The mis-specification of the expected rescaled adjusted range

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 which calculated results can be compared. One recent paper in Physica A by Couillard and Davison [Physica A 348 (2005) 404] concludes that the Anis and Lloyd [Biometrika 63 (1976) 111] model of the expected rescaled adjusted range is more accurate than that proposed by Peters [Fractal Market Analysis, Wiley, New York, 1994]. This finding is contrary to the evidence presented by Peters. This paper reveals significant inconsistencies in the empirical results reported by Peters, which when considered, support the conclusions of Couillard and Davison and explain the apparent contradiction in their results versus those of Peters.