Nonlinear Dynamics and Chaos Analysis of Nigerian Agricultural Commodity Price Series

Agricultural commodity prices in Nigerian markets are characterised by episodic turbulence that disrupts food security and farmer income planning, yet the underlying dynamic structure of these price series remains analytically underexplored in the Nigerian mathematical modelling literature. This study applies nonlinear time series analysis and chaos theory methods to examine the dynamic properties of monthly prices for cassava, yam, beans, and palm oil from markets across the six geopolitical zones over the period January 2014 to December 2023. Phase space reconstruction using delay embedding, estimation of the largest Lyapunov exponent, computation of the correlation dimension, and Brock-Dechert-Scheinkman nonlinearity tests are applied systematically to each price series. Results confirm nonlinearity in all four commodity price series, with positive Lyapunov exponents of 0.31 to 0.48 bits per unit time indicating sensitive dependence on initial conditions consistent with low-dimensional chaos. Correlation dimensions between 2.1 and 3.4 indicate that the underlying attractor dynamics are governed by two to three effective degrees of freedom. Surrogate data testing confirms that the chaotic signatures are not artefacts of nonlinear monotonic transformation of a linear process. These findings imply that short-horizon price forecasting is feasible through nonlinear local approximation methods, while long-run deterministic prediction is fundamentally bounded by the chaotic nature of the dynamics. Keywords: chaos theory, Lyapunov exponent, agricultural commodity prices, nonlinear dynamics, Nigeria.