Correlation filtering in financial time series (Invited Paper)

We apply a method to filter relevant information from the correlation coefficient matrix by extracting a network of relevant interactions. This method succeeds to generate networks with the same hierarchical structure of the Minimum Spanning Tree but containing a larger amount of links resulting in a richer network topology allowing loops and cliques. In Tumminello et al.,1 we have shown that this method, applied to a financial portfolio of 100 stocks in the USA equity markets, is pretty efficient in filtering relevant information about the clustering of the system and its hierarchical structure both on the whole system and within each cluster. In particular, we have found that triangular loops and 4 element cliques have important and significant relations with the market structure and properties. Here we apply this filtering procedure to the analysis of correlation in two different kind of interest rate time series (16 Eurodollars and 34 US interest rates).

[1]  Tomaso Aste,et al.  GLASS TRANSITION IN SELF-ORGANIZING CELLULAR PATTERNS , 1999 .

[2]  T. Alderweireld,et al.  Detailed empirical study of the term structure of interest rates. Emergence of power laws and scaling laws , 2003, cond-mat/0305689.

[3]  M. Potters,et al.  Phenomenology of the Interest Rate Curve , 1997 .

[4]  Tomaso Aste,et al.  Interest rates hierarchical structure , 2005 .

[5]  M Tumminello,et al.  A tool for filtering information in complex systems. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[6]  K. Kaski,et al.  Dynamics of market correlations: taxonomy and portfolio analysis. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Riccardo Rebonato,et al.  Interest-rate option models , 1996 .

[8]  R. Mantegna.  Hierarchical structure in financial markets , 1998, cond-mat/9802256.

[9]  HOW DOES THE EURODOLLAR INTEREST RATE BEHAVE , 2001, cond-mat/0101009.

[10]  G. Ringel,et al.  Solution of the heawood map-coloring problem. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[11]  T. Di Matteo,et al.  Complex networks on hyperbolic surfaces , 2004, cond-mat/0408443.

[12]  T. Aste,et al.  The topological structure of 2D disordered cellular systems , 1997, cond-mat/9709227.

[13]  Vance L. Martin,et al.  Modeling the term structure , 1995 .

[14]  K. Kaski,et al.  Dynamic asset trees and portfolio analysis , 2002, cond-mat/0208131.

[15]  An interest rates cluster analysis , 2004, cond-mat/0401443.

[16]  Tomaso Aste,et al.  Two-dimensional froths and the dynamics of biological tissues , 1998 .

[17]  On pricing of interest rate derivatives , 2004, cond-mat/0401445.

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  K. Kaski,et al.  Dynamic asset trees and Black Monday , 2002, cond-mat/0212037.