Investigating Mean Reversion Phenomenon and Forecasting Natural Gas Daily Spot Prices Using Ornstein-Uhlenbeck Mean Reverting Model

Economic growth has been tied to the growth of fuels consumption like natural gas. The inherent features of natural gas market like its dependence on wellhead price, long-distance transportation costs, gas pipeline systems, economies of scale, non-existence of monopoly market for the end user, large proportion of fixed costs compared to variable costs, relatively low income elasticities, etc., have created different market structures which affect the price (Khaleghi, 2010; Whitesitt, 2005; Mansour Kiaei, 2008). Moreover, extensive governmental interventions in gas pricing, have led to the adoption of diversified pricing systems so that there is not any global gas price (Jensen, 2011; Vafee Najjar, 2008).
The gas market has experienced dramatic changes that began with the liberalization process of the market in the 1980s, the result of which was the creation of a spot market (Jafari Samimi et al., 2007; Manzoor & Niakan, 2011; Apergis, Bowden, & Payne, 2015). This market determines the opportunities offered by firms and investors, especially the opportunity cost of stagnant assets by price detecting. Hence, spot prices estimation that uses behavioral characteristics like mean reversion can be useful in future prices evolution (Hull, 2000).
In financial economics literature, it is thought that mean reversion is a sign of inefficient market, and it runs counter to the assumption of random walk. Exley, Mehta, & Smith (2004) state that mean reversion is not necessarily a sign of inefficiency in the market. They believe that it could be due to risk aversion or return distribution over time. Since the world's most mobile gas market, which determines the basic price of the gas exchanges in other countries, including Iran, is located in the U.S. Henry Hub, this hub is being mentioned here.

Departures from normal price spreads are possible in the short run under abnormal market conditions, but in the long run, supply will be adjusted and the prices will move to the level dictated by the marginal cost of production. The basic theory of microeconomics states that in the long run, the price of an energy commodity must be related to its long-run marginal cost (Begg & Smith, 2007; Rahimi, 2008). In this paper, we analyze mean reversion, which was first described by Vasicek (1977) and was subsequently widely adapted.
Mean reversion is a normal logarithmic diffusion process, but its variance is not proportional to the incremental time intervals. The variance initially grows and then stabilizes in a certain amount (Geman, 2005; Wittig, 2007). This process has contains two components: the first one indicates drift with rate of mean reversion speed and equilibrium long run mean, and the second component of this process is diffusion term and shows its randomness.

This paper aims at mean reversion verification, estimating Ornstein-Uhlenbeck Mean Reverting Model (OUMRM) and forecasting gas daily prices based on Henry Hub data (07/01/1997-20/03/2012). Using different mean-reverting statistics like Unit-Root, autocorrelation coefficients reveal that price returns of natural gas prices do not follow a random walk process. Therefore, there can be a sign of mean reversion. The non-decreasing gradual correlation coefficients of returns indicate that the historical information available in long-term lags can be effective in determining future prices like information in the short-term lags.
The results show the existence of mean reversion using the methods of linear regression and maximum likelihood. The long-run mean price is 4.16 $/mmBtu and it takes the market around 48 weeks to remove daily price shocks. Finally, it is observed that performance evaluation criteria are highly dependent on the number of random simulation paths and the best performances are satisfied with 1000 simulation paths mean.

Energy price changes and volatilities have led to an increase in the uncertainty and potential value of predicted prices. Hence, providing models for accurate prediction of natural gas prices with regard to its characteristics like mean reversion is important because it can be applied to determine a wide range of regulatory decisions both on the supply and demand sides of the market. The results of this study is similar to Geman (2007), Skorodumov (2008), Cheong (2009), and Chikibvou and Chinhamu’s (2013) studies and reveas that the existence of the mean reversion phenomenon varies depending on the length of the study period.
Moreover, because of the mobility and transparency of information in gas markets in recent years, as returning to the recent periods, the mean reversion speed becomes higher. It shows higher adjusting speed of mean reversion and faster removal of price distortion caused by shocks. In addition, the more we approach to the recent years, the more long-run mean price is. This implies that investors and traders are expecting a surge in prices and the price volatility in the prices above long-run mean is higher than the prices below it. Therefore, these achievements in determining the behavior of this commodity can lead to a reduction in risk and a great help in predicting the path of the price of long-term contracts