TIGHT PACKING A HYPERSPHERE WITH OTHERS OF LIKE KIND

Abstract

This study provides three results of note. First, analysis of information can be abstracted from monetary values in special cases to variability of returns in general cases. Second, with an appropriately chosen model one can separate and calculate independently the influences on a stochastic process of having either more timely information, or better quality information, or both. Third, one can bring methods of statistical inference to stochastic analysis. The paper develops a theory of applying variance ratio tests to problems of inference, and by so doing, enables one to determine the separate influences of timely and superior information on results. Numerous examples illustrate the theory.