The dynamics of a nonlinear relationship between crude oil spot and futures prices: A multivariate threshold regression approach

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This paper segments daily data from January of 1986 to April of 2007 into three periods based on certain important events. Both periods I and II indicate that the spot prices in general are higher than futures prices as was well-known in the literature. Only period-III (2001/9/11–2007/4/30) displays a reverse phenomenon: futures prices, in general, exceed spot prices. When the absolute value of a basis (futures-spot) is greater than the threshold value in the arbitrage area (regime 1 and 3), at least one of the error correction coefficients, representing adjustment towards equilibrium, is statistically significant. That is, there exists a tendency in the oil market in which prices move toward equilibrium. With respect to the short-run dynamic interaction between spot price change (Δ s t ) and futures price change (Δ f t ), our results indicate that when the spot price is higher than futures price, and the basis is less than certain threshold value (regime 3), there exists at least one causal relationship between Δ s t and Δ f t . Conversely, when the futures price is higher than spot price and the basis is higher than certain threshold value (regime 1), there exists at least one causal relationship between Δ s t and Δ f t . Finally, we use the method suggested by Diebold and Mariano [Diebold, Francis X., Mariano, Roberto S., 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics 13 (3), 253–263] to compare the predictive power between the linear and nonlinear models. Our empirical results indicate that the in-sample prediction of the nonlinear model is clearly superior to that of the linear model.