Investigation of the Wave Nature of the Ukrainian Stock Market

In this work we concentrate on the long-term and short term cycles of Ukrainian stock market, being based on the nonlinear approach of the analysis of open systems. First, the paper gives an algorithmic model for the investigation of the nonlinear nature of stock market, which comprises five individual stages. Then, by analyzing the Hurst coefficient for the PFTS index for the Ukrainian stock market it is shown that it is persistent, i.e. contains the fractals. As the results, a parabolic function is used for the approximation of a nonlinear trend in the PFTS series. Moreover, the major tendency of the PFTS index gives the correlation trends of "blue chips". The elimination of trends and the usage of Fourier analysis allow one to determine the long-term and short-term cycles in the index and shares. Finally, by investigating the weight of the long-term harmonics in the cyclic component of the PFTS index, the stability of Ukrainian stock market is studied in a short-time period. The application of the results involves the forecasting of the crisis points of stock market and proves the effectiveness of shareholders