Predicting Oil and Gas Spot Prices Using Chaos Time Series Analysis and Fuzzy Neural Network Model.
Authors: Agbon I.S. , Araque J.C. 
Published: December 2007

Abstract
The non-linear nature of historical oil and gas spot prices makes prediction very difficult. An evaluation of historical time series spot prices data with Fourier power spectrum analysis and autocorrelation function shows the likelihood of chaotic behavior. Characterization and identification of the data with the Lyapunov exponent suggest the existence of chaos. A chaos theory analysis is therefore used for the space phase reconstruction of the strange attractors in the oil and gas markets. The optimal embedding dimension, time delay and predictability are obtained with a spatial minimization of the root mean square error. The embedding dimension and time delay are then used as inputs in a fuzzy neural network model.
The time series spot price data is embedded and divided into training and testing sets. A fuzzy neural network model is constructed using the training set and checked with the testing set. A good match is obtained between the predicted and historical time series data. The paper concludes that the chaotic behavior of the historical oil and gas spot prices prevents the long-term forecast of future spot prices and limits the short-term forecast to the embedding prediction horizon.

Introduction
A good estimate of future oil and gas prices is essential to the economic evaluation of oil and gas projects. It is also necessary for planning purposes in public institutions, national budgets of producing nations, financial institutions and future markets. In the past, linear models were used to forecast oil and gas prices. These models assumed monotonic increases based on historical trends. A sensitivity analysis was done with an optimistic case, most likely case (historical averages) and a pessimistic case1. Some of these models were based on price elasticity analysis. For example, Roberts2 argued that price elasticity and economic growth affected the direction of oil prices. He therefore developed a model with price elasticity and energy intensity as input variables. Inikori et al.3 also used price elasticity and supply demand balances as input variables. A linear regression model of lagged world/US drilling rig count was used for the forecasting. However, historical oil and gas prices are not constant nor do they increase monotonically.
Price data show fluctuations and seems to be influenced by political events, supply, demand, technological changes, environmental concerns and inventories. Caldwell and Heather4 concluded that crude oil price has a stochastic nature and behaved as if it was normally distributed most of the time. However, it sometimes behaved in a nonlinear manner. Skov5 thought that large fluctuations in oil prices could occur because prices were not only determined by supply and demand but also by technology, culture, resource base, consumption patterns and population growth. Linear models were therefore most likely to give incorrect crude oil price forecasts. Dougherty6 advises that we should be concerned about the danger of linearity. He argued that the primary determinant of oil price was oil supply (the amount of oil offered for sale). He also focused on price elasticity because small changes in supply generated large changes in prices. He advocated a compressive analysis of production, reserves and cash flow in order to understand the impact of a price change.
Linear models are based on the assumption that in a system, similar conditions generate similar responses when subjected to similar stimuli. Forecasting uses observed behavior of the system to predict future outcomes given similar conditions. Unfortunately, most linear forecast of commodity prices do not reflect their historical behavior. This is probably because economic systems have many autonomous variables including human agents who sometimes behave differently under similar stimuli. There is the probability of nonlinearity in the historical price data of many commodities.