"Chaos" in energy and commodity markets: a controversial matter
  We test whether the futures prices of some commodity and energy markets are determined by stochastic rules or exhibit nonlinear deterministic endogenous fluctuations. As for the methodologies, we use the maximal Lyapunov exponents (MLE) and a determinism test, both based on the reconstruction of the phase space. In particular, employing a recent methodology, we estimate a coefficient $\kappa$ that describes the determinism rate of the analyzed time series. We find that the underlying system for futures prices shows a reliability level $\kappa$ near to $1$ while the MLE is positive for all commodity futures series. Thus, the empirical evidence suggests that commodity and energy futures prices are the measured footprint of a nonlinear deterministic, rather than a stochastic, system. 
Loretta Mastroeni and Pierluigi Vellucci
q-fin.ST