Using of Fractal Analysis and Artificial Neural Networks to Build a Mathematical Model for Determining Trends

Abstract

In modern society, it is difficult to overestimate the impact of information on economic processes. Due to the evolution of global networks and communications, appearing of any information (including false) in the media, can have a significant impact on financial markets. Therefore, the possession of correct and relevant data is important for all players on the burse. The more complete information about an asset will have a financial investor, the more accurate predictions for the future he can build. Forecasting, in turn, requires the use of various mathematical and economic models, which based on both theoretical information on the mechanisms of market processes and practical knowledge of the market, obtained from experience. The methods of statistical analysis are the most common ways to study time and finance series. This paper contains a description of the methodology to determine the state of the currency market based on the use of fractal and cluster analyzes. As an example, the quotes of the single European currency (euro) against the Russian ruble for the period from 2010 to 2017 were investigated. The authors reviewed the behavior of the euro price and calculated the monthly fractal dimensions for the corresponding time series in order to identify their relationship with the trends. Then a cluster analysis was carried out using artificial neural network technology, which revealed various types of situations (trends) emerging on the currency market: stability, pre-crisis period and crisis situations. Testing of the built mathematical model for determining the trends was carried out by using information about euro rates for the first 8 months of 2018 year. Theoretical studies in conjunction with the obtained results made it possible to conclude, that the method proposed by the authors for determining the situation on the financial market is universal and can also be used to analyze the behavior of the securities rates.