Crude Oil and Natural Gas

Econbrowser has the explanations and the equations.

"Let Δo_t denote the monthly percent change in in oil prices (technically, the change in the natural logarithm) and z_t the percentage gap in cost (technically, z_t = ln(o_t/6g_t)). If you use a regression to try to predict oil prices from their own lagged values and the lagged oil-gas cost gap, a positive gap such as we have at the moment does tend to tug down future oil prices slightly, though the coefficient is not statistically significant. Here are the regression coefficients, with standard errors in parentheses:

On the other hand, the cost gap does seem to help significantly to predict where natural gas prices might go. With the gap currently at z_t = 1.13, the historical regression below might lead you to expect natural gas prices to climb by 10% a month (0.103 x 1.13 = 0.116) until the gap is closed.

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