. In particular, many of the monthly time series contained abrupt changes and breaks. This thesis therefore focuses on the detection of change-points with particular application to hydrological time series. Additional data-sets with a simpler structure, United Kingdom Blackwater rainfall proportion and Haemolytic Uraemic Syndrome (HUS) disease data are used to estimate and explain positions of change-points. An extensive literature review is given including a theoretical demonstration showing why some standard statistical theories fail some regularity conditions for this problem. A wide variety of techniques to detect change-points are considered, with illustrations on different hydrological data-sets using profile likelihood and Markov Chain Monte-Carlo (MCMC) to estimate change- points. A conclusion is that although the sample size may hinder the accurate change-point detection in some series, state-space models provide a promising framework for the analysis of complex series in which multiple change-points may be present. This will help in detecting the potential presence of changes indicating data quality problems and signifying the direction of solutions towards future work.
|Title:||Change-point detection in time series with hydrological applications|
|Open access status:||An open access version is available from UCL Discovery|
|Keywords:||Water pollution, Change-points, Regularity, Markov Chain Monte Carlo, Profile likelihood, State-space model|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science|
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