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A detailed analysis of correlation between stock returns at high frequency is compared with simple models of random walks. The authors focus in particular on the dependence of correlations on time scales - the so-called Epps effect. This provides a characterization of stochastic models of stock price returns which is appropriate at very high frequency. The study of covariances between stocks is a central problem in finance, both to achieve theoretical understanding of market structure and to exploit its relevant applications, such as portfolio optimization.
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