Bottom-up change point detection in time series data
Time series analysis involves the study of the evolution of one or more variables over time. A critical aspect of time series analysis is the detection of significant changes in the underlying data-generating mechanism. In recent years, researchers across various fields have rekindled their interest in solving the change point detection problem. Specifically, change point detection poses a challenge and finds application in diverse disciplines, e.g., financial time series analysis (e.g., identifying shifts in volatility), signal processing (e.g., conducting structural analysis on EEG signals), geology data analysis (e.g., examining volcanic eruption patterns), and environmental research (e.g., detecting shifts in ecological systems caused by critical climatic thresholds). In this paper, we introduce a rigorous bottom-up approach to change point detection. More precisely, our approach divides the original signal into numerous smaller sub-signals, calculates a difference metric between adjacent segments and, at each iteration, selects the time points with the smallest differences. We demonstrate the effectiveness of this bottom-up approach through its application to both simulated and real-world data.