Application of the Hurst coefficient, calculated with the use of the Siroky method on financial markets
Application of the Hurst coefficient, calculated with the use of the Siroky method on financial markets

Summary/Abstract: The paper analyses the Hurst exponents calculated with the use of the Siroky method in two time intervals of 625 and 1250 sessions for the group of 570 financial instruments (Warsaw Stock Exchange equities – 320, equity indexes – 7, commodities – 41, and FX market – 135). The study also covers an analysis of the normality of the distribution of logarithmic rates of return, and the verification of statistical hypotheses with the use of the following statistical tests: Jarque-Bera (JB), Shapiro-Wilk (SW), and d’Agostino-Pearson (DA).In the second part of the paper, the change of the Hurst coefficient over time was analysed, while in the third part two linear regressions of the form H(t) = a + m ∙ t were performed for each of the analysed assets, as well as the determination factor R2. This part of the study aims to answer the question whether the slope of the regression line has a positive or negative value and what the quality of such a fit is with the use of linear regression. Such an analysis enables to observe changes in the fractal dimension, and thus the risk in financial markets over a long period of time.The main conclusion that was drawn from the research may be formulated as follows: the value of the H exponents decreased in the analysed time windows, which means an increase in the fractal dimension (d), and thus the investment risk in financial markets. The obtained results can be used in the process of constructing an investment portfolio in financial markets.The research is part of the ongoing discussion on the effectiveness of financial markets.

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