IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2004cf292.html
   My bibliography  Save this paper

Some Improvements in Numerical Evaluation of Symmetric Stable Density and its Derivatives

Author

Listed:
  • Muneya Matsui

    (Graduate School of Economics, University of Tokyo)

  • Akimichi Takemura

    (Graduate School of Information Science and Technology, University of Tokyo)

Abstract

We propose improvements in numerical evaluation of symmetric stable density and its partial derivatives with respect to the parameters. They are useful for more reliable evaluation of maximum likelihood estimator and its standard error. Numerical values of the Fisher information matrix of symmetric stable distributions are also given. Our improvements consist of modification of the method of Nolan (1997) for the boundary cases, i.e., in the tail and mode of the densities and in the neighborhood of the Cauchy and the normal distributions.

Suggested Citation

  • Muneya Matsui & Akimichi Takemura, 2004. "Some Improvements in Numerical Evaluation of Symmetric Stable Density and its Derivatives," CIRJE F-Series CIRJE-F-292, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2004cf292
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2004/2004cf292.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-285, July-Sept.
    2. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
    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. Davood Farbod & Karen V. Gasparian, 2012. "On the confidence intervals of parametric functions for Distributions Generated by Symmetric Stable Laws," Statistica, Department of Statistics, University of Bologna, vol. 72(4), pages 405-413.
    2. Tibor K. Pogány & Saralees Nadarajah, 2015. "Remarks on the Stable S α (β,γ,μ) Distribution," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 515-524, June.

    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. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    2. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2020. "Growth, development, and structural change at the firm-level: The example of the PR China," Papers 2012.14503, arXiv.org.
    3. Runde, Ralf & Scheffner, Axel, 1998. "On the existence of moments: With an application to German stock returns," Technical Reports 1998,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Graves, Timothy & Franzke, Christian L.E. & Watkins, Nicholas W. & Gramacy, Robert B. & Tindale, Elizabeth, 2017. "Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 60-71.
    5. Menn, Christian & Rachev, Svetlozar T., 2006. "Calibrated FFT-based density approximations for [alpha]-stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1891-1904, April.
    6. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    7. Stavros Degiannakis & Alexandra Livada & Epaminondas Panas, 2008. "Rolling-sampled parameters of ARCH and Levy-stable models," Applied Economics, Taylor & Francis Journals, vol. 40(23), pages 3051-3067.
    8. Diongue, Abdou Kâ & Guégan, Dominique, 2007. "The stationary seasonal hyperbolic asymmetric power ARCH model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1158-1164, June.
    9. Koenker, Roger & Portnoy, Stephen, 2000. "Some pathological regression asymptotics under stable conditions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 219-228, November.
    10. Mittnik, Stefan & Paolella, Marc S., 2003. "Prediction of Financial Downside-Risk with Heavy-Tailed Conditional Distributions," CFS Working Paper Series 2003/04, Center for Financial Studies (CFS).
    11. 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.
    12. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    13. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    14. José Dias Curto & João Tomaz & José Castro Pinto, 2009. "A new approach to bad news effects on volatility: the multiple-sign-volume sensitive regime EGARCH model (MSV-EGARCH)," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 8(1), pages 23-36, April.
    15. Pewsey, Arthur, 2008. "The wrapped stable family of distributions as a flexible model for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1516-1523, January.
    16. Andrea Fontanari & Nassim Nicholas Taleb & Pasquale Cirillo, 2017. "Gini estimation under infinite variance," Papers 1707.01370, arXiv.org, revised Dec 2017.
    17. Giulio Bottazzi & Angelo Secchi, 2011. "A new class of asymmetric exponential power densities with applications to economics and finance," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 20(4), pages 991-1030, August.
    18. Mahdi Teimouri & Saralees Nadarajah, 2022. "Maximum Likelihood Estimation for the Asymmetric Exponential Power Distribution," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 665-692, August.
    19. Prasad Bidarkota & J Huston Mcculloch, 2004. "Testing for persistence in stock returns with GARCH-stable shocks," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 256-265.
    20. Djahoué Mangblé Gérald, 2018. "Estimating and Forecasting West Africa Stock Market Volatility Using Asymmetric GARCH Models," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 8(6), pages 1-4.

    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:tky:fseres:2004cf292. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    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.