Nonlinear Market Coupling During COVID-19 and the Global Financial Crisis: A Convergent Cross-Mapping Analysis of US and European Equity Indices

During financial crises, markets do not only fall or become more volatile. They may also become more dynamically coupled, with the behaviour of one market becoming more recoverable from another. The purpose of this study is to examine whether crisis periods strengthen nonlinear coupling between major US and European equity indices, using Convergent Cross-Mapping as a state-space reconstruction method. Daily log returns for the Dow Jones Industrial Average, S&P 500, FTSE 100 and DAX are analysed across pre-crisis, crisis and post-crisis windows for the COVID-19 market shock and the Global Financial Crisis. Pairwise bidirectional Convergent Cross-Mapping is used to estimate cross-map skill, convergence and directional asymmetry, with a focused lagged analysis of key transatlantic pairs during COVID-19. Cross-map skill is interpreted as the strength of the recoverable dynamical footprint between markets. The results show that nonlinear coupling, measured as recoverable dynamical information between reconstructed market states, increases during crisis phases. During COVID-19, mean late-library cross-map skill rises from the pre-crisis to the crisis period, and all tested directional relationships satisfy the convergence criterion. The Global Financial Crisis also shows increased crisis-period coupling, with stronger persistence into the post-crisis phase. Lagged COVID-19 results indicate that the strongest recoverability occurs over a short contemporaneous-to-three-trading-day alignment window. The findings position Convergent Cross-Mapping as a complementary mathematical modelling framework for identifying recoverable dynamical information between markets during financial stress.