Discrete Dynamics in Nature and Society
Volume 6 (2001), Issue 2, Pages 101-120

The angular distribution of asset returns in delay space

Roger Koppl1 and Carlo Nardone2

1Department of Economics and Finance, Fairleigh Dickinson University, Madison 07940, NJ, USA
2Sun Microsystems Italia SpA, via G. Romagnosi 4, Roma I-00196, Italy

Received 14 May 2000

Copyright © 2001 Roger Koppl and Carlo Nardone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Plotting asset returns against themselves with a one-period lag reveals the “compass rose” pattern of Crack and Ledoit (1996). They describe the pattern, caused by discreteness, as “subjective”. We develop a new and original set of “objective” statistical procedures to quantify the compass rose and detect changes in it. empirical and bootstrapped “theta histograms” permits hypothesis testing. Simulations suggest that intertemporal statistical dependence skews the compass rose in ways that mimic ARCH phenomena. Using our techniques on “credit ruble” data, we test the hypothesis that “Big Players” influence the degree of this “X-skewing” and, therefore, apparent ARCH behavior.