1 research outputs found
The components of empirical multifractality in financial returns
We perform a systematic investigation on the components of the empirical
multifractality of financial returns using the daily data of Dow Jones
Industrial Average from 26 May 1896 to 27 April 2007 as an example. The
temporal structure and fat-tailed distribution of the returns are considered as
possible influence factors. The multifractal spectrum of the original return
series is compared with those of four kinds of surrogate data: (1) shuffled
data that contain no temporal correlation but have the same distribution, (2)
surrogate data in which any nonlinear correlation is removed but the
distribution and linear correlation are preserved, (3) surrogate data in which
large positive and negative returns are replaced with small values, and (4)
surrogate data generated from alternative fat-tailed distributions with the
temporal correlation preserved. We find that all these factors have influence
on the multifractal spectrum. We also find that the temporal structure (linear
or nonlinear) has minor impact on the singularity width of the
multifractal spectrum while the fat tails have major impact on ,
which confirms the earlier results. In addition, the linear correlation is
found to have only a horizontal translation effect on the multifractal spectrum
in which the distance is approximately equal to the difference between its DFA
scaling exponent and 0.5. Our method can also be applied to other financial or
physical variables and other multifractal formalisms.Comment: 6 epl page