A novel detection approach of bifurcation-induced tipping points with generalized Ornstein-Uhlenbeck process in finance

Abstract

Detecting bifurcation-induced tipping points can help prevent the collapse of dynamic financial systems. Current detection methods, such as the Bai and Perron test and the Markov-switching model, identify tipping points based on probabilistic assumptions. However, these conventional methods often fail to capture the complex underlying mechanisms of financial markets. Additionally, traditional methods are less effective when applied to systems affected by internal and external interactions. To address these limitations, we propose an alternative detection method based on the Generalized Ornstein-Uhlenbeck (GOU) process. In this study, we develop a parameter estimation strategy for the bifurcation-induced tipping points detection (BTPD) method in dynamic financial systems. This novel method employs a stochastic differential equation (SDE) governed by the GOU process, providing improved sensitivity to detect transitions. We prove the asymptotic normality and consistency of the parameter estimators under standard regularity conditions. We demonstrate the effectiveness of the BTPD method using data from crude oil futures, other commodity futures, major stock indices and exchange rates. This approach provides a more comprehensive toolkit for anticipating critical transitions in complex financial systems.