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A graphical test for local self-similarity in univariate data

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  • Rakhee Dinubhai Patel
  • Frederic Paik Schoenberg

Abstract

The Pareto distribution, or power-law distribution, has long been used to model phenomena in many fields, including wildfire sizes, earthquake seismic moments and stock price changes. Recent observations have brought the fit of the Pareto into question, however, particularly in the upper tail where it often overestimates the frequency of the largest events. This paper proposes a graphical self-similarity test specifically designed to assess whether a Pareto distribution fits better than a tapered Pareto or another alternative. Unlike some model selection methods, this graphical test provides the advantage of highlighting where the model fits well and where it breaks down. Specifically, for data that seem to be better modeled by the tapered Pareto or other alternatives, the test assesses the degree of local self-similarity at each value where the test is computed. The basic properties of the graphical test and its implementation are discussed, and applications of the test to seismological, wildfire, and financial data are considered.

Suggested Citation

  • Rakhee Dinubhai Patel & Frederic Paik Schoenberg, 2011. "A graphical test for local self-similarity in univariate data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2547-2562, January.
  • Handle: RePEc:taf:japsta:v:38:y:2011:i:11:p:2547-2562
    DOI: 10.1080/02664763.2011.559211
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    References listed on IDEAS

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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    2. Roger D. Peng & Frederic Paik Schoenberg & James A. Woods, 2005. "A Space-Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 26-35, March.
    3. Y. Malevergne & V. Pisarenko & D. Sornette, 2005. "Empirical distributions of stock returns: between the stretched exponential and the power law?," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 379-401.
    4. Pisarenko, V. & Sornette, D., 2006. "New statistic for financial return distributions: Power-law or exponential?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 387-400.
    5. Yannick Malevergne & Vladilen Pisarenko & Didier Sornette, 2006. "On the Power of Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) Estimators for Empirical Distributions of Stock Returns," Post-Print hal-02311834, HAL.
    6. G.-F. Gu & W.-X. Zhou, 2009. "On the probability distribution of stock returns in the Mike-Farmer model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(4), pages 585-592, February.
    7. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    8. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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