Scale-adjusted volatility and the Dow Jones index

This paper extends research by Batten and Ellis [Econ. Lett. 72 (2001) 291] to propose a simple model of scale-adjusted volatility which measures the extent to which the Gaussian scaling law mis-estimates long-horizon volatility. Applied to the Dow Jones industrial average, the results of our model show a dramatic improvement over the Gaussian scaling law in predicting long-horizon volatility. Our model provides a general framework for estimating scaled volatility that may be also applied to other fields of study where the Hurst exponent is commonly used.