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.
Highlights
A financial market is a highly complex and continuously evolving system [1,2,3]
We present a study of time evolution of the cross-correlation structures of return time series for N stocks, and determination of the optimal number of market states; the dynamical evolution of the market states over different time-epochs
We have studied the identification of market states and long-term precursors to critical states in financial markets, based on the probabilistic occurrences of correlation patterns, determined using noise-suppressed short-time correlation matrices
Summary
A financial market is a highly complex and continuously evolving system [1,2,3]. To understand the statistical behavior of the financial market and its constituent sectors [4,5,6,7,8,9], researchers focused their attention on the information of co-movements and correlations among the stocks of the market. Certain correlation structures seem to occur more frequently than by pure chance (randomness), specially when markets approach a critical period or crash [11,12] To identify such similar (clusters) correlation patterns, referred as “market states”, as was previously attempted by Munnix et al [13, 14], is rather challenging due to many factors. Munnix et al [13] had provided a scheme where all the correlation frames at different timeepochs were initially regarded as a single cluster and divided into sub-clusters by a procedure based on the k-means algorithm They stopped the division process when the average distance from each cluster center to its members became smaller than a certain threshold.
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