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

Abstract

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.

arXiv comment13 pages, accepted for publication in Physica A

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