Universality and Heterogeneity of Stylized Facts in Cryptocurrency and Equity Markets

This study investigates whether the macroscopic statistical maturity of cryptocurrencies implies dynamical equivalence with traditional equity markets. We analyze high-frequency data (2020--2025) using the Complexity--Entropy Causality Plane (CECP) and directed horizontal visibility graphs (directed HVG) to uncover complex temporal patterns and time-directed structures in the return series. While conventional stylized facts show striking convergence across all assets, structural diagnostics reveal a compelling paradox: cryptocurrencies appear more locally random than the equity benchmark during ordinary periods, yet exhibit significantly stronger directional time-irreversibility around high-visibility return events. The absolute-return results show that large cryptocurrency fluctuations tend to begin abruptly and remain elevated afterward. Separate analyses of positive returns and negative-return magnitudes show that this pattern is shared across cryptocurrencies on the upside but varies across assets on the downside. We conclude that statistical maturity is only skin-deep; the underlying dynamical processes of mature cryptocurrencies remain fundamentally distinct from traditional benchmarks.