Instability of Financial Time Series Revealed by Irreversibility Analysis.

Since the 2008 global economic crisis, the detection of financial instabilities has garnered extensive research attention, particularly through the application of time-series analysis. In this study, a novel time-series analysis method, integrating the Kullback-Leibler Divergence (KLD) metric with a sliding window technique, is proposed to detect instabilities in time-series data, especially in financial markets. Global financial time series from 2004 to 2022 were analyzed. The raw time series were preprocessed into return rate series and transformed into complex networks using the directed horizontal visibility graph (DHVG) algorithm, effectively preserving temporal variabilities in network topologies. The KLD method was evaluated through both retrospective analysis and real-time monitoring. It successfully identified idiosyncratic incidents in the financial market, correlating them with specific economic events. Compared to traditional metrics (e.g., moments) and econometric methods, KLD demonstrated superior performance in capturing sequence information and detecting anomalies without requiring linear regression models. Although initially designed for financial data, the KLD method is versatile and can be applied to other types of time series as well.