Nonlinear State‐Dependent Transmission of Climate, Energy, and Fertilizer Shocks to Global Grain Markets: A BART–TVP‐VAR Connectedness and Food‐Price Early‐Warning Framework

This study develops a nonlinear, state-dependent framework for measuring and forecasting shock transmission across global grain markets. Monthly World Bank Pink Sheet prices for maize, U.S. hard red winter wheat, Thai 5% rice, soybeans, and soybean meal are combined with crude-oil returns, a fertilizer-price index, and the Oceanic Niño Index from January 1990 to December 2025. The proposed state-conditioned Bayesian additive regression-tree time-varying vector autoregression (SC-BART–TVP-VAR) treats energy, fertilizer, and climate conditions as lagged effect modifiers of a nonlinear grain-return system. Local posterior Jacobians translate the BART response surface into time-varying propagation matrices; generalized forecast-error variance decompositions then yield total, directional, and net connectedness without recursive ordering. A complementary linear VAR, rolling VAR, regime summaries, and chronologically separated out-of-sample forecasts provide transparent benchmarks. The linear full-sample total connectedness index is 33.44%, whereas the nonlinear local index averages 35.46% and ranges from 31.21% to 57.72%. Rice remains the most segmented market in the linear system, while soybean-related markets form the strongest bilateral transmission channel. High climate states are associated with greater rolling connectedness, but energy and fertilizer regimes do not generate uniformly larger spillovers. Out-of-sample BART forecasts yield lower RMSE than the linear VAR for all five commodities in the common holdout, although RF is slightly better for maize and none of the BART–VAR or BART–RF Diebold–Mariano comparisons are significant at the 5% level. The findings therefore support a state-dependent early-warning interpretation and competitive nonlinear forecasting rather than a claim of universal statistically significant superiority. The framework contributes a reproducible bridge between flexible Bayesian prediction, dynamic connectedness, and food-price surveillance, while retaining explicit safeguards against look-ahead bias and causal overstatement.