  We propose to use the rescaled range analysis to examine the records of
rapidity-dependence of multiplicities in high-energy collision processes. We
probe event by event the existence of global statistical dependence in the
system of produced hadrons, and demonstrate the effectiveness of the
above-mentioned statistical method by applying it to the cosmic-ray data of the
JACEE collaboration, and by comparing the obtained results with other
experimental results for similar reactions at accelerator and collider
energies. We present experimental evidence for the validity of Hurst's
empirical law, and the evidence for the existence of global statistical
dependence, fractal dimension, and scaling behavior in such systems of hadronic
matter. None of these features is directly related to the basis of the
conventional physical picture. Hence, it is not clear whether (and if yes, how
and why) these striking empirical regularities can be understood in terms of
the conventional theory.
