Change-point analysis in predictive relationships

Data is the foundation of the Information Age. Knowing how to perform proper data analysis is essential and unavoidable for most companies today because it gives meaning to meaningless numbers and shows the hidden insights of information behaviour. From this perspective, change-point analysis is one of the most interesting and crucial fields, as it studies change detection in data structures and the way these changes affect underlying relationships. Change-point analysis has a considerably long history. However, the biggest part of the proposed techniques in this field are designed with a number of model restrictions, which significantly reduces the number of possible applications. In this Dissertation, we aim to study and develop robust approaches to solve the change detection problem in high-dimensional predictive structures. In Essay I, we develop a technique that allows to estimate the unknown number of changes in large datasets under normality assumptions. The proposed approach, called PSA (Parametric Splitting Algorithm), appears to be considerably accurate and efficient. In Essay II,we study a way to extend the PSA method to nonparametric settings and test it with different artificial datasets. We describe this extension as the new algorithm NSA (Nonparametric Splitting Algorithm), which solves the change detection problem in a robust manner. In Essay III, we continue considering the same problem and present the new method NDP (Nonparametric Dynamic Programming) along with the proofs of its consistency. We test NDP against NSA and other baselines and conclude that, although NDP has a higher accuracy, NSA is still more preferred due to its computational efficiency. Finally, we apply NSA to news analytics to study the financial crisis of 2006–2009. Taken all together, the Essays in this Dissertation present the continuous development of the ideas towards finding a robust solution for structural changepoint detection problems in predictive relationships