In this paper, we use the generalized Hurst exponent approach to study the
multi- scaling behavior of different financial time series. We show that this
approach is robust and powerful in detecting different types of multiscaling.
We observe a puzzling phenomenon where an apparent increase in multifractality
is measured in time series generated from shuffled returns, where all
time-correlations are destroyed, while the return distributions are conserved.
This effect is robust and it is reproduced in several real financial data
including stock market indices, exchange rates and interest rates. In order to
understand the origin of this effect we investigate different simulated time
series by means of the Markov switching multifractal (MSM) model,
autoregressive fractionally integrated moving average (ARFIMA) processes with
stable innovations, fractional Brownian motion and Levy flights. Overall we
conclude that the multifractality observed in financial time series is mainly a
consequence of the characteristic fat-tailed distribution of the returns and
time-correlations have the effect to decrease the measured multifractality
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.
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