The angular distribution of asset returns in delay space

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.