Testing the efficiency of the futures market for crude oil using weighted least squares

Abstract

It is well known that parameter estimates obtained from ordinary least squares can be distorted by outliers. Given the dramatic fluctuations observed in the price of crude oil, it is surprising that the robustness of parameter estimates has not been scrutinized more closely. This article investigates the efficiency of the New York futures market for crude oil using the basis regression. In addition to ordinary least squares, the model’s parameters are estimated using weighted least squares and trimmed least squares. The results suggest that the presence of outliers may distort parameter estimates obtained from ordinary least squares away from a finding of an inefficient futures market.

Keywords:

• crude oil
• futures market
• weighted least squares
• trimmed least squares

JEL Classification:

• C10
• G14

Notes

¹ For example, see Rousseeuw and Leroy (1987) for a discussion of this point.

² See the survey provided by Boyer et al. (2003).

³ The dropped observations are chosen based on estimation of Equation 1 using the least median of squares model of Rousseeuw (1984).

⁴ The percentage of the data set which may be composed of outliers without distorting parameter estimates.

⁵ The WLS estimator is from the rlm function, while robust regression used to identify outliers for the TLS estimator is from the lmsreg function, both of the MASS packages credited to Venables and Ripley (2002). The OLS estimator is from the lm function of the stats package; R Core Team (2011).

⁶ This conclusion is obtained from a variety of tests, the results of which are not displayed to conserve space.

⁷ It should be noted that parameter estimates obtained via least absolute deviation are very similar to those obtained from WLS.

⁸ Repeating this exercise using levels in place of logs produces a maximum p-value of 0.0832.

⁹ The null hypothesis of efficiency is rejected for all TLS specifications which drop more than four observations. The results are similar when levels are used in place of log values.