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Grafting of higher-order correlations of real financial markets into herding models
Authors:Sanghyun Ahn  Gyuchang Lim  Sooyong Kim  Kyungsik Kim
Institution:1. Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea;2. Department of Physics, Pukyong National University, Pusan 608-737, Republic of Korea
Abstract:In this work, we graft the volatility clustering observed in empirical financial time series into the Equiluz and Zimmermann (EZ) model, which was introduced to reproduce the herding behaviors of a financial time series. The original EZ model failed to reproduce the empirically observed power-law exponents of real financial data. The EZ model ordinarily produces a more fat-tailed distribution compared to real data, and a long-range correlation of absolute returns that underlie the volatility clustering. As it is not appropriate to capture the empirically observed correlations in a modified EZ model, we apply a sorting method to incorporate the nonlinear correlation structure of a real financial time series into the generated returns. By doing so, we observe that the slow convergence of distribution of returns is well established for returns generated from the EZ model and its modified version. It is also found that the modified EZ model leads to a less fat-tailed distribution.
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