In this paper we study the possible "chaotic" nature of some energy and commodity futures time series (like heating oil and natural gas, among the others). In particular the sensitive dependence on initial conditions (the so called "butterfly effect", which represents one of the characterizing properties of a chaotic system) is investigated estimating the Kolmogorov entropy, in addition to the maximum Lyapunov exponent. The results obtained with these two methods are consistent and should indicate the presence of butterfly effect. Nevertheless, this phenomenon - which is usually showed by deterministic systems - is not here completely deterministic. In fact, using a test introduced by Kaplan and Glass, we prove that , for all the series analyzed here, the stochastic component and the deterministic one turn up to be approximately in the same proportions. The presence of butterfly effect in energy futures markets is a controversial matter, and the evaluations obtained here confirm the findings of some authors cited in this paper . Thus, we can say with reasonable certainty that in energy futures markets we cannot talk about deterministicbutterfly effect .
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 .
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In this paper we study the possible "chaotic" nature of some energy and commodity futures time series (like heating oil and natural gas, among the others). In particular the sensitive dependence on initial conditions (the so called "butterfly effect", which represents one of the characterizing properties of a chaotic system) is investigated estimating the Kolmogorov entropy, in addition to the maximum Lyapunov exponent. The results obtained with these two methods are consistent and should indicate the presence of butterfly effect. Nevertheless, this phenomenon - which is usually showed by deterministic systems - is not here completely deterministic. In fact, using a test introduced by Kaplan and Glass, we prove that , for all the series analyzed here, the stochastic component and the deterministic one turn up to be approximately in the same proportions. The presence of butterfly effect in energy futures markets is a controversial matter, and the evaluations obtained here confirm the findings of some authors cited in this paper
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
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we can say with reasonable certainty that in energy futures markets we cannot talk about deterministicbutterfly effect
the empirical evidence suggests that commodity and energy futures prices are the measured footprint of a nonlinear deterministic, rather than a stochastic, system