IDEAS home Printed from https://ideas.repec.org/p/cam/camdae/1517.html
   My bibliography  Save this paper

Volatility Modeling with a Generalized t-distribution

Author

Listed:
  • Andrew Harvey
  • Rutger-Jan Lange

Abstract

Beta-t-EGARCH models in which the dynamics of the logarithm of scale are driven by the conditional score are known to exhibit attractive theoretical properties for the t-distribution and general error distribution (GED). The generalized-t includes both as special cases. We derive the information matrix for the generalized-t and show that, when parameterized with the inverse of the tail index, it remains positive definite as the tail index goes to infinity and the distribution becomes a GED. Hence it is possible to construct Lagrange multiplier tests of the null hypothesis of light tails against the alternative of fat tails. Analytic expressions may be obtained for the unconditional moments in the EGARCH model and the information matrix for the dynamic parameters obtained. The distribution may be extended by allowing for skewness and asymmetry in the shape parameters and the asymptotic theory for the associated EGARCH models may be correspondingly extended. For positive variables, the GB2 distribution may be parameterized so that it goes to the generalised gamma in the limit as the tail index goes to infinity. Again dynamic volatility may be introduced and properties of the model obtained. Overall the approach offers a unified, flexible, robust and practical treatment of dynamic scale.

Suggested Citation

  • Andrew Harvey & Rutger-Jan Lange, 2015. "Volatility Modeling with a Generalized t-distribution," Cambridge Working Papers in Economics 1517, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1517
    Note: ach34
    as

    Download full text from publisher

    File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1517.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Arslan, Olcay, 2004. "Family of multivariate generalized t distributions," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 329-337, May.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    4. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    5. Kai-Li Wang & Christopher Fawson & Christopher B. Barrett & James B. McDonald, 2001. "A flexible parametric GARCH model with an application to exchange rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 521-536.
    6. Sean Holly & Ivan Petrella & Emiliano Santoro, 2013. "Aggregate fluctuations and the cross-sectional dynamics of firm growth," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(2), pages 459-479, February.
    7. Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
    8. Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2014. "Maximum Likelihood Estimation for Score-Driven Models," Tinbergen Institute Discussion Papers 14-029/III, Tinbergen Institute, revised 23 Oct 2017.
    9. Zhu, Dongming & Zinde-Walsh, Victoria, 2009. "Properties and estimation of asymmetric exponential power distribution," Journal of Econometrics, Elsevier, vol. 148(1), pages 86-99, January.
    10. 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, vol. 20(4), pages 991-1030, August.
    11. Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.
    12. Bickel, David R., 2002. "Robust estimators of the mode and skewness of continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 153-163, April.
    13. Zhu, Dongming & Galbraith, John W., 2011. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 765-778, September.
    14. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    15. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(03), pages 428-457, December.
    16. Brazauskas, Vytaras, 2002. "Fisher information matrix for the Feller-Pareto distribution," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 159-167, September.
    17. Andrew Harvey & Rutger-Jan Lange, 2015. "Modeling the Interactions between Volatility and Returns," Cambridge Working Papers in Economics 1518, Faculty of Economics, University of Cambridge.
    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. Andrew Harvey & Ryoko Ito, 2017. "Modeling time series with zero observations," Economics Papers 2017-W01, Economics Group, Nuffield College, University of Oxford.
    2. Ryoko Ito, 2016. "Asymptotic Theory for Beta-t-GARCH," Cambridge Working Papers in Economics 1607, Faculty of Economics, University of Cambridge.
    3. Ayala, Astrid & Blazsek, Szabolcs Istvan & Escribano Sáez, Álvaro, 2019. "Score-driven time series models with dynamic shape : an application to the Standard & Poor's 500 index," UC3M Working papers. Economics 28133, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Blazsek, Szabolcs Istvan & Ayala, Astrid & Escribano Sáez, Álvaro, 2017. "Dynamic conditional score models with time-varying location, scale and shape parameters," UC3M Working papers. Economics 25043, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Ito, R., 2016. "Spline-DCS for Forecasting Trade Volume in High-Frequency Finance," Cambridge Working Papers in Economics 1606, Faculty of Economics, University of Cambridge.
    6. Harvey, A. & Liao, Y., 2019. "Dynamic Tobit models," Cambridge Working Papers in Economics 1913, Faculty of Economics, University of Cambridge.

    More about this item

    Keywords

    Asymmetric price transmission; cost pass-through; electricity markets; price theory; rockets and feathers;

    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:cam:camdae:1517. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jake Dyer) The email address of this maintainer does not seem to be valid anymore. Please ask Jake Dyer to update the entry or send us the correct email address. General contact details of provider: http://www.econ.cam.ac.uk/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.