Global and Local Dynamics in Correlated Systems

author: Tiziana Di Matteo, Department of Applied Mathematics, Australian National University

Description

In this talk, we will show results concerning the characterization and visualization of correlations in financial systems by means of network analysis [1-4]. We will discuss results from the application of a new method which is able to construct complex graphs from cross-correlation matrices. Dynamical changes in the local topology and hierarchy of these graphs are detected and related to markets fluctuations [5]. [1] T. Aste, T. Di Matteo, S. T. Hyde, Physica A 346 (2005) 20-26; [2] M. Tumminello, T. Aste, T. Di Matteo, R. N. Mantegna, PNAS 102, n. 30 (2005) 10421 10426; [3] T. Aste and T. Di Matteo, Physica A 370 (2006) 156-161; [4] M. Tumminello, T. Aste, T. Di Matteo, and R. N. Mantegna, EPJB 55 (2007) 209-217; [5] F. Pozzi, T. Di Matteo, T. Aste, in preparation (2007).

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*Slides*
0:00	Global and local dynamics in correlated systems
0:37	Brief overview
1:50	“The architecture of networks: Characterization and Visualization of complex systems as fluctuating networks”
3:03	WHY SURFACES?
4:34	Which SURFACES?
4:53	Planar graph g=0
5:37	WEIGHTS - part 1
5:53	WEIGHTS - part 2
6:39	Application to interest rates - part 1
7:20	Application to interest rates - part 2
8:06	Metric graphs
9:59	MINIMUM SPANNING TREE (MST)
11:07	Graph g=0 embedded on a sphere
11:26	Graph g=0 embedded on a sphere
11:51	Network relaxation procedure
11:55	Hierarchy
12:44	CLUSTERING - part 1
13:43	CLUSTERING - part 2
14:54	CLUSTERING - part 3
15:54	100 stocks in the USA equity markets
16:46	Graph richer of links but preserving the MST hierarchical structure
17:27	4-cliques structure - part 1
18:37	4-cliques structure - part 2
19:26	5 min time horizon
19:32	1 day time horizon
19:39	5 min time horizon- 1 day time horizon
20:05	Topological properties
20:59	Average length of shortest path as function of the sampling time horizon of return
21:29	Betweenness of GE and PPG evaluated in the PMFG as function of the time horizon
22:06	Degree of GE and PPG evaluated in the PMFG as function of the time horizon - part 1
22:26	Degree of GE and PPG evaluated in the PMFG as function of the time horizon - part 2
23:50	Connection strength evaluated by the number of intra-sector 3-cliques (C3)
24:16	Conglomerates and capital goods
25:34	Sub-sectors
26:04	Nature and properties of the MST and PMFG at different time series windows: 1, 2, 3, 4, 6, 12 months moving through the time series
27:04	Nature and properties of the MST and PMFG at different time series windows: 1, 2, 3, 4, 6, 12 months moving through the time series - graph 1
27:58	Nature and properties of the MST and PMFG at different time series windows: 1, 2, 3, 4, 6, 12 months moving through the time series - graph 2
28:39	Nature and properties of the MST and PMFG at different time series windows: 1, 2, 3, 4, 6, 12 months moving through the time series - graph 3
28:54	Nature and properties of the MST and PMFG at different time series windows: 1, 2, 3, 4, 6, 12 months moving through the time series - graph 4
28:57	Nature and properties of the MST and PMFG at different time series windows: 1, 2, 3, 4, 6, 12 months moving through the time series - graph 5
28:59	Nature and properties of the MST and PMFG at different time series windows: 1, 2, 3, 4, 6, 12 months moving through the time series - graph 6
30:23	Conclusion - part 1
31:25	Conclusion - part 2
31:59	Conclusion - part 3

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