Financial dynamics and interconnectedness between layer-1 and layer-2 blockchains

This study investigates the financial dynamics and interdependencies between Layer-1 (L1) blockchains (Bitcoin and Ethereum) and their respective Layer-2 (L2) solutions through the lens of multifractal analysis. Using high-frequency 15-minute price data from leading L2 projects (including Arbitrum, Immutable, Loopring, Metis, Mantle, Skale, Polygon, Stacks), we examine both univariate multifractality and bivariate cross-correlations. The results reveal that L1 and L2 cryptocurrencies exhibit significant nonlinear dependencies and multifractal characteristics across different moments and time scales. Specifically, while persistent cross-correlations dominate under small market fluctuations, extreme fluctuations are marked by anti-persistent dynamics. The strength of multifractality is found to vary across pairs, with ETH-linked L2 solutions (particularly Arbitrum and Immutable) demonstrating the most pronounced multifractal behavior. Moreover, shuffled and surrogate tests confirm that the sources of multifractality primarily stem from long-memory effects and heavy-tailed distributions, indicating an empirical rather than intrinsic form of multifractality. These findings provide novel insights into the complexity of blockchain ecosystems, offering implications for portfolio diversification, systemic risk assessment, and the financial viability of L2 scalability solutions.