In this talk I will briefly give a broad overview of the state of the art in Econophysics: a discipline that has already a rich history and even controversial trends [1]. In particular, I will show results concerning complex financial datasets. There are two main elements that define the complexity of financial time series: the first is multifractality [2], which is associated to the behavior of each single variable and the way it scales in time; the second is the structure of dependency between time series, associated with the collective behavior of the whole set of variables [3-5]. So far, these two manifestations of complexity have been investigated separately. In this talk I will point out that -in fact- they might be related [6]. I will first introduce a graph-theoretic approach to extract clusters and hierarchies in an unsupervised and deterministic manner, without the use of any prior information [4] showing that applications to financial data-sets can meaningfully identify industrial activities and structural market changes [7]. I will then show new empirical observations of a deep interplay between cross-correlations hierarchical properties and multifractality [6]. In particular the degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations.
[1] “Topical Issue: Trends in Econophysics” in EPJB, Vol. 55, No. 2 (2007).
[2] T. Di Matteo, Quantitative Finance 7(1) (2007) 21.
[3] M. Tumminello, T. Aste, T. Di Matteo, R. N. Mantegna, “A tool for filtering information in complex systems”, PNAS 102, n. 30 (2005) 10421.
[4] Won-Min Song, T. Di Matteo, T. Aste, PLoS One 7(3) (2012) e31929.
[5] F. Pozzi, T. Di Matteo and T. Aste, Scientific Reports 3 (2013) 1665.
[6] R. Morales, T. Di Matteo, T. Aste, Scientific Reports 4 (2014) 4589.
[7] N. Musmeci, T. Aste, T. Di Matteo, Clustering and hierarchy in financial markets: advantages of the DBHT, (2014) submitted.