Prof. Thomas Seligman: Identifying States of a Financial Market
Source: Monday physics colloquium
Identifying States of a Financial Market
Prof. Thomas Seligman, Instituto de Ciencias Fisicas, UNAM, Cuernavaca, Mexico
Time series are the typical form in which we obtain experimental or observational data. In the analysis of such series, stationary situations have been extensively studied and correlations have been found to be a powerful tool. Yet most natural processes are non-stationary. In particular, in times of crisis, accident or trouble, stationarity is lost. As examples we may think of financial markets, biological systems, reactors (both chemical and nuclear) or the weather. In non-stationary situations analysis becomes very difficult and noise is a severe problem. Following a natural urge to search for order in the system, we endeavor to define states through which systems pass and in which they remain for times sog¿hort compared to the data sets we have, yet long compared to fluctuations. Success in this respect would allow to get a better understanding of the system and might even lead to methods for controlling the system in more efficient ways. We here concentrate on financial markets because of the easy access we have to good data, because of our previous experience and last but not least because of the strong non-stationary effects recently seen. 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''. Once the states are defined and identified the challenge ist to characterize the transitions between states, and clearly we would like to be able to anticipate a change of state. This is music of the future, which we are working on, with particular attention to chemical reactors.