MATHEMATICAL MODEL OF THE CURRENCY MARKET, BASED ON FRACTAL ANALYSIS AND ANN CLUSTERING ALGORITHMS
Abstract. In the modern economic situation, stock returns and the deviations like market collapses depend on many external factors. When studying financial time series, in order to build a reliable model, it is necessary to use various types of hypotheses regarding the structure of market processes. The main task of a financial investor is to search for information able to predict the immediate future of the asset being studied. Market behavior is modeled both on the basis of theoretical arguments about the nature of market processes and the experimentally gained market knowledge. Basically, the study of financial time series uses methods of statistical analysis. In this paper, a method for determining trends of a time series of financial indicators based on fractal and cluster analyzes is proposed. This
procedure was considered on the example of the study of time series of quotations of foreign currency exchange rates, in particular, the euro from 2010 to 2017. The authors found monthly fractal dimensions of the studied time series and identified the relationship between trends and fractal dimension. Next, a cluster analysis was conducted on fractal dimensions using algorithms based on the use of artificial neural networks (ANN), on the basis of which the types of trends, such as stability, pre-crisis period and crisis situations were determined. To verify the proposed algorithm for
determining the trend of a time series of financial quotations, the euro rate was considered in the period from January 2018 to August 2018. This technique, proposed by the authors for determining the types of periods of time series of financial assets and considered on the example of the euro exchange rate quotations, is universal and can be applied both for securities and financial indicators of commercial enterprises.
Keywords: fractal analysis, cluster analysis, system stability, crisis situations, artificial neural networks
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