Self-Affinity in Financial Asset Returns

39 Pages Posted: 7 Sep 2012

See all articles by John Goddard

John Goddard

Bangor University - Bangor University

Enrico Onali

University of Exeter Business School

Date Written: April 24, 2012


We test for departures from normal and independent and identically distributed (NIID) log returns, when log returns under the alternative hypothesis are self-affine and either long-range dependent, or drawn randomly from an L-stable distribution with infinite higher-order moments. The finite sample performance of estimators of the two forms of self-affinity is explored in a simulation study. In contrast to rescaled range analysis and other conventional estimation methods, the variant of fluctuation analysis that considers finite sample moments only is able to identify both forms of self-affinity. When log returns are self-affine and long-range dependent under the alternative hypothesis, however, rescaled range analysis has higher power than fluctuation analysis. The techniques are illustrated by means of an analysis of the fractal properties of the daily log returns for the indices of 11 stock markets of developed countries. Several of the smaller stock markets by capitalization exhibit evidence of long-range dependence in log returns.

Suggested Citation

Goddard, John and Onali, Enrico, Self-Affinity in Financial Asset Returns (April 24, 2012). International Review of Financial Analysis, Forthcoming, Available at SSRN:

John Goddard (Contact Author)

Bangor University - Bangor University ( email )

Bangor, Wales LL57 2DG
United Kingdom

Enrico Onali

University of Exeter Business School ( email )

United Kingdom

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