Main Article Content

Oleksandr SERDIUK


This article demonstrates the possibility of constructing indicators of critical and crash phenomena in the volatile market of cryptocurrency.

The possibility of constructing dynamic measures of complexity as quantum econophysical behaving in a proper way during actual pre-crash periods has been shown. This fact is used to build predictors of crashes and critical events phenomena on the examples of all the patterns recorded in the time series of the key cryptocurrency Bitcoin, the effectiveness of the proposed indicators-precursors of these falls has been identified. From positions, attained by modern theoretical physics the concept of economic Planсk's constant has been proposed.

The theory on the economic dynamic time series related to the cryptocurrencies market has been approved. Then, combining the empirical cross-correlation matrix with the Random Matrix Theory, we mainly examine the statistical properties of cross-correlation coefficient, the evolution of the distribution of eigenvalues and corresponding eigenvectors of the global cryptocurrency market using the daily returns of cryptocurrencies price time series all over the world from 2013 to 2018.

The result has indicated that the largest eigenvalue reflects a collective effect of the whole market, and is very sensitive to the crash phenomena. It has been shown that both the introduced economic mass and the largest eigenvalue of the matrix of correlations can act like quantum indicators-predictors of falls in the market of cryptocurrencies.

Article Details

Applied Mathematics
Author Biographies

Vladimir SOLOVIEV, Kryvyi Rih State Pedagogical University

Head of the Department of Informatics and Applied Mathematics

Oleksandr SERDIUK, The Bohdan Khmelnytsky National University of Cherkasy

Department of Informatics and Applied Mathematics


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