# State Space Model of Brent Oil Price Dynamics

### Abstract

The constant concern in commodities market, particularly in oil price, has necessitated accurate models to aid in the generation of relatively good synthetic oil price data. Oil prices are subject to high volatility and its impact on economic growth has continued to generate controversies among economic researchers and policymakers. In this paper, a state space model approach was developed to describe the dynamics of Brent crude oil prices. The dynamics were examined as a continuous time stochastic process generalized as an Ornstein-Uhlenbeck equation. The result revealed that the dynamic behaviour of Brent oil price is an Ornstein-Uhlenbeck equation depicting a mean reversion process in crude oil prices. The process is stationary Gauss-Markov process and is the only nontrivial process that satisfies the conditions of allowing linear transformations of the space and time variables. The Ornstein-Uhlenbeck process in this paper is considered as the continuous time analogue of the discrete-time autoregressive process of order one (AR(1)).

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*International Journal of Mathematical Analysis and Optimization: Theory and Applications*,

*2019*(2), 571 - 580. Retrieved from http://jsrd.unilag.edu.ng/index.php/ijmao/article/view/544