Is energy risk scale Invariant? evidence from crude oil futures

This study diverges from earlier research by utilizing power-law functions to model realized variances in crude oil prices and analyzing these functions across various time scales. The findings reveal several key insights. First, uncertainty in crude oil markets exhibits fractal-like properties, manifested in scale invariant power-law behavior. Second, the estimated power-law exponent demonstrates invariance in the intertemporal dimension, a result confirmed through the test for total invariance, which did not reject the hypothesis of total invariance in power-law behavior. Third, the study provides evidence that the variance of crude oil price variance is statistically infinite, rendering sample variance estimates inherently context-dependent. Fourth, in contrast to earlier literature supporting the lognormal model, the findings decisively reject the lognormal model as a valid data-generating process for realized crude oil price variances across all time scales. These results have significant theoretical and practical implications. The fractal properties and infinite variance challenge conventional assumptions about crude oil market dynamics, while the rejection of the lognormal model highlights the need for alternative frameworks in modeling and risk management.