Change point detection in time series. Case study on a diabetes dataset

Change point detection methods are important tools for identifying structural breaks in time series. These methods have found applications in a variety of fields including economics, biomedicine, engineering, forecasting and quality control, where identifying abrupt transitions can help to identify timely interventions or model adaptations. There is a wide literature in change point detection methods. In its first part the thesis offers an overview of main methods based on moving sums in stochastic sequences and time series. In particular, four well established approaches are examined: the Moving Sums (MOSUM) method, a local, window-based technique designed to detect abrupt changes in the mean, the Multiscale Change Point (MSCP) method, which adopts a hierarchical, scale-sensitive framework for detecting shifts in the mean as well as the Pruned Exact Linear Time (PELT) algorithm which operates like the Optimal Partitioning algorithm but adds a pruning step in order to decrease computational complexity and the Binary Segmentation (BS), an approximate algorithm for finding the strongest changes iteratively. This thesis introduces a novel approach for change point detection in stochastic sequences and time series with weak dependencies, based on the assumption of a piecewise linear trend. Two algorithms are proposed, namely the Linear Regression Change Point (LRCP) and the modified LRCP, which are multiscale hypotheses testing framework for change points detection using local linear models. The proposed methods iteratively apply least squares estimation to two consecutive windows to model local linear behavior and perform statistical tests to assess whether the same linear model underlies both segments. Rejections of the hypotheses indicate a potential change point in the structure. The main contribution of this thesis is a novel multiscale approach for change point detection that considers linear regression models, hypothesis testing and additional decision criteria for change points. The algorithms are implemented in the statistical software R and are validated through simulations, which demonstrate their efficency and performance compared to the stablished approaches reviewed in this work, namely the MOSUM, MSCP, PELT and BS.In many real-world scenarios, especially in biomedical contexts such as glucose monitoring, changes in the underlying trend may occur gradually rather than abruptly. This phenomena is efficiently captured by the proposed method, the LRCP, when it was applied to a diabetes data set from the literature. There it successfully identifies relevant change points in glucose levels of patients with type 1 diabetes mellitus, illustrating its practical relevance in clinical time series analysis. This thesis contributes to the broader field of change point detection in time series by offering a general framework for detecting change points in piecewise linear trends. Our approach shows great potential for analyzing real-world datasets arising from complex systems.