Dynamics of a financial market based on correlation analysis

Abstract

A recent movement to inter-disciplinary researches is deeply and securely rooted at the complexity, which is hardly possible to be described by a single equation of motion or a simple sum of those things. Among many complex systems, the human brain and the economy are very interesting subjects because we humans are always concerned about them. Especially, about economic systems, the constituents are beings with consciousness. Therefore, the complexity they make is more than that observed from physical systems. In this dissertation, the dynamics of financial markets and their statistical features are closely examined. Although the random walk formalism introduced by Bachelier in 1900 has been successful in theorizing fluctuations of various financial securities, it is also true that aberrations from the standard finance theory overwhelm its simplicity. Especially, the existence of higher-order temporal correlations between fluctuations enforces the complexity of economic systems. Since the so-called stylized facts such as fat-tailed distributions of returns and volatility clustering are greatly due to the inter-dependence among fluctuations at more than two times, it is very important and urgent to investigate the structure of higher-order correlations and to infer the response and/or recognition made by investors on the market circumstances. First, we analyzed the structure of correlations among returns over various financial securities in terms of multifractality and found that the time-dependence is a core-property. And non-universality of statistical features is observed at different times as well as over different financial securities. Further, by distinguishing several levels of correlations, we observed that most correlations are rooted at negative fluctuations. This observation seems to support the fact that investors are apt to behave as if there is a rule or a pattern to follow. This tendency has been proposed in the monumental paper “The prospec...