Discovering nonlinear interactions between China's financial markets: A data-driven approach

With the rapid advancement of global economic and financial amalgamation, coupled with the expansive liberalization of the Chinese economy, the interconnections among the foreign exchange, stock, and housing markets have become more pronounced. This paper studies these three markets as a cohesive framework, scrutinizing the reciprocal influences and feedback loops among them, with a focus on the period following the 2005 exchange rate reform. We first estimate pairwise copulas to verify the dependence between these markets, and then propose a data-driven framework that posits an intrinsic entanglement within this triad of markets. Our methodology involves the implementation of a modified differential evolution algorithm to estimate a class of nonlinear systems that feature a flexible form of interactions. Moreover, we elucidate with empirical evidence the structural flow diagram, the delineation of equilibria, the local stability, and the evolutionary trajectories of the system under examination. The analysis yields evidence for the simultaneous existence of dual equilibrium states: a stable focus alongside a saddle−node, the former exhibiting bi-dimensional stability and the latter, mono-dimensional instability in their respective manifolds. Moreover, the impact of the RMB exchange rate on the changes in the stock price manifests through a nonlinear dynamic, akin to a quadratic function, delineated by an upward-opening parabolic path.