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

Records of the traded value f(i) of stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average < f(i)>: sigma(i)proportional to < f(i)>(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.