Predicting the price of crude oil based on the stochastic dynamics learning from prior data.

Energy is vital to international trade, social security, and financial markets. Crude oil, as a non-renewable resource, is affected by complex factors. To better capture this influence, we introduce stochastic differential equations (SDEs) to depict crude oil prices. This paper establishes time-dependent linear and space-dependent nonlinear SDEs respectively. Time-dependent linear SDEs are established by recovering the drift and diffusion terms based on point estimation and sliding window. Space-dependent nonlinear SDEs are established by sparse Bayesian learning. Empirical results show that time-dependent linear SDE can better describe the actual fluctuations of historical crude oil prices, and can predict more accurately compared with constant coefficient linear SDE, namely geometric Brownian motion. The space-dependent nonlinear SDE can achieve the effect of time-dependent linear SDEs on historical data, while the former is more accurate in predicting. In addition, the former gained an in-depth understanding of the intrinsic dynamics. In summary, the models proposed in this study provide powerful tools for better understanding and predicting crude oil prices, which make a positive impact on the stability of the global economy and energy markets. [ABSTRACT FROM AUTHOR]