Extracting phases of ￣nancial markets

Abstract

While the existence of different phases in financial markets such as bull/bear or bubble/non-bubble has been widely recognized among investors, few stylized facts about the different phases has been revealed so far due to diffculty of analyzing tail behavior. In particular, the sudden phase shift from bull to bear markets, or financial bubble burst, damages economies very severely, and it is urgent social requirement to provide early warning system for helping policy makers to alleviate the damage. The aim of this study is to classify financial markets into several phases, and warn the change of the phase at appropriate timing. Phase extraction and the statistical analysis is based on moving densities estimated by adaptive kernel density estimator, that exhibits a good performance for fitting fat-tailed and multi-modal densities which are typical to phenomena involving phase transitions. Based on the analysis of New York Stock Exchange index daily returns from 1966 to 2009, the shape of the estimated return density is classified into four phases by using the detected cyclical pattern of risk-return relationship. Moreover, most of the bubble burst or sudden change in the price trend could be warned several months prior to the price peak point.