Filtering Noise from Correlation Matrices : Paper 3 in a Series 'Uncovering Hidden Dependencies'

Alexander Izmailov, Ph.D (theoretical physics) and Brian Shay, Ph.D (mathematics) of Market Memory Trading, L.L.C., present in a series of white papers, aspects of a revolutionary advance in uncovering hidden dependencies via filtering noise from correlation matrices developed by the New York based company, Market Memory Trading, L.L.C. (MMT). Correlations are quantitative measures of these dependencies and noise filtering increases their accuracy as a decision-making tool, from asset allocation to LIBOR Surveillance and cyber security.“FILTERING NOISE FROM CORRELATION MATRICES.” White Paper 3, dated January 15, 2013 provides a demonstration of the omnipresence of noise in financial correlation/covariance matrices revealed by means of random matrix theory, a branch of probability theory; and an introduction of the Shannon entropy as a measure of noise in correlation matrices; and demonstration of substantial entropy decrease as a result of noise filtering on a few examples. Refer to Appendix A for Complete Series