A note on scaled variance ratio estimation of the Hurst exponent with application to agricultural commodity prices

The measure of long-term memory is important for the study of economic and financial time series. This paper estimates the Hurst exponent from a Scaled Variance Ratio model for 17 commodity price series under the efficient market null H0:H=0.5. The distribution about the estimates of H are obtained from 90%, 95% and 99% confidence intervals generated from 20,000 Monte Carlo replications of a geometric Brownian motion. The results show that the scaled variance ratio provides a very good and stable estimate of the Hurst exponent, but the estimates can be quite different from the measure obtained from rescaled range or R–S analysis. In general commodity prices are consistent with the underlying assumption of a geometric Brownian motion.