by using a finite number of records $T$ sampling the behavior of the $N$ elements of the system. Due to the unavoidable finiteness of $T$, the estimation of the sample correlation matrix presents a degree of statistical uncertainty that can be characterized under widespread statistical assumptions. Physicists (Laloux et al., 1999; Plerou et al., 1999), have contributed to the quantitative estimation of the statistical uncertainty of the correlation matrix by using tools and concepts of random matrix theory. However, theoretical results providing the statistical reliability of hierarchical trees and correlation based networks are still not available and therefore, a bootstrap approach has been used to quantify the statistical reliability of both hierarchical trees (Tumminello et al., 2007d) and correlation based networks (Tumminello et al., 2007c).

The hierarchical tree characterizing a complex system can also be used to extract a factor model with independent factors acting on different elements in a nested way. In other words, the number of factors controlling each element may be different and different factors may act at different hierarchical levels. Tumminello et al. (2007d) have shown how to associate a hierarchically nested factor model to a system described by a given hierarchical structure.

Having available a 