Time Series Modeling for U.S. Natural Gas Forecasting

Faced with diminishing supplies of domestic crude oil and increased demand for energy, the US has come to rely on imported crude and domestic supplies of natural gas. During the last decade US natural gas production has risen about 10%, but it still does not succeed to meet demand. This supply shortage has resulted in significant increases in natural gas prices. We believe that developing a reliable method to forecast US natural gas production rates and reserves will benefit gas producers, consumers and policy makers. This paper presents one methodology for developing forecasting models for predicting U.S. natural gas production, proved reserves, and annual depletion to year 2025 using a stochastic (time series) modeling approach. The methodology is not mechanistic. A mechanistic model would examine individual geologic settings, exploration success, the physics of gas production, and the rate of exploitation for provinces, basins, and reservoirs. However, to do so would result in an extraordinarily massive model that would be difficult, if not impossible, to develop and use. Instead we used a simpler approach which takes advantage of established trends in easily obtained published data. Various time series models were tested and validated using data that are not used in the mathematical development of the models. Having adequately validated these time series models using historical data we believe that they can be used to make at least short time forecasts. Comparison of results of this study with other published forecast is also presented. Our forecasts show that U.S. gas production rate will maintain a production plateau of 18.7 Tcf/yr from 2005 to 2008 after which gas production will increase gradually from 19.0 Tcf/yr in 2010 to reach 22.5 Tcf/yr in 2025. We predict that U.S. gas production will have an average annual rate of increase of 0.5% from 2005 to 2015 after which the average annual rate of change of production will increase to 1.2% for the period of 2015 to 2025. Our forecasts also show that U.S. gas depletion rate will increase from 10.6%/yr in 2005 to 13.4%/yr in 2025. While the reserves discovery rate increases, U.S. gas proved reserves are predicted to increase from 197 Tcf in 2005 to 215 Tcf in 2010. Afterwards, the gas proved reserves will increase at an annual rate of 1.3% and are expected to reach 263 Tcf in 2025. Introduction The time-series analysis can be classified as descriptive, inferential, predictive, and control. Stochastic or time series models are the models for time series that are needed to achieve optimal forecasting. They are used to compute the probability of future values lying between two specified limits. Time series analysis accounts for the fact that data points taken over time may have an internal structure (such as autocorrelation, trend or seasonal variation) that should be accounted for. The usage of time series is two-fold: obtaining an understanding of the underlying forces and structure that produced the observed data, and fitting the model for forecasting. There are many e-journal of petroleum management and economics http://petroleumjournals.com Page 2 of 17 (page number not for citation purposes) methods that are used to model and forecast time series. The most common classes of time series methods are the autoregressive integrated moving average (ARIMA) models, developed by Box and Jenkins, and often referred to as Box-Jenkins models. The ARIMA approach has become popular in many areas and research practice confirms its power and flexibility. The basic assumption of ARIMA methodology is that the past behavior of the actual time series will continue into the future. The ARIMA method is appropriate only for a stationary time series, meaning that the mean, variance, and autocorrelation of the series should be approximately constant through time. It is also assumed that the values of the estimated parameters are constant throughout the series. The following section describes the Box-Jenkins models. Moving Average Model The moving average (MA) model describes a time series that is a linear function of the current and previous random shocks (e). The random shocks are also called errors, residuals or a white noise process. A time series, xt, is said to be a moving average process of order q, MA(q), if q t q t t t t x − − − − ⋅ ⋅ ⋅ − − − = e θ e θ e θ e 2 2 1 1 , ..... .. (1) where xt is the current value of time series data; et, et-1, et-2, et-q the current and previous errors or random shocks; and θ1, θ2, θq the moving average model parameters. Autoregressive Model A time series is said to follow an autoregressive (AR) model of order p if the current value of the series can be expressed as a linear function of the previous values of the series plus a random shock term. The general equation of an autoregressive model of order p, AR(p), can be written as t p t p t t t x x x x e φ φ φ + + ⋅ ⋅ ⋅ ⋅ ⋅ + + = − − − 2 2 1 1 , ... (2) where φ1, φ2, φp are the autoregressive model parameters. Autoregressive Moving Average Model While the AR and MA models can be used for many data sets, they are not adequate for some data, and a more general set of models is needed. The autoregressive moving average (ARMA) models contain both AR and MA processes. Alternatively, a time series xt is said to follow an autoregressive moving average model of orders p and q, ARMA(p,q), if xt satisfies the following difference equation q t q t t t p t p t t t x x x x