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The art of fitting financial time series with Levy stable distributions

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  • Enrico Scalas
  • Kyungsik Kim

Abstract

This paper illustrates a procedure for fitting financial data with $\alpha$-stable distributions. After using all the available methods to evaluate the distribution parameters, one can qualitatively select the best estimate and run some goodness-of-fit tests on this estimate, in order to quantitatively assess its quality. It turns out that, for the two investigated data sets (MIB30 and DJIA from 2000 to present), an $\alpha$-stable fit of log-returns is reasonably good.

Suggested Citation

  • Enrico Scalas & Kyungsik Kim, 2006. "The art of fitting financial time series with Levy stable distributions," Papers physics/0608224, arXiv.org.
    • Handle: RePEc:arx:papers:physics/0608224
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    1. Rafal Weron, 1996. "Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables"," HSC Research Reports HSC/96/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    2. Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
    3. Rafał Weron, 2001. "Levy-Stable Distributions Revisited: Tail Index> 2does Not Exclude The Levy-Stable Regime," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 209-223.
    4. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    6. 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..
    7. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
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    Cited by:

    1. José Antonio Climent Hernández & Carolina Cruz Matú, 2017. "Pricing of a structured product on the SX5E when the uncertainty of returns is modeled as a log-stable process," Contaduría y Administración, Accounting and Management, vol. 62(4), pages 1160-1182, Octubre-D.
    2. Christophe Schinckus, 2011. "What can econophysics contribute to financial economics?," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 58(2), pages 147-163, June.
    3. Climent-Hernández, José Antonio & Venegas-Martínez, Francisco & Ortiz-Arango, Francisco, 2014. "Portafolio óptimo y productos estructurados en mercados alpha-estables: un enfoque de minimización de riesgo [Optimal Portfolio and Structured Notes in alpha-stable Markets: a Risk Minimization App," MPRA Paper 57740, University Library of Munich, Germany.
    4. Climent Hernández José Antonio & Venegas Martínez Francisco, 2013. "Valuación de opciones sobre subyacentes con rendimientos a-estables," Contaduría y Administración, Accounting and Management, vol. 58(4), pages 119-150, octubre-d.
    5. José Antonio Climent-Hernández, 2017. "Portafolios de dispersión mínima con rendimientos log-estables Minimum dispersion portfolios with log-stable returns," Remef - The Mexican Journal of Economics and Finance, Instituto Mexicano de Ejecutivos de Finanzas. Remef, March.
    6. José Antonio Climent Hernández, 2017. "Portafolios de dispersión mínima con rendimientos log-estables," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 12(2), pages 49-69, Abril-Jun.

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • G00 - Financial Economics - - General - - - General

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