Abstract

Price series that are 21.5 years long for six agricultural futures markets, corn, soybeans, wheat, hogs, coffee, and sugar, exhibit time-varying volatility, carry long-range dependence, and portray excessive skewness and kurtosis, though they are covariance stationary. This suggests that the series contain nonlinear dynamics. ARCH and long memory are the two stochastic nonlinear models that are able to produce these symptoms. Though standard ARCH tests suggest that all series might contain ARCH effects, further diagnostics show that the series cannot be ARCH processes. The martingale difference null cannot be rejected by the ARCH model. Three long memory techniques, the classical R/S analysis, the modified R/S analysis, and the AFIMA model, are applied to test the martingale difference null against the long memory alternative. The nonparametric method, the classical R/S analysis, suggests there might be long memory structures in the series. However, two other more robust tests, the modified R/S analysis and the AFIMA model, confirm the case of sugar, but reject this proposition for the other five markets.

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