From Close-to-Open to Open-to-Close: Multifractal Signatures and Cross-Scale Dependence Across International Equity Indices

Abstract Using daily data for major global equity indices over 2010–2025, this study decomposes close-to-close price changes into an overnight opening gap (diffrate) and an within-session return (intradayrate), and quantifies their multiscale structure using Multifractal Detrended Moving Average analysis (MFDMA) and Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). We document three robust patterns. First, the overnight component is typically more persistent and more heterogeneous: MFDMA estimates show higher h (2) and larger multifractality proxies for diffrate in most markets, consistent with information accumulation and cross-market spillovers being compressed into a single opening price-discovery event. Second, intraday and overnight dynamics are nontrivially coupled: within-index MF-DCCA yields cross-Hurst exponents centered around h xy (2) ≈ 0.49, and the cross-exponent declines monotonically as q increases, indicating tighter coupling in calm regimes than during extreme co-movements. Third, international comovement is stronger in opening gaps than in intraday returns, suggesting that global information is synchronized primarily at the open, while continuous trading reflects more local microstructure and liquidity conditions. Clustering based on multifractal signatures further reveals richer regime heterogeneity overnight than intraday.