Revealing dynamic intrinsic temporal and spatial scale characteristics of oil price volatility in bubble and non-bubble periods

This paper is to reveal the dynamic characteristics of crude oil price bubble volatility from intrinsic temporal and spatial scales. For this purpose, volatility series is mapped to the dynamic model described by the Langevin equation viewed from mathematical differentiation. And the Backward Sup Augmented Dickey-Fuller is used to divide the bubble and non-bubble period. In the intrinsic temporal scale, volatility always has no long-term memory and is more volatile in the bubble period. The intrinsic time of crude oil price fluctuations varies proportionally with trading time. In the spatial scale, the range of price fluctuations during bubbles is smaller.