This paper studies the extreme dependencies between energy, agriculture and metal commodity markets, with a focus on local co-movements, allowing the identification of asymmetries and changing trend in the degree of co-movements. More precisely, starting from a non-parametric mixture copula, we use a novel copula-based local Kendall's tau approach to measure nonlinear local dependence in regions. In all pairs of commodity indexes, we find increased co-movements in extreme situations, a stronger dependence between energy and other commodity markets at lower tails, and a 'V-type' local dependence for the energy-metal pairs. The three-dimensional Kendall's tau plot for upper tails in quantiles shows asymmetric co-movements in the energy-metal pairs, which tend to become negative at peak returns. Therefore, we show that the energy market can offer diversification solutions for risk management in the case of extreme bull market events.
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