Regime Discovery and Intra-Regime Return Dynamics in Global Equity Markets

Financial markets alternate between tranquil periods and episodes of stress, and return dynamics can change substantially across these regimes. We study regime-dependent dynamics in developed and developing equity indices using a data-driven Hilbert--Huang-based regime identification and profiling pipeline, followed by variable-length Markov modeling of categorized returns. Market regimes are identified using an Empirical Mode Decomposition-based Hilbert--Huang Transform, where instantaneous energy from the Hilbert spectrum separates Normal, High, and Extreme regimes. We then profile each regime using Holo--Hilbert Spectral Analysis, which jointly resolves carrier frequencies, amplitude-modulation frequencies, and amplitude-modulation energy (AME). AME, interpreted as volatility intensity, declines monotonically from Extreme to High to Normal regimes. This decline is markedly sharper in developed markets, while developing markets retain higher baseline volatility intensity even in Normal regimes. Building on these regime-specific volatility signatures, we discretize daily returns into five quintile states $\mathtt{R}_1$ to $\mathtt{R}_5$ and estimate Variable-Length Markov Chains via context trees within each regime. Unconditional state probabilities show tail states dominate in Extreme regimes and recede as regimes stabilize, alongside persistent downside asymmetry. Entropy peaks in High regimes, indicating maximum unpredictability during moderate-volatility periods. Conditional transition dynamics, evaluated over contexts of length up to three days from the context-tree estimates, indicate that developed markets normalize more effectively as stress subsides, whereas developing markets retain residual tail dependence and downside persistence even in Normal regimes, consistent with a coexistence of continuation and burst-like shifts.