  In this paper, we consider daily financial data of a collection of different
stock market indices, exchange rates, and interest rates, and we analyze their
multi-scaling properties by estimating a simple specification of the
Markov-switching multifractal model (MSM). In order to see how well the
estimated models capture the temporal dependence of the data, we estimate and
compare the scaling exponents $H(q)$ (for $q = 1, 2$) for both empirical data
and simulated data of the estimated MSM models. In most cases the multifractal
model appears to generate `apparent' long memory in agreement with the
empirical scaling laws.
