Extracting meaningful information from financial data

A method for extracting information carrying eigenvalues of the correlation matrix is presented based on the topological transformation of the manifold defined by the data matrix itself. The transformation, performed with the use of the minimum spanning tree and the barycentric transformation, linearizes the topological manifold and the singular value decomposition is performed on the fnal data matrix corresponding to the linearized hypersurface. It is shown that the results of this procedure are superior to the results of the random matrix theory as applied to the financial data. The method may be used independently or in conjunction with the random matrix theory. Other possible uses of the method are mentioned. (C) 2000 Elsevier Science B.V. All rights reserved.