MATHEMATICAL PREDICTION FOR SHORT PERIODS OF TIME USING THE SLIDING METHOD OF SMOOTHING THE VARIABLE DIFFERENCE "ASYMMETRIC FOUR-POINT FUNCTION"

In this article, the author proposes to include in the neural network, when predicting the next value of the time series, mathematical prediction methods by sliding smoothing with a variable difference "asymmetric four-point function". In addition, the article proposed an original and fairly simple method for setting mathematical prediction parameters by adjusting the prediction result parameters in accordance with the parameters of the original time series. Using the example of studying a sample from a numerical series of Dow Jones indices, the author shows a detailed implementation of the proposed prediction methods and a method for adjusting their characteristics. Of course, the main idea of the presented work is to optimize the use of earth resources through their mathematical prediction, which ultimately will certainly lead to an improvement in the quality of our life. The author believes that many of the quantities characterizing certain phenomena (events) can not constantly increase or decrease. As practice shows, in nature, oscillatory changes in quantities are more characteristic; they are described by a sum of harmonics with modulated values of amplitudes and phases and with the presence of a random component that cannot be described by any known mathematical functions. In other words, in some time sections (mostly linear), the least squares method works well, in others – sliding smoothing (suppression of high-frequency bursts) works, and in the third, the simplest “closest neighbour (primitive method)” is best. Therefore, each new proposed effective method of mathematical prediction is a significant contribution to the study of mathematical prediction as a branch of mathematics in general. And, as shown by the analysis of the mathematical prediction methods proposed by the author, using the example of studying the predicted values of the Dow Jones index, the methods can be practically used along with other existing mathematical prediction methods in neural networks of artificial intelligence.