IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1706.09756.html
   My bibliography  Save this paper

Parameter estimation for stable distributions with application to commodity futures log returns

Author

Listed:
  • Michael Kateregga
  • Sure Mataramvura
  • David Taylor

Abstract

This paper explores the theory behind the rich and robust family of {\alpha}-stable distributions to estimate parameters from financial asset log-returns data. We discuss four-parameter estimation methods including the quantiles, logarithmic moments method, maximum likelihood (ML), and the empirical characteristics function (ECF) method. The contribution of the paper is two-fold: first, we discuss the above parametric approaches and investigate their performance through error analysis. Moreover, we argue that the ECF performs better than the ML over a wide range of shape parameter values, {\alpha}{\alpha} including values closest to 0 and 2 and that the ECF has a better convergence rate than the ML. Secondly, we compare the t location-scale distribution to the general stable distribution and show that the former fails to capture skewness which might exist in the data. This is observed through applying the ECF to commodity futures log-returns data to obtain the skewness parameter.

Suggested Citation

  • Michael Kateregga & Sure Mataramvura & David Taylor, 2017. "Parameter estimation for stable distributions with application to commodity futures log returns," Papers 1706.09756, arXiv.org.
    • Handle: RePEc:arx:papers:1706.09756
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1706.09756
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Benoit Mandelbrot, 1962. "Paretian Distributions and Income Maximization," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 76(1), pages 57-85.
    2. Jun Yu, 2004. "Empirical Characteristic Function Estimation and Its Applications," Econometric Reviews, Taylor & Francis Journals, vol. 23(2), pages 93-123.
    3. 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..
    4. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. M. Kateregga & S. Mataramvura & D. Taylor & Xibin Zhang, 2017. "Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1384125-138, January.
    2. Taurai Muvunza, 2020. "An $\alpha$-Stable Approach to Modelling Highly Speculative Assets and Cryptocurrencies," Papers 2002.09881, arXiv.org, revised Jul 2023.
    3. Bielak, Łukasz & Grzesiek, Aleksandra & Janczura, Joanna & Wyłomańska, Agnieszka, 2021. "Market risk factors analysis for an international mining company. Multi-dimensional, heavy-tailed-based modelling," Resources Policy, Elsevier, vol. 74(C).
    4. Abootaleb Shirvani & Svetlozar T. Rachev & Frank J. Fabozzi, 2019. "Multiple Subordinated Modeling of Asset Returns," Papers 1907.12600, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. Kateregga & S. Mataramvura & D. Taylor, 2017. "Parameter estimation for stable distributions with application to commodity futures log-returns," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1318813-131, January.
    2. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    3. W. Walls, 2005. "Modeling Movie Success When ‘Nobody Knows Anything’: Conditional Stable-Distribution Analysis Of Film Returns," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 29(3), pages 177-190, August.
    4. Pernagallo, Giuseppe & Torrisi, Benedetto, 2020. "Blindfolded monkeys or financial analysts: Who is worth your money? New evidence on informational inefficiencies in the U.S. stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    5. Drew Creal & Siem Jan Koopman & André Lucas & Marcin Zamojski, 2015. "Generalized Autoregressive Method of Moments," Tinbergen Institute Discussion Papers 15-138/III, Tinbergen Institute, revised 06 Jul 2018.
    6. Coppes, R. C., 1995. "Are exchange rate changes normally distributed?," Economics Letters, Elsevier, vol. 47(2), pages 117-121, February.
    7. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    8. José Antonio Climent Hernández & Gabino Sánchez Arzate & Ambrosio Ortiz Ramírez, 2021. "Portafolios ?-estables del G20: Evidencia empírica con Markowitz, Tobin y CAPM," 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. 16(4), pages 1-28, Octubre -.
    9. Hayley Jang & Young Hoon Lee & Rodney Fort, 2019. "Winning In Professional Team Sports: Historical Moments," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 103-120, January.
    10. Andria, Joseph & di Tollo, Giacomo & Kalda, Jaan, 2022. "The predictive power of power-laws: An empirical time-arrow based investigation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. ROCKINGER, Michael & JONDEAU, Eric, 1999. "The Tail Behavior of Stock Returns: Emerging versus Mature Markets," HEC Research Papers Series 668, HEC Paris.
    12. Nicolau, João & Rodrigues, Paulo M.M. & Stoykov, Marian Z., 2023. "Tail index estimation in the presence of covariates: Stock returns’ tail risk dynamics," Journal of Econometrics, Elsevier, vol. 235(2), pages 2266-2284.
    13. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    14. Carlos León, 2014. "Scale-free tails in Colombian financial indexes: A primer," Borradores de Economia 812, Banco de la Republica de Colombia.
    15. ROCKINGER, Michael & JONDEAU, Eric, 2000. "Conditional Volatility, Skewness, and Kurtosis : Existence and Persistence," HEC Research Papers Series 710, HEC Paris.
    16. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    17. W. D. Walls & Jordi McKenzie, 2020. "Black swan models for the entertainment industry with an application to the movie business," Empirical Economics, Springer, vol. 59(6), pages 3019-3032, December.
    18. Alexander Eastman & Brian Lucey, 2008. "Skewness and asymmetry in futures returns and volumes," Applied Financial Economics, Taylor & Francis Journals, vol. 18(10), pages 777-800.
    19. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
    20. Ortobelli, Sergio & Rachev, Svetlozar & Schwartz, Eduardo, 2000. "The Problem of Optimal Asset Allocation with Stable Distributed Returns," University of California at Los Angeles, Anderson Graduate School of Management qt3zd6q86c, Anderson Graduate School of Management, UCLA.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1706.09756. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.