Identifying states of a financial market

The understanding of complex systems has become a central issue because such systems exist in a wide range of scientific disciplines. We here focus on financial markets as an example of a complex system. In particular we analyze financial data from the S&P 500 stocks in the 19-year period 1992–2010. We propose a definition of state for a financial market and use it to identify points of drastic change in the correlation structure. These points are mapped to occurrences of financial crises. We find that a wide variety of characteristic correlation structure patterns exist in the observation time window and that these characteristic correlation structure patterns can be classified into several typical “market states”. Using this classification we recognize transitions between different market states. A similarity measure we develop thus affords means of understanding changes in states and of recognizing developments not previously seen.MCM acknowledges financial support from the Fulbright program and from Studienstiftung des Deutschen Volkes. TS acknowledges support from the JSPS Institutional Program for Young Researcher Overseas Visits, Grant-in-Aid for Young Scientists (B) no. 21740284 MEXT, Japan, and the Aihara Project, the FIRST program from JSPS, initiated by CSTP. THS acknowledges support from project 79613 of CONACYT, Mexico. HES thanks the NSF for support. (Fulbright program; Studienstiftung des Deutschen Volkes; JSPS; 21740284 - MEXT, Japan; Aihara Project; FIRST program from JSPS; CSTP; 79613 - CONACYT, Mexico; NSF)Published versio