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The angular distribution of asset returns in delay space. (English) Zbl 0988.91038

Summary: Plotting asset returns against themselves with a one-period lag reveals the “compass rose” pattern of T. F. Crack and O. Ledoit [“Robust Structures Without Predictability: The ‘Compass Rose’ Pattern of the Stock Market”, J. Finance 61, 751-762 (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. Comparing empirical and bootstrapped “theta histograms” permits hypothesis testing. Simulations suggest that intertemporal statistical dependence skews the campass 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.

MSC:

91B28 Finance etc. (MSC2000)
91B82 Statistical methods; economic indices and measures
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