the correlation matrix of a complex system with tools of hierarchical clustering has been useful in the multivariate characterization of stock return time series (Mantegna, 1999; Bonanno et al., 2001; Bonanno et al., 2003), market index returns of worldwide stock exchanges (Bonanno et al., 2000), and volatility increments of stock return time series (Micciche et al., 2003), where the estimation of statistical reliable properties of the correlation matrix is crucial for several financial decision processes such as asset allocation, portfolio optimization (Tola et al., 2008), derivative pricing, etc. We have termed the selection of statistical reliable information of the correlation matrix with the locution “filtering procedure” in Ref. Tumminello et al. (2007a). Hierarchical clustering procedures are filtering procedures. Other filtering procedures which are popular within the econophysics community are procedures based on the random matrix theory (Laloux et al., 1999; Plerou et al., 1999; Rosenow et al., 2002; Coronnello et al., 2005; Potters et al., 2005; Tumminello et al., 2007a), and procedures using the concept of shrinkage of a correlation matrix (Ledoit and Wolf, 2003; Schäfer and Strimmer, 2005; Tumminello et al., 2007b). Many others might be devised and their effectiveness tested.

The correlation matrix of the time series of 