A STUDY OF CHAOS THEORY IN CRYPTOCURRENCY MARKETS

The growth of cryptocurrencies as financial instruments have raised questions about modelling their markets due to a high volatility and speculative nature. This study investigates the presence of deterministic chaos in the daily price movements of Bitcoin (BTC), Ethereum (ETH), and Solana (SOL), from April 2020 to February 2025. Employing a multi-faceted methodological approach, the study conducted Brock-Dechert-Scheinkman (BDS) tests for non-linearity, calculated the Largest Lyapunov Exponents (LLE) to gauge sensitivity to initial conditions, performed Recurrence Quantification Analysis (RQA) to detect deterministic structure, and derived Hurst Exponents to assess long-term memory. Post-filtering, significant non-linearity persisted in the BDS test. LLEs indicated dynamics at the “edge of chaos,” but RQA and Hurst Exponents revealed strong deterministic structures. Collectively, these results reveal characteristics of a low-dimensional chaotic system, challenging the random walk hypothesis and implying a degree of short-term predictability with significant implications for quantitative finance and regulation.