Phase distribution and phase correlation: Evidence in international financial markets

The aim of this study was to investigate phase distribution and phase correlation dynamics across international financial markets to uncover cyclical patterns, synchronization, and contagion effects. The sample financial markets were the S&P 500, DAX, Nikkei 225, FTSE 100, Shanghai Composite, BSE Sensex with daily closing prices ranging from 2018–2023. Using the Hilbert-Huang Transform complemented by Phase Concentration Index, Kuiper tests, and Granger causality, the results reveal distinct phase clustering in the Shanghai and BSE Sensex. Developed markets exhibit lower volatility clustering (S&P 500: 28% high-volatility phases) but stronger cross-market synchronization (S&P-DAX: 0.82 correlation), underscoring their interconnectedness. The S&P 500 emerges as a global anchor, Granger-causing European and Asian markets with 1.8–3.5-day lags. Crisis periods, particularly COVID-19, amplify synchronization (average correlation=0.92), while non-crisis phases show market-specific volatility (correlation=0.65). Emerging markets demonstrate regional co-movement (Shanghai-BSE: 0.73), offering diversification opportunities. The findings highlight the hierarchical structure of global markets, where developed economies drive cycles, while emerging markets remain prone to instability. This study advances phase-based methodologies as tools for systemic risk monitoring, providing insights into crisis contagion and investor strategies balancing short-term synchronization with long-term diversification.