TIME-SERIES PRICE STUDY OF CRYPTOCURRENCY: FRACTAL DIMENSIONS AND INTERPOLATION FUNCTIONS

Shubham Kumar Verma () and Salah Mahmoud Boulaaras
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Shubham Kumar Verma: School of Management, Dr. B. R. Ambedkar University Delhi, Delhi 110006, India
Salah Mahmoud Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-17

Abstract: This research primarily focuses on the volatility of cryptocurrency prices. In this study, the top five cryptocurrencies based on their market capitalization and data for the financial year 2022–2023 are considered for analysis via fractal dimensions and fractal functions, well-known tools in the subject of Fractal Geometry for measuring and modeling irregular and non-smooth phenomena. By integrating abnormal return with the capital asset pricing model, we ascertain the response of the acquiring cryptocurrency’s price. The study finds that BTC has consistency in its fluctuations, TETH has shown greater volatility over time, and ETH has shown some consistency; at α = 0.5, XRP is riskier than the others. While BNB is easily predictable at α = 0.5, it does not fluctuate in a systematic manner at α = 0.3. AAR indicates a short-term profit, while CAAR is decreasing, suggesting a long-term lack of profit. These reasons stem from investors’ increased expectations of specific strongholds in the cryptocurrency market, as well as increased investment.

Keywords: Cryptocurrency; IFS; Fractal Interpolation; α-Fractal Function; Fractal Dimension; Crypto Prices; Nonlinear Equations; Fractional Derivatives (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X2540078X

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