Abstract: V. Soloviev, O. Serdiuk, S. Semerikov, A. Kiv (2020)

The article considers the possibility of analyzing the dynamics of changes in the characteristics of time series obtained on the basis of recurrence plots. The possibility of using the studied indicators to determine the presence of critical phenomena in economic systems is considered. Based on the analysis of economic time series of different nature, the suitability of the studied characteristics for the identification of critical phenomena is assessed. The description of recurrence diagrams and characteristics of time series that can be obtained on their basis is given. An analysis of seven characteristics of time series, including the coefficient of self-similarity, the coefficient of predictability, entropy, laminarity, is carried out. For the entropy characteristic, several options for its calculation are considered, each of which allows the one to get its own information about the state of the economic system. The possibility of using the studied characteristics as precursors of critical phenomena in economic systems is analyzed. We have demonstrated that the entropy analysis of financial time series in phase space reveals the characteristic recurrent properties of complex systems. The recurrence entropy methodology has several advantages compared to the traditional recurrence entropy defined in the literature, namely, the correct evaluation of the chaoticity level of the signal, the weak dependence on parameters. The characteristics were studied on the basis of daily values of the Dow Jones index for the period from 1990 to 2019 and daily values of oil prices for the period from 1987 to 2019. The behavior of recurrence entropy during critical phenomena in the stock markets of the USA, Germany and France was studied separately. As a result of the study, it was determined that delay time measure, determinism and laminarity can be used as indicators of critical phenomena. It turned out that recurrence entropy, unlike other entropy indicators of complexity, is an indicator and an early precursor of crisis phenomena. The ways of further research are outlined.

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Recurrence plot-based analysis of financial-economic crashes