Nonlinear manifold learning for early warnings in financial markets

A financial market is a complex, dynamic system with an underlying governing manifold. This study introduces an early warning method for financial markets based on manifold learning. First, we restructure the phase space of a financial system using financial time series data. Then, we propose an information metric-based manifold learning (IMML) algorithm to extract the intrinsic manifold of a dynamic financial system. Early warning ranges for critical transitions of financial markets can be detected from the underlying manifold. We deduce the intrinsic geometric properties of the manifold to detect impending crises. Experimental results show that our IMML algorithm accurately describes the attractor manifold of the financial dynamic system, and contributes to inform investors about the state of financial markets.