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The near-extreme density of intraday log-returns

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  • Politi, Mauro
  • Millot, Nicolas
  • Chakraborti, Anirban

Abstract

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focussing, instead, on the closely related density of “near-extremes”–the distance between a record and the maximal value–can render the statistical methods to be more suitable in the practical applications and/or validations of models. We apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations.

Suggested Citation

  • Politi, Mauro & Millot, Nicolas & Chakraborti, Anirban, 2012. "The near-extreme density of intraday log-returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 147-155.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:1:p:147-155
    DOI: 10.1016/j.physa.2011.05.029
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    References listed on IDEAS

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    1. Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2025-2034.
    2. Coronel-Brizio, H.F. & Hernández-Montoya, A.R., 2010. "The Anderson–Darling test of fit for the power-law distribution from left-censored samples," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3508-3515.
    3. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    4. Austin Gerig & Javier Vicente & Miguel A. Fuentes, 2009. "Model for Non-Gaussian Intraday Stock Returns," Papers 0906.3841, arXiv.org, revised Dec 2009.
    5. Lisa Borland & Jean-Philippe Bouchaud, 2004. "A non-Gaussian option pricing model with skew," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 499-514.
    6. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    7. H. F. Coronel-Brizio & A. R. Hernandez-Montoya, 2010. "The Anderson-Darling test of fit for the power law distribution from left censored samples," Papers 1004.0417, arXiv.org.
    8. L. Borland & J. P. Bouchaud, 2004. "A Non-Gaussian Option Pricing Model with Skew," Papers cond-mat/0403022, arXiv.org, revised Mar 2004.
    9. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169.
    10. Lin, Jin-Guan & Huang, Chao & Zhuang, Qing-Yun & Zhu, Li-Ping, 2010. "Estimating generalized state density of near-extreme events and its applications in analyzing stock data," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 13-20, August.
    11. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2008. "Martingales, nonstationary increments, and the efficient market hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3916-3920.
    12. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
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    Cited by:

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    2. Arias-Calluari, Karina & Najafi, Morteza. N. & Harré, Michael S. & Tang, Yaoyue & Alonso-Marroquin, Fernando, 2022. "Testing stationarity of the detrended price return in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    3. Karina Arias-Calluari & Morteza. N. Najafi & Michael S. Harr'e & Fernando Alonso-Marroquin, 2019. "Stationarity of the detrended price return in stock markets," Papers 1910.01034, arXiv.org, revised Aug 2020.
    4. Ming-Chi Tsai & Ching-Hsue Cheng & Meei-Ing Tsai & Huei-Yuan Shiu, 2018. "Forecasting leading industry stock prices based on a hybrid time-series forecast model," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-24, December.

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    Keywords

    Extreme events; Intraday returns;

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