Modeling Nonlinear and Time-Varying Price Discovery: A Novel Granger Causality Framework Based on Distributional Forecasting

The price-leadership relationship between stock index futures and spot markets is crucial for assessing market efficiency and implementing risk management. Traditional Granger causality tests based on conditional methods cannot capture their nonlinear and time-varying characteristics. In this study, we innovatively construct a Granger causality testing framework based on distributional forecasting. By integrating nonlinear modeling, time-varying volatility estimation, and rolling-window distributional forecasting techniques, the framework identifies and characterizes the price-leadership mechanism from the perspective of out-of-sample forecast performance improvement. Monte Carlo simulations verify that the proposed test possesses desirable finite-sample properties. An empirical study of China’s CSI 300 stock index futures and spot markets reveals a significant bidirectional nonlinear leadership relationship with distinct time-varying features. Specifically, futures lead spot through linear information transmission with lags of three to four periods, whereas spot leads futures through a rapid one-period impact and continuous feedback with lags of three to four periods. The seemingly counter-intuitive three- to four-day lag is attributable to daily price limits, a retail-dominated investor structure, and arbitrage constraints. Cross-market transmission is dominated by linear spillovers, whereas nonlinear effects are primarily internalized within each market’s respective volatility structure. This study not only transcends the classical linear and static analysis paradigm but also provides new methodological support and a decision-making basis for optimizing dynamic hedging strategies and cross-market risk early warning.