Quantitative features of multifractal subtleties in time series

By Stanislaw Drozdz, Jaroslaw Kwapien, P. Oświȩcimka, R. Rak. 2009

171 citations recorded by the source corpus.

Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian distribution, both uncorrelated and correlated in time, are used. For the uncorrelated series at the border (q=5/3) between the Gaussian and the Levy basins of attraction asymptotically we find a phase-like transition between monofractal and bifractal characteristics. This indicates that these may solely be the specific nonlinear temporal correlations that organize the series into a genuine multifractal hierarchy. For analyzing various features of multifractality due to such correlations, we use the model series generated from the binomial cascade as well as empirical series. Then, within the temporal ranges of well-developed power law correlations we find a fast convergence in all multifractal measures. Besides its practical significance this fact may reflect another manifestation of a conjectured q-generalized Central-Limit Theorem.

Subfields: Condensed Matter Physics, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ab073cedc36bb5bccede25c27a5674d8d6fc7c2e

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In Condensed Matter Physics

Wei‐Xing Zhou

In Economics and Econometrics

In Statistical and Nonlinear Physics

Citations in the corpus

The components of empirical multifractality in financial returns (2009, methodology): “Extensive numerical experiments using uncorrelated time series obeying q-Gaussian distributions with different tail exponents unveil a convergence to monofractalilty in the Gaussian attraction basin and to bifractality in the Lévy attraction basin [49], which is consistent with the analytic derivati”