Non-Gaussian statistics of oil pricing time-series: A case study

The stochastic nature of oil price fluctuations is investigated over a twelve-year period, borrowing feedback from an existing database (USA Energy Information Administration database, available online). We evaluate the scaling exponents of the fluctuations by employing different statistical analysis methods, namely rescaled range analysis (R/S), scale windowed variance analysis (SWV) and the generalized Hurst exponent (GH) method. Relying on the scaling exponents obtained, we apply a rescaling procedure to investigate the complex characteristics of the probability density functions (PDFs) dominating oil price fluctuations. It is found that PDFs exhibit scale invariance, and in fact collapse onto a single curve when increments are measured over microscales (typically less than 30 days). The time evolution of the distributions is well fitted by a Lévy-type stable distribution. The relevance of a Lévy distribution is made plausible by a simple model of nonlinear transfer. Our results also exhibit a degree of multifractality as the PDFs change and converge toward to a Gaussian distribution at the macroscales.