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 patte rn, 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. Comparing empirical and bootstrapped "theta histogram s" permits hypothesis testing. Simulations suggest that intertemporal stati stical 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, appar ent ARCH behavior.