Abstract:

This study is devoted to development of an algorithm for identifying critical points of trend change or sharp jumps in economic systems. The time series of fractal dimension local values serves as an indicator of the economic system stability. The paper analyzes the stock quotes fractal characteristics of the five largest companies in different periods of time. The relationship between the dynamic stability violation and the fractal dimension deviation from the optimal value has been proven. These stability boundaries are built on the basis of a linearly weighted moving average and time series fractal dimension. Prediction of critical points and sharp jumps of trend is reduced to determining the intersection points of the fractal dimension local values curve with the curve of the normal system state boundaries. Threshold values of fractal dimension local values are analyzed to identify critical points. The results showed that the accuracy of determining the critical points using the fractal dimension local values increment is higher in comparison with the method of threshold values. However, the type of critical point can only be determined using the last one.