What do market-calibrated stochastic processes indicate about the long-term price of crude oil?

a r t i c l e i n f o JEL classification: C52 C53 Q47 Keywords: Oil prices Futures markets Stochastic processes Kalman filter Forecasting Stochastic process models of commodity prices are important inputs in energy investment evaluation and planning problems. In this paper, we focus on modeling and forecasting the long-term price level, since it is the dominant factor in many such applications. To provide a foundation for our modeling approach we first evaluate the empirical characteristics of crude oil price data from 1990 to 2013 using unit root and variance ratio tests. Statistical evidence from these tests shows only weak support for the applicability of stationary mean-reverting type processes up through 2004, with non-stationary Brownian motion type processes becoming more plausible when the data from 2005 to 2013 is added. We then apply a Kalman filtering method with maximum likelihood approach to estimate the model parameters for both a single-factor Geometric Brownian motion (GBM) process as well as the two-factor Schwartz and Smith (2000) process. The latter process decomposes the spot price into unobservable factors for the long-term equilibrium level and short-term deviation, and it accommodates aspects of both a GBM process and a mean-reverting process. Both empirical and simulated data are analyzed with these models, and we quantify the increases in both the drift rate and volatility of these processes that result from developments in the crude oil markets since the middle of the last decade. We conclude by comparing and contrasting both historical accuracy and forecasts from the parameterized models, and show that when the emphasis is on the long-term expectations, a single factor GBM forecast may be sufficient. Given that crude oil is generally expected to play a significant role in meeting the world's energy needs for the foreseeable future, forecasting the price of this commodity will be important for planning continuing oil exploration and production investments. Additionally, oil price forecasting can provide insights for determining the potential impact of energy costs on the broader economy and developing appropriate policies for the eventual transition to alternative energy sources. These issues are more likely to depend on the long-term expectations for crude oil price rather than short-term fluctuations; therefore, a primary objective of this paper is to evaluate different approaches for developing long-term forecasts based on the most recent developments in crude oil prices. There are several different approaches to developing longer-term forecasts for commodity …