Research of Real Fractals of Leading Indicators

The article explores the applicability of fractal analysis in sociology and stock market analytics. The author considers the possibility of using the fractal principle to  study socio-economic indicators  and  forecast  stock market  activity. The purpose of the study is to demonstrate the potential of fractal methodology as an interdisciplinary analysis tool combining sociological observations, economic indicators and technical methods of stock market analysis. Main tasks: to analyze the theoretical foundations of the fractal approach; to identify the features of fractal structures in social and economic processes; to evaluate the effectiveness of fractal analysis in comparison with traditional methods of stock forecasting. The methodology includes: a review of the scientific literature on fractal analysis in finance and sociology; application of the concept of scalable invariance and fractional dimension; correlation analysis of dynamic series; modeling cyclic fractality on different horizons of expectations (micro, media and macrocycles). Results: The cyclical nature of social fractals and their ability to form sequences on the curve of median values of indicators have been confirmed. The scalability of fractal structures has been revealed, which makes it possible to expand the horizon of forecasting leading indicators. The correlation coefficient of dynamic series is calculated, demonstrating the stability of similarity regardless of the expectation horizon. It is shown that microcycles show a higher similarity to macrocycles, while the similarity to media cycles is less pronounced. Conclusions. Fractal analysis has advantages over traditional stock analysis methods (technical, fundamental) due to the numerical estimation of the probability of events, the volatility vector, the designation of trend reversal periods, and the scalability of invariants. The method is promising for macroeconomic forecasting, strategic planning and risk management, especially in combination with other indicators. However, fractal analysis is not universal: its effectiveness depends on the context and requires consideration of limitations (for example, the relativity of social time, the multifractality of data). The practical significance lies in the possibility of using fractal models to: refine stock forecasts; synthesize leading data; fill in the information gaps between regular reports (weekly, monthly).

1. Mandelbrot B., Hudson R. L. (Not)compliant markets. Fractal revolution in finance. Moscow: Williams; 2006. 408 p. URL: https://archive.org/details/20250615_20250615_1132 (In Russ.).

2. Peters E. Fractal analysis of financial markets. Application of chaos theory in investments and economics. Moscow: Internet Trading; 2004. 304 p. URL: https://archive.org/details/fractalmarketana0000pete (In Russ.).

3. Shannon B. Technical Analysis Using Multiple Timeframes. 2008. URL: https://oceanofpdf.com/authors/brian-shannon/pdf-technical-analysis-using-multiple-timeframes-download/

4. Zhukov D. S., Lyamin S.K. Methodology of fractal modeling in historical, political science and other social research: features of the conceptual and analytical apparatus. Bulletin of Tambov State University. Series: Humanities. 2010;7(87):223-234. URL: https://www.elibrary.ru/msvjtf (In Russ.).

5. Serikov A. E. Fractal analysis of time series. Sociology: methodology, methods, mathematical models. 2006;22:162-183. URL: https://www.elibrary.ru/kvkiup (In Russ.).

6. Dubovikov M.M., Kryanev A.V., Starchenko N.V. Index of variation and fractal analysis of time series. In collection: Scientific session of MEPhI 2004. Vol. 7: Astrophysics and Cosmophysics. Problems of modern mathematics. Beam physics and accelerator technology. 2004. URL: https://scipeople.ru/publication/61054/?ysclid=mlf24pgbdq688239033 (In Russ.).

7. Vinberg E. B. On non-Euclidean geometry. Mathematical education. 2021;3(27):29-40. URL: https://www.mathnet.ru/links/e9bf08d0c0633401ef58d725e327b182/mp994.pdf (In Russ.).

8. Perepelitsa V. A., Tambieva D. A., Komissarova K. A. Investigation of the R/S trajectory of one insurance time series. Researched in Russia. 2004;7:2663-2672. URL: http://zhurnal.ape.relarn.ru/articles/2004/248.pdf (In Russ.).

9. Gregory-Williams J., Williams B. Trading Chaos: Applying Expert Techniques to Maximize Your Profits. 1958. URL: https://archive.org/details/tradingchaosappl0000will/page/n5/mode/2up

10. Almazov A. A. Fractal theory of the Forex market. Moscow: Admiral Markets; 2009. 296 p. URL: https://rusneb.ru/catalog/004796_000040_TVERS-RU%7C%7C%7CTOUNB%7C%7C%7CBIBL%7C%7C%7C96508/?ysclid=mlf0yswonc151853516 (In Russ.).

11. Davydov A.A. Modular theory of society. Problems of theoretical sociology. Issue. 2. Collection of articles. Saint Petersburg: St. Petersburg University Press; 1996. URL: https://spblib.ru/en/catalog/-/books/12280856modul-naya-teoriya-sotsiuma?ysclid=mlf2ehtuyo838806930 (In Russ.).

12. Varyash I.Y. Research of the model of leading indicators of investment conditions. Banking business. 2022;21:13-21. URL: https://www.elibrary.ru/kiywxr (In Russ.).

13. Burova T. F., Varyash I.Yu., Panasenko K. K. Research of models of leading indicators of financing conditions. CHRONOS. 2019;11(98):100-114. URL: https://www.elibrary.ru/njzzlv (In Russ.).

14. Elokhova O.I. Fractality of virtual reality. Bulletin of the Bashkir State University. 2014;19(1):210-214. URL: https://www.elibrary.ru/xhoqmr (In Russ.).

15. Makarov S.V. Great Russian sociomaterial matryoshka. History and historical memory. 2024;28-29:11- 24. URL: https://www.elibrary.ru/olfazg (In Russ.).

16. Kolmogorov A.N. On the representation of continuous functions of several variables by superpositions of continuous functions of a smaller number of variables. Reports of the USSR Academy of Sciences. 1956;108:179-182. URL: https://bigenc.ru/b/o-predstavlenii-nepreryvny5e6285?ysclid=mlf1zpkbty280921913 (In Russ.).