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 crosscorrelation structure patterns of short-time epochs for a 32 year period . 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.

Structural Entropy: Monitoring Correlation-Based Networks Over Time With Application To Financial Markets

“…For example, a recent work by Pharasi et al . 29 , used a power map to filter the noise from extremely short time frames and identify markets states. The researchers have isolated different independent markets states and analyzed the transition probability from one state to the other.…”

Complex Market Dynamics in the Light of Random Matrix Theory

“…The power mapping method suppresses noise present in the correlation structure of short-time series (see e.g., Refs. [9,18,22,24,33] for recent studies and applica- The densities of non-zero eigenvalues are closely described by the Marcenko-Pastur distributions, but the emerging spectra move towards the main spectra as the value of ε increases. The emerging spectra is absent at ε = 0, while it merges with the main spectrum at high values of distortion parameter, e.g., ε = 0.8.…”

“…Figure adapted from Ref. [24]. different initial conditions (choices of random coordinates for the k-centroids or equivalently random initial clustering of n objects); each set of initial conditions usually results in slightly different clustering of the n objects representing different correlation matrices.…”

“…Each point on the MDS map represents a stock of the market. The points are scattered in the map, based on the crosscorrelations among the stocks -more correlated stocks are placed nearby and less correlated are placed far apart (see also Ref [24]…”

Complexity Changes in the US and China’s Stock Markets: Differences, Causes, and Wider Social Implications

“…There has been much effort to empirically test the validity of EMH in various markets. Major approaches include using traditional statistical methods such as autocorrelation or cross-correlation [ 5 , 6 , 7 ], variance ratio [ 8 , 9 , 10 , 11 ], the state space model [ 12 ], as well as metrics from complexity science such as Lempel–Ziv complexity (LZ) [ 13 , 14 , 15 , 16 , 17 , 18 , 19 ], permutation entropy (PE) [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 ], and Hurst parameter and multifractal measures [ 11 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 ]. The approaches from complexity science are especially appealing as they are fundamentally different from machine-learning-based black-box approaches.…”