Complexity, Chaos, and the Duffing-Oscillator Model: An Analysis of Inventory Fluctuations in Markets

Apparently random financial fluctuations often exhibit varying levels of complexity, chaos. Given limited data, predictability of such time series becomes hard to infer. While efficient methods of Lyapunov exponent computation are devised, knowledge about the process driving the dynamics greatly facilitates the complexity analysis. This paper shows that quarterly inventory changes of wheat in the global market, during 1974-2012, follow a nonlinear deterministic process. Lyapunov exponents of these fluctuations are computed using sliding time windows each of length 131 quarters. Weakly chaotic behavior alternates with non-chaotic behavior over the entire period of analysis. More importantly, in this paper, a cubic dependence of price changes on inventory changes leads to establishment of deterministic Duffing-Oscillator-Model(DOM) as a suitable candidate for examining inventory fluctuations of wheat. DOM represents the interaction of commodity production cycle with an external intervention in the market. Parameters obtained for shifting time zones by fitting the Fourier estimated time signals to DOM are able to generate responses that reproduce the true chaotic nature exhibited by the empirical signal at that time. Endowing the parameters with suitable meanings, one may infer that temporary changes in speculation reflect the pattern of inventory volatility that drives the transitions between chaotic and non-chaotic behavior.