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NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS

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Author Info
Ling, Shiqing
McAleer, Michael

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Abstract

Although econometricians have been using Bollerslev s (1986, Journal of Econometrics 31, 307 327) GARCH(r, s) model for over a decade, the higher order moment structure of the model remains unresolved. The sufficient condition for the existence of the higher order moments of the GARCH(r, s) model was given by Ling (1999a, Journal of Applied Probability 36, 688 705). This paper shows that Ling s condition is also necessary. As an extension, the necessary and sufficient moment conditions are established for Ding, Granger, and Engle s (1993, Journal of Empirical Finance, 1, 83 106) asymmetric power GARCH(r, s) model.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 18 (2002)
Issue (Month): 03 (June)
Pages: 722-729
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Handle: RePEc:cup:etheor:v:18:y:2002:i:03:p:722-729_18

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127. [Downloadable!] (restricted)
  2. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  3. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-58, February. [Downloadable!] (restricted)
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  4. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December. [Downloadable!]
  5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  6. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May. [Downloadable!] (restricted)
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