The local Hurst exponent, a measure employed to detect the presence of dependence in a time series, may also be used to investigate the source of intraday variation observed in the returns in foreign exchange markets. Given that changes in the local Hurst exponent may be due to either a...

The classical rescaled adjusted range (R/S) statistic is a popular and robust tool for identifying fractal structures and long-term dependence in time-series data. Subsequent to Mandelbrot and Wallis [Water Resour. Res. 4 (1968) 909] who proposed the statistic be measured over several subseries...

Rescaled range analysis has regained popularity in the recent econophysics literature as a means of identifying long-term dependence in time-series data. Conclusions derived from the rescaled adjusted range statistic are conditional however upon the choice of an appropriate benchmark against...

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...