The instability of the price dynamics of the energy market from a theoretical point of view indicates the inadequacy of the dominant paradigm of the quantitative description of pricing processes, and from a practical point of view, it leads to abnormal shocks and crashes. A striking example is the COVID-stimulated spring drop of spot prices for crude oil by 305% to $36.73 a barrel. The theory of complex systems with the latest complex networking achievements using pragmatically verified econophysical approaches and models can become the basis of modern environmental science. In this case, it is possible to introduce certain measures of complexity, the change in the dynamics of which makes it possible to identify and prevent characteristic types of critical phenomena. In this paper, the possibility of using some econophysical approaches for quantitative assessment of complexity measures: (1) informational (Lempel-Ziv measure, various types of entropies (Shannon, Approximate, Permutation, Recurrence), (2) fractal and multifractal (Multifractal Detrended Fluctuation Analysis), (3) recurrent (Recurrence Plot and Recurrence Quantification Analysis), (4) Lévy’s stable distribution properties, (5) network (Visual Graph and Recurrence based) and (6) quantum (Heisenberg uncertainty principle) is investigated. Each of them detects patterns that are general for crisis states. 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. Proposed quantitative measures of complexity classified and adapted for the crude oil market. Their behavior in the face of known market shocks and crashes has been analyzed. It has been shown that most of these measures behave characteristically in the periods preceding the critical event. Therefore, it is possible to build indicators-precursors of crisis phenomena in the crude oil market.

Cryptocurrencies refer to a type of digital asset that uses distributed ledger, or blockchain technology to enable a secure transaction. Like other financial assets, they show signs of complex systems built from a large number of nonlinearly interacting constituents, which exhibits collective behavior and, due to an exchange of energy or information with the environment, can easily modify its internal structure and patterns of activity. We review the econophysics analysis methods and models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. Quantitative measures of complexity have been proposed, classified, and adapted to the cryptocurrency market. Their behavior in the face of critical events and known cryptocurrency market crashes has been analyzed. It has been shown that most of these measures behave characteristically in the periods preceding the critical event. Therefore, it is possible to build indicators-precursors of crisis phenomena in the cryptocurrency market.

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.

The focus of this study to measure the varying irreversibility of stock markets. A fundamental idea of this study is that financial systems are complex and nonlinear systems that are presented to be non-Gaussian fractal and chaotic. Their complexity and different aspects of nonlinear properties, such as time irreversibility, vary over time and for a long-range of scales. Therefore, our work presents approaches to measure the complexity and irreversibility of the time series. To the presented methods we include Guzik’s index, Porta’s index, Costa’s index, based on complex networks measures, Multiscale time irreversibility index and based on permutation patterns measures. Our study presents that the corresponding measures can be used as indicators or indicator-precursors of crisis states in stock markets.

Cryptocurrencies refer to a type of digital asset that uses distributed ledger, or blockchain technology to enable a secure transaction. Like other financial assets, they show signs of complex systems built from a large number of nonlinearly interacting constituents, which exhibits collective behavior and, due to an exchange of energy or information with the environment, can easily modify its internal structure and patterns of activity. We review the econophysics analysis methods and models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. Quantitative measures of complexity have been proposed, classified, and adapted to the cryptocurrency market. Their behavior in the face of critical events and known cryptocurrency market crashes has been analyzed. It has been shown that most of these measures behave characteristically in the periods preceding the critical event. Therefore, it is possible to build indicators-precursors of crisis phenomena in the cryptocurrency market.