Identifying long-term precursors of financial market crashes using correlation patterns

Abstract

The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial markets as an example of a complex system, and do comparative analyses of two stock markets—the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of cross-correlation structure patterns of short-time epochs for a 32 year period (1985–2016). We identify ‘market states’ as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the evolution of the market states. Power mapping method from the random matrix theory is used to suppress the noise on correlation patterns, and an adaptation of the intra-cluster distance method is used to obtain the ‘optimum’ number of market states. We find that the S&P 500 is characterized by four market states and Nikkei 225 by five. We further analyze the co-occurrence of paired market states; the probability of remaining in the same state is much higher than the transition to a different state. The transitions to other states mainly occur among the immediately adjacent states, with a few rare intermittent transitions to the remote states. The state adjacent to the critical state (market crash) may serve as an indicator or a ‘precursor’ for the critical state and this novel method of identifying the long-term precursors may be helpful for constructing the early warning system in financial markets, as well as in other complex systems.

Keywords

• market crash
• market state
• power mapping method
• multidimensional scaling
• return cross-correlations