Modelling Long-Term Memory Dynamics of the Russian Stock Market Prices

This paper is devoted to identify the advantages of accounting for long-term memory in prediction the time series of the returns of Russian shares. The first chapter analyses the mismatch between theoretical and practical understanding of stock pricing in the Russian market. The efficient market hypothesis states that the dynamics of stocks is unpredictable and has the dynamics of random walk. However, the presence of crises and the distribution of returns with fat tails does not correspond to the premises of the theoretical hypothesis. Then an alternative hypothesis was presented, the fractal market hypothesis, which claims to have a long-term relationship (long-term memory) between observations that are far behind in time. That is why it is believed that the future share price can be predicted. The second chapter consists of substantiating the hypothesis that there is the long-term memory in the Russian stock market and identifying long-term dependence in all Russian stocks and for all intervals using R/S analysis and spectral analysis. The result is the separation of time series by the level of long-term memory. The third chapter presents the modelling of time series with different levels of long-term memory using the ARIMA, ARFIMA, ARIMA-GARCH, ARFIMA-GARCH and ARFIMA-FIGARCH models, as well as forecasting for 1, 5 and 10 days in advance. The result of forecasting is to estimate the accuracy of forecasts using the mean absolute error (MAE). In the study, it was possible to show that there is the long-term memory on the Russian stock market, and it is possible to improve the forecast accuracy when using models that take into account long-term dependence.