In this paper, the possibility of using some econophysical methods for quantitative assessment of complexity measures: entropy (Shannon, Approximate and Permutation entropies), fractal (Multifractal detrended fluctuation analysis – MF-DFA), and quantum (Heisenberg uncertainty principle) is investigated. Comparing the capability of both entropies, it is obtained that both measures are presented to be computationally efficient, robust, and useful. Each of them detects patterns that are general for crisis states. The similar results are for other measures. MF-DFA approach gives evidence that Dow Jones Sustainability Index is multifractal, and the degree of it changes significantly at different periods. Moreover, we demonstrate that the quantum apparatus of econophysics has reliable models for the identification of instability periods. We conclude that these measures make it possible to establish that the socially responsive exhibits characteristic patterns of complexity, and the proposed measures of complexity allow us to build indicators-precursors of critical and crisis phenomena.

The frequent financial critical states that occur in our world, during many centuries have attracted scientists from different areas. The impact of similar fluctuations continues to have a huge impact on the world economy, causing instability in it concerning normal and natural disturbances [1]. The an- ticipation, prediction, and identification of such phenomena remain a huge chal- lenge. To be able to prevent such critical events, we focus our research on the chaotic properties of the stock market indices. During the discussion of the re- cent papers that have been devoted to the chaotic behavior and complexity in the financial system, we find that the Largest Lyapunov exponent and the spec- trum of Lyapunov exponents can be evaluated to determine whether the system is completely deterministic, or chaotic. Accordingly, we give a theoretical background on the method for Lyapunov exponents estimation, specifically, we followed the methods proposed by J. P. Eckmann and Sano-Sawada to compute the spectrum of Lyapunov exponents. With Rosenstein’s algorithm, we com- pute only the Largest (Maximal) Lyapunov exponents from an experimental time series, and we consider one of the measures from recurrence quantification analysis that in a similar way as the Largest Lyapunov exponent detects highly non-monotonic behavior. Along with the theoretical material, we present the empirical results which evidence that chaos theory and theory of complexity have a powerful toolkit for construction of indicators-precursors of crisis events in financial markets.