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Introduction. The crisis is virtually unpredictable, destructive and creative phenomenon, causing a huge impact on the economy of the country, which has the crisis, and the economy of the whole world. To analyze stock indices in the form of time series, statistic modeling methods are traditionally used. However, since these time series show nonlinear behaviour, and stock markets producing these series are complex systems, traditional methods do not work. Constant monitoring of the financial and economic systems is a necessity, so there is a need for the automated methods to predict such phenomena as crises. The paper proposes the use of interdisciplinary approaches, including borrowed from physics, permutation entropy, which is a new and promising method for studying long and complicated time series. Purpose. The purpose of the article is to study the behaviour of permutation entropy in pre-crisis and crisis periods on the example of generally accepted historical chronology of the crisis on stock markets and determining an opportunity of its use as an indicator-precursor of crises. Methods. To achieve this purpose, economic-physical methods (permutation entropy) and graphic-analytical method are used. Results. The paper uses real signals, namely, the index of Dow Jones Industrial Average (DJIA) of US stock market. This rather long series was not chosen by chance, but to analyze PermEn for the different states of stock market includeing 19 officially recorded crises. This allows to consider the possibility of this indicator to detect and prevent different crises according to the cause, nature and depth. We compare the dynamic of permutation entropy and source series for different parameters. We consider the characteristic sharp drop in the values of permutation entropy in pre-crisis periods. The behaviour of entropy index is characteristic and general for the considered crises. This allows to use PermEn as an indicator-precursor of a crisis. We calculate the value of permutation entropy with other parameters. We show that a significant parameter is to choose a moving window. Originality. The authors propose and practically prove the opportunity of using permutation entropy as an indicator-precursor of crisis phenomena in stock markets. Conclusions. The obtained results of the research determine the relevance of using permutation entropy as an effective tool of monitoring the state of financial and economic systems. In particular, we consider it necessary to use permutation entropy as an indicator-precursor of crises in stock market that is shown by numerous experimental results.

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Bandt, C.and B. Pompe (2002). «Permutation entropy: A natural complexity measure for time series». PhysicalReview Letters 88(17): 174102.

Veisi, I., Pariz, N., Karimpour, A. (2007). Fast and Robust Detection of Epilepsy in Noisy BEG Signals UsingPermutation Entropy. 7th IEEE International Conference on Bioinformatics and Bioengineering.

Danylchuk, H., & Lukyanchuk, O., & Soloviev, V. (2013). Entropy analysis of the global banking system.Cherkasy : Brama-Ukraine (in Ukr).

Avilov O., Popov A., & Kanaikin O. (2013). Permutation entropy of EEG signals for different sampling rateand time lag combinations. SPS-2013, 5-7 June 2013.: proceedings. – Warsaw, 2013. – ISBN 978-1-4673-6318-1

Avilov, O. O. Borovskyi, I. I., Zhukov, M. A., Ivanko, K. O., Popov, A. A. & Fesechko, V. A. (2013).«Permutation entropy of fetal heart rate with extraction of maternal heartbeats». Electronics andCommunications 5(76), 43-48.

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