A metric and topological analysis of determinism in the crude oil spot market

a r t i c l e i n f o We test whether the spot price of crude oil is determined by stochastic rules or exhibits deterministic endog-enous fluctuations. In our analysis, we employ both metric (correlation dimension and Lyapunov exponents) and topological (recurrence plots) diagnostic tools for chaotic dynamics. We find that the underlying system for crude oil spot prices (i) is of high dimensionality (no stabilization of the correlation dimension), (ii) does not exhibit sensitive dependence on initial conditions, and (iii) is not characterized by the recurrence property. Thus, the empirical evidence suggests that stochastic rather than deterministic rules are present in the system dynamics of the crude oil spot market. Recurrent plot analysis indicates that volatility clustering is an adequate, but not complete, explanation of the morphology of oil spot prices. In this study, we research the issue of deterministic chaos in crude oil spot prices employing both metric and topological diagnostics. Chaos refers to bounded steady-state behavior that is not an equilibrium point, not quasi-periodic, and not periodic. Certain parameteri-zations of nonlinear difference equations or systems of at least three nonlinear differential equations can produce chaotic behavior. Sensitive dependence on initial conditions is the distinctive feature of chaotic dynamical systems. This property means that nearby points become exponentially separated in finite time (repelling trajectories), which makes the evolution of those systems very complex and essentially random by standard statistical tests. Combined with measurement limitations of the current (initial) state, sensitive dependence places an upper bound on the ability to forecast chaotic systems, even if the model is known with certainty. Predictability (ordered motion) is possible only on short time scales. In search of a deeper understanding of the underlying laws of motion , chaotic dynamical analysis has extensively been applied in economic and financial systems. The concepts of self-generating dynamically complex structures and limited forecasting ability have a strong appeal for financial behavior. For review of theoretical modeling and empirical applications of chaos and complex dynamics in economics and finance, see Baumol and Benhabib (1989), LeBaron (1994), and Puu (2000), to mention a few. Crude oil is the world's most actively traded commodity in both volume and value. A significant academic literature points to the importance of oil prices for economic activity as large and protracted increases in the price of oil have been typically associated with sharp downturns in economic activity and high inflation …