Fractal and Multifractal Time Series

Kantelhardt, Jan W.

doi:10.1007/978-0-387-30440-3_221

Cited by 140 publications

(151 citation statements)

References 81 publications

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“…Interestingly, one exponent g is not enough to characterize the whole aspect of one specific phenomenon. Normally, the exponent g changes depending on the scale s. There might exist a crossover * s where the exponent g changes from g 1 to g 2 (Kantelhardt 2009). The change of the exponent implies the emergence of new governing physics around the scale * s .…”

Section: Methodsmentioning

confidence: 99%

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Physical length scales of wind-blown snow redistribution and accumulation on relatively smooth Arctic first-year sea ice

Moon

Nandan

Scharien

et al. 2019

Environ. Res. Lett.

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Snow thickness measurements over relatively smooth Arctic first-year sea ice, obtained near Cambridge Bay in the Canadian Arctic (2014, 2016 and 2017) and near Elson Lagoon in the Alaskan Arctic (2003 and, are analyzed to quantify physical length-scales and their relevant scaling behaviors. We use the multi-fractal temporally weighted detrended fluctuation analysis method to detect two major physical length-scales from the two independent study locations. Our results suggest that physical processes underlying the formation of snow dunes are consistent and that the wind is the main process shaping the snow thickness variability and redistribution. One scale, around 10 m, appears to be related to the formation of the snow 'dunes', while the other scale, between 30 and 100 m, is likely associated with the various interactions of the snow dunes such as merging, calving and lateral linking. Results imply that snow on level sea ice shows self-organized characteristics.

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Section: Methodsmentioning

confidence: 99%

“…Numerous methods have been introduced to construct the multiple correlation exponents based on power spectrum, wavelet transform and fluctuation analyses to overcome the limits of the direct calculation of the autocorrelation (Kantelhardt 2009). In this research, we rely on the MF-TWDFA, an upgraded version of the MF-DFA.…”

Section: Methodsmentioning

confidence: 99%

Physical length scales of wind-blown snow redistribution and accumulation on relatively smooth Arctic first-year sea ice

Moon

Nandan

Scharien

et al. 2019

Environ. Res. Lett.

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“…We invite readers interested in the case of high frequency series to see, for instance, J.W. Kantelhardt (2008) for testing for the existence of fractal or multi-fractal properties, suggesting the case of a PL distribution.…”

Section: Information-theoretic Maximum Entropy Principlementioning

confidence: 99%

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2019

Non-Extensive Entropy Econometrics for Low Frequency Series

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Appendix 198 Annex C. Computational Aspects of Using GAMS 198 My thanks are addressed to De Gruyter, the publisher, for its decisive financial support for publishing this monograph. I would like to acknowledge De Gruyter editors for their diligent and meticulous work to render this book scientifically understandable. I thank the University of Information Technology and Management in Rzeszów for its assistance and its support of my research. I am grateful to my former supervisor, M. Rocki, for his precious advice during the writing of the document. My particular thanks go to L. Tomasiewicz and J. Boratyński, both from the Łódź Department of Econometrics, for their technical advice on Polish National Accounts. Impressive work has been carried out by J. Kwapień and S. Drożdż, both specialists in thermodynamic statistics, who have identified omissions and errors over a large part of the book during the middle stage of its redaction. To them, I express all my gratitude. I express my thanks to A. Jakimowicz for his precious review comments. My thanks go also to the research institution Clersé at the University of Lille I in France, and in particular to N. Vaneecloo for having arranged my fruitful stay in that institution during my sabbatical year 2010-2011. I would like to thank F. Scheuren for having particularly increased my interest in the theory of information through the rich literature on the subject which was made available to me. Without the many months of sacrifice of M. Bloom for making this document readable, the publication of this work would not have been possible. Many thanks to all the other persons from my institution who at different levels have contributed directly or indirectly to improve the quality of this book. To all these people, I am most grateful, and for any errors or shortcomings which may remain in this book, they are absolved from all blame.

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“…Then * corresponding author; e-mail: dgrech@ift.uni.wroc.pl the correlations between values of the signal also depend on the time scale in which these data are observed. Such systems are called multifractal [6].…”

Section: Introductionmentioning

confidence: 99%

“…The accurate estimation of variety of scaling exponents appearing in similar cases is also fundamental to develop suitable simulation or forecasting methods [6].…”

Section: Introductionmentioning

confidence: 99%

Multifractality of Nonlinear Transformations with Application in Finances

Grech

Pamuła

2013

Acta Phys. Pol. A

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We study the multifractal eects of nonlinear transformations of monofractal, stationary time series and apply the found results to measure the true unbiased multifractality generated only by multiscaling properties of initial (primary) data before transformations. A dierence is stressed between naive observed multifractal eects calculated directly within detrended multifractal analysis as the spread ∆h of the generalized Hurst exponents h(q) and the more reliable unbiased multifractality received after subtraction of residual bias eects generated by nonlinear transformations of initial data and coupled with nite size eects in time series. This property is investigated for volatile series of the real main world nancial indices. A dierence between multifractal properties of intraday and interday quotes is also pointed out in this context for the Warsaw Stock Exchange WIG index.Finally, based on the observed feature of real nonstationary data, a new measure of unbiased multifractality in signals is introduced. This measure comes from an analysis of the whole generalized Hurst exponent prole instead of looking just at its edge behavior h ± ≡ h(q → ±∞). Such an approach seems to be particularly useful when h(q) is not a monotonic function of the moment order q. Interesting examples with extreme events from nance are presented. They convince that an analysis directed only on investigation of the edges h ± in multifractal spectrum may be misleading.

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Fractal and Multifractal Time Series

Cited by 140 publications

References 81 publications

Physical length scales of wind-blown snow redistribution and accumulation on relatively smooth Arctic first-year sea ice

Physical length scales of wind-blown snow redistribution and accumulation on relatively smooth Arctic first-year sea ice

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Multifractality of Nonlinear Transformations with Application in Finances

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