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A Cautionary note on modeling with fractional Lévy flights

Author

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  • Heyde, C.C.
  • Sly, Allan

Abstract

Temporal scaling and infinite variance are two stylized features often seen together in times series of complex systems. We find that because of their infinite moments samples from fractional Lévy flights produce bi-linear scaling functions which may be incorrectly attributed as evidence of multifractality. We argue that it is unnecessary to consider truncated fractional Lévy flights which are inherently problematic.

Suggested Citation

  • Heyde, C.C. & Sly, Allan, 2008. "A Cautionary note on modeling with fractional Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5024-5032.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:21:p:5024-5032
    DOI: 10.1016/j.physa.2008.05.029
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    Cited by:

    1. Imai, Junichi & Kawai, Reiichiro, 2011. "On finite truncation of infinite shot noise series representation of tempered stable laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4411-4425.
    2. Grahovac, Danijel & Leonenko, Nikolai N., 2014. "Detecting multifractal stochastic processes under heavy-tailed effects," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 78-89.

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