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

True and Apparent Scaling: The Proximity of the Markov-Switching Multifractal Model to Long-Range Dependence