In this talk I will give a broad overview of the state of the art of our contribution to Econophysics up to now. In particular, I will discuss the two main elements that define the complexity of financial time series: the first is multifractality [1], which is associated to the behaviour 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 behaviour of the whole set of variables [2,3]. For the first analysis I will show results on the application of the Generalized Hurst exponent tool and the Empirical Mode Decomposition method [4,5] and for the second application of network-filtered theoretic tools to different sets of financial market data sets [6,7]. In particular I will introduce a new algorithm, the TMFG (Triangulated Maximally Filtered Graph), that is a scalable and adaptable methodology to efficiently extract a planar filtering graph [8].

References

[1] T. Di Matteo, Quantitative Finance 7(1) (2007) 21.

[2] Won-Min Song, T. Di Matteo, T. Aste, PLoS One 7(3) (2012) e31929.

[3] F. Pozzi, T. Di Matteo and T. Aste, Scientific Reports 3 (2013) 1665.

[4] Noemi Nava, T. Di Matteo, T. Aste, "Time-dependent scaling patterns in high frequency financial data", (2014) submitted.

[5] Noemi Nava, T. Di Matteo, T. Aste,"Anomalous volatility scaling in high frequency financial data", (2015) submitted.

[6] N. Musmeci, T. Aste, T. Di Matteo "Relation between Financial Market Structure and the Real Economy: Comparison between Clustering Methods", (2015) PLoS ONE 10(3): e0116201.

[7] N. Musmeci, Tomaso Aste, T. Di Matteo, "Risk diversification: a study of persistence with a filtered correlation-network approach ", (2015) Journal of Network Theory in Finance 1(1), 1-22.

[8] Guido Previde Massara, T. Di Matteo, T. Aste, "Network Filtering for Big Data: Triangulated Maximally Filtered Graph", (2015) submitted.

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1.  Multiscaling: real source and consequence