IDEAS home Printed from https://ideas.repec.org/a/oup/jfinec/v23y2025i2p1194-1209..html
   My bibliography  Save this article

Analytic Moments of TGARCH(1,1) Models with Polynomially Adjusted Densities

Author

Listed:
  • M Angeles Carnero
  • Angel León
  • Trino-Manuel Ñíguez

Abstract

This article extends He, Silvennoinen, and Teräsvirta (2008, J Finan Econ, 6, 208–230) and Francq and Zakoïan (2010, GARCH Models) by providing analytical expressions for the moments of the unconditional distribution of the TGARCH(1,1) under alternative specifications for the conditional mean and different skewed distributions for the innovations. We consider polynomially adjusted (PA) densities, such as the PA Logistic, PA hyperbolic secant, and the PA Gaussian, along with the skewed Student-t. Our results show that (i) the main driver of the skewness of the TGARCH(1,1) is the skewness of the innovations, while the excess kurtosis has a comparatively lesser impact. However, both skewness and kurtosis of the innovations significantly affect the TGARCH(1,1) kurtosis; (ii) if the conditional mean is not constant, returns can be asymmetric even if innovations are symmetric; (iii) skewed innovations can generate cross-correlations different from zero, indicating leverage effect, even when the volatility model is symmetric. Finally, we illustrate our theoretical results with an empirical application to stock indices.

Suggested Citation

  • M Angeles Carnero & Angel León & Trino-Manuel Ñíguez, 2025. "Analytic Moments of TGARCH(1,1) Models with Polynomially Adjusted Densities," Journal of Financial Econometrics, Oxford University Press, vol. 23(2), pages 1194-1209.
  • Handle: RePEc:oup:jfinec:v:23:y:2025:i:2:p:1194-1209.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/jjfinec/nbae019
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    asymmetry; cross-correlation; equity screening; leverage effect; unconditional skewness; unconditional kurtosis;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    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:oup:jfinec:v:23:y:2025:i:2:p:1194-1209.. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Oxford University Press (email available below). General contact details of provider: https://edirc.repec.org/data/sofieea.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.