A robust filter in stock networks analysis

• Published in: Physica A Vol. 391; no. 20; pp. 5049 - 5057
• Main Author: Djauhari, Maman A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.10.2012
• Subjects: Fuzzy relation; Minimal spanning tree; Min–max transitive closure; Network topology; Sub-dominant ultrametric; Minimal spanning tree; Network topology; Min–max transitive closure; Sub-dominant ultrametric; Fuzzy relation
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2012.05.060

We show that the use of a minimal spanning tree (MST) to filter important information in a complex system is not robust except when the system contains a unique MST. In this paper we propose to use the forest of all MSTs as a robust filter. According to this filter, centrality measures are also robust. For that purpose an algorithm, which can also be used to detect the uniqueness of an MST, will be provided. A simple hypothetical example will clarify the construction of the proposed filter and a real problem in filtering the information contained in NYSE 100 stocks will illustrate its advantages compared to the MST-based filter. ► In practice, it is very often that a network between stocks contains more than one minimal spanning tree. ► A necessary and sufficient condition for the uniqueness of the minimal spanning tree is presented. ► If the minimal spanning tree is not unique, its use to filter important information might be misleading. Then it is non-robust. ► We propose then to use the forest of all minimal spanning trees as a robust filter. ► For practical purpose, an algorithm to construct that forest is developed.