Scaling theory of temporal correlations and size-dependent fluctuations in the traded value of stocks

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Abstract
Records of the traded value of fi stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average : sigma(i) is proportional to alpha, with a strong time scale dependence alpha(Delta(t)). The nontrivial (i.e., neither 0.5 nor 1) value of alpha may have different origins and provides information about the microscopic dynamics. We present a set of stylized facts and then show their connection to such behavior. The functional form alpha(Delta(t)) originates from two aspects of the dynamics: Stocks of larger companies both tend to be traded in larger packages and also display stronger correlations of traded value. The results are integrated into a general framework that can be applied to a wide range of complex systems.

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