Wilkie, Tessa and Fearnhead, Paul and Eckley, Idris and Hartog, Jarno (2025) Novel Methods for Detecting Changepointsin Time Series Structures. PhD thesis, Lancaster University.
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Abstract
This thesis makes three contributions. The first addresses the problem of finding a single changepoint in a time series of air quality measurements observed in and around Glasgow in the run up to, and aftermath of, measures introduced to improve air quality in the city. Since weather influences air quality and we have a time series of weather variables observed daily, we model this time series as a Vector Autoregressive process with exogenous variables (VAR-X). We adapt an existing changepoint method designed to detect a change in one or more series in an independent and identically distributed multivariate time series to finding a single change in a VAR or a VAR-X process. Changepoint detection in the presence of missing data is relatively under-explored. Most existing methods assume that the data they are run on are complete. Some have explored replacing the missing values with imputed ones. The second contribution of this thesis is introducing a novel method for detecting changepoints in a linear regression model that is subject to missingness — in certain patterns — in the independent variables, without the need to impute separately. The third contribution is the introduction of a novel likelihood ratio test based method for detecting a changepoint in a series of count data with trend. This is applied to interpolated count data: counts of infant mortality by year in selected local government districts in England between 1911 and 1973. We use the changepoint detection method to detect errors in the interpolation process, which manifest as abrupt changes, while allowing for historical trend which is present in all series.