Abstract:
In the tasks of analyzing economic or biometric data, the Hurst indicator is a functional that does not work well on small samples, which is primarily caused by the fact that it does not feel which positively or negatively corre-lated data it analyzes. It is assumed that it is possible to make the Hurst indicator sensitive to the trend sign of the analyzed data if it is evaluated separately for positive and negative regression. The aim of the article is to eliminate the uncertainty of the empirical Hurst index through reflections of values to the right and/or left of the centre of its scale. The neural network approach to estimating the regression sign of unrelated data is considered, which is based on the use of three different statistical criteria. The first criterion is based on the estimation of the mutual location of the minimum and maximum values in the analyzed sample. The second criterion is the sign of the correlation coefficient calculated by the classical Pearson-Edgeworth-Edleton formula of the late 19th century. The third criterion is the accumulated sum of differences of adjacent samples of a small sample. It is shown that the selected criteria can be represented as a network of three binary neurons responding with an output code with threefold code redundancy. Elimination of threefold redundancy of the output code allows to raise the level of reliability of the decisions made on small samples consisting of 21 experiments. The software implementation of the numerical experiment and statistical distributions of output state values of three used criteria are given. It is shown that the correlation of the responses of the three criteria considered in the paper is significantly less than the unit correlation: 0.31; 0.51; 0.61. This allows to raise the accuracy of predicting the value of the sign of the Hurst neuron index for a small sample.
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