Bootstrap validation of links of a minimum spanning tree

We describe two different bootstrap methods applied to the detection of a minimum spanning tree obtained from a set of multivariate variables. We show that two different bootstrap procedures provide partly distinct information that can be informative about the investigated complex system. We investigate two case studies by considering daily returns of two portfolios of stocks traded in the US equity markets in different time periods. The first method performs a “row bootstrap” whereas the second method performs a “pair bootstrap” to obtain a bootstrap replica of each correlation coefficient. We show that the parallel use of the two methods can highlight details about the stability of links selected by the minimum spanning tree associated with the correlation matrix of stock portfolios that can be missed by applying only a single bootstrap methods.