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Extreme Value Theory as a Theoretical Background for Power Law Behavior

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  • Alfarano, Simone
  • Lux, Thomas

Abstract

Power law behavior has been recognized to be a pervasive feature of many phenomena in natural and social sciences. While immense research efforts have been devoted to the analysis of behavioral mechanisms responsible for the ubiquity of power-law scaling, the strong theoretical foundation of power laws as a very general type of limiting behavior of large realizations of stochastic processes is less well known. In this chapter, we briefly present some of the key results of extreme value theory, which provide a statistical justification for the emergence of power laws as limiting behavior for extreme fluctuations. The remarkable generality of the theory allows to abstract from the details of the system under investigation, and therefore allows its application in many diverse fields. Moreover, this theory offers new powerful techniques for the estimation of the Pareto index, detailed in the second part of this chapter.

Suggested Citation

  • Alfarano, Simone & Lux, Thomas, 2010. "Extreme Value Theory as a Theoretical Background for Power Law Behavior," MPRA Paper 24718, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:24718
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    References listed on IDEAS

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    1. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    2. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    3. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
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    Cited by:

    1. repec:spr:joevec:v:27:y:2017:i:5:d:10.1007_s00191-017-0504-x is not listed on IDEAS
    2. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    3. Noemi Schmitt & Frank Westerhoff, 2017. "Heterogeneity, spontaneous coordination and extreme events within large-scale and small-scale agent-based financial market models," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1041-1070, November.

    More about this item

    Keywords

    Extreme Value Theory; Power Laws; Tail index;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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