IDEAS home Printed from https://ideas.repec.org/p/hhs/hastef/0345.html
   My bibliography  Save this paper

Fourth Moment Structure of a Family of First-Order Exponential GARCH Models

Author

Listed:
  • He, Changli

    () (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    () (Dept. of Economic Statistics, Stockholm School of Economics)

  • Malmsten, Hans

    () (Dept. of Economic Statistics, Stockholm School of Economics)

Abstract

In this paper we consider the fourth moment structure of a class of first-order Exponential GARCH models. This class contains as special cases both the standard Exponential GARCH model and the symmetric and asymmetric Logarithmic GARCH one. Conditions for the existence of any arbitrary moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of squared observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard first-order GARCH process. In particular, it is seen that, contrary to the standard GARCH case, the decay rate of the autocorrelations is not constant and that the rate can be quite rapid in the beginning, depending on the parameters of the model.

Suggested Citation

  • He, Changli & Teräsvirta, Timo & Malmsten, Hans, 1999. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models," SSE/EFI Working Paper Series in Economics and Finance 345, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0345
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    3. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, pages 1-26.
    4. Ram Bhar & Carl Chiarella, 1995. "Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    5. Björk, Tomas & Gombani, Andrea, 1997. "Minimal Realizations of Forward Rates," SSE/EFI Working Paper Series in Economics and Finance 182, Stockholm School of Economics.
    6. Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257.
    7. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, pages 573-592.
    8. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 423-440, September.
    9. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    10. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    11. Björk, Tomas & Landen, Camilla, 2000. "On the construction of finite dimensional realizations for nonlinear forward rate models," SSE/EFI Working Paper Series in Economics and Finance 420, Stockholm School of Economics.
    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. Paolo Girardello & Orietta Nicolis & Giovanni Tondini, 2003. "Comparing Conditional Variance Models: Theory and Empirical Evidence," Multinational Finance Journal, Multinational Finance Journal, vol. 7(3-4), pages 177-206, September.
    2. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, pages 1-23.
    3. Menelaos Karanasos, "undated". "The Covariance Structure of Mixed ARMA Models," Discussion Papers 00/10, Department of Economics, University of York.
    4. P. Girardello & Orietta Nicolis & Giovanni Tondini, 2002. "Comparing conditional variance models: Theory and empirical evidence," Departmental Working Papers 2002-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    5. Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, June.
    6. Pasquale Tridico & Riccardo Pariboni, 2017. "Structural Change, Aggregate Demand And The Decline Of Labour Productivity: A Comparative Perspective," Departmental Working Papers of Economics - University 'Roma Tre' 0221, Department of Economics - University Roma Tre.
    7. BAUWENS, Luc & GALLI, Fausto & GIOT, Pierre, 2003. "The moments of Log-ACD models," CORE Discussion Papers 2003011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Carnero, María Ángeles & Peña, Daniel & Ruiz, Esther, 2001. "Outliers and conditional autoregressive heteroscedasticity in time series," DES - Working Papers. Statistics and Econometrics. WS ws010704, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Davide De Gaetano, 2017. "A Bootstrap Bias Correction Of Long Run Fourth Order Moment Estimation In The Cusum Of Squares Test," Departmental Working Papers of Economics - University 'Roma Tre' 0220, Department of Economics - University Roma Tre.

    More about this item

    Keywords

    autocorrelation function of squared observations; conditional variance model; heavy tails; exponential GARCH; logarithmic GARCH;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:hhs:hastef:0345. 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: (Helena Lundin). General contact details of provider: http://edirc.repec.org/data/erhhsse.html .

    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 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 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.