Sang-Heon Lee does some analysis:

Pairs trading literature use the Hurst exponent frequently since it gives an simple and intuitive indicator for the behavior of stock returns. Using S&P 500 returns, let’s learn how to estimate it using R code manually and then use R package conveniently.

Click through for those two examples, as well as a more detailed explanation of the math driving this. H/T R-Bloggers.