Numerical algorithm for neural network recognition of persistent and antipersistent market conditions

Background. In the last century, Hearst proposed his own statistical indicator, exploring the history of the Nile floods. Unfortunately, the Hurst index is insensitive to the sign of the correlation coefficients between the analyzed data and the time scale. As a result, the Hearst indicator alone is not enough for reliable statistical analysis: market data, data from complex social systems, biometric data of people. The purpose of the work is to synthesize a neural network generalization of the Hurst index (the Hurst neuron is amplified by two additional neurons). This makes it possible to distinguish between persistent and anti-persistent market conditions, as well as to evaluate the coherence indicator of transients in a particular complex system. Materials and methods. It is proposed to programmatically mark up market data into sections corresponding to a “bearish” trend of falling prices or a “bullish” trend of rising prices. Through numerical experiment, it is shown that positively correlated persistent market data always have a more likely state of “bullish” price increases. For the anti-persistent market, the opposite situation is observed with the predominance of “bearish” trends in falling prices. Results. It is proposed to evaluate the indicator of market coherence due to its non-stationary component by taking into account the statistics of the random change of the persistent state of the market to the anti-persistent one. Conclusions. It is assumed that the persistent and antipersistent states and the persistent distribution of the empirical Hurst index should be described in two different scales, each of which is obtained by a mirror image from the point of ideal white noise.