  Multiplicative random cascade model naturally reproduces the intermittency or
multifractality, which is frequently shown among hierarchical complex systems
such as turbulence and financial markets. As described herein, we investigate
the validity of a multiplicative hierarchical random cascade model through an
empirical study using financial data. Although the intermittency and
multifractality of the time series are verified, random multiplicative factors
linking successive hierarchical layers show strongly negative correlation. We
extend the multiplicative model to incorporate an additional stochastic term.
Results show that the proposed model is consistent with all the empirical
results presented here.
