Visualization and prediction of financial crisis by stock correlations

Abstract

We attempt to visualize the collective behaviour of markets at financial crisis through cross-correlations between typical Japanese stocks by making use of multi-dimensional scaling. Then, we make a clustering of the scattered plots by minimizing the energy function of the so-called Potts spin-glasses having pair-wise interactions between spins (stocks) as correlation coefficients in stocks. We also propose a theoretical framework to predict several time-series simultaneously by using cross-correlations in financial markets. Our model system is basically described by a variant of the Ising model introduced by Kaizouji (2000). The justification and validity of our approaches are numerically examined for Japanese NIKKEI stocks around 11 March 2011, and for foreign currency exchange rates around Greek crisis in spring 2010.