Properties of moments of a family of GARCH processes
AbstractThis paper considers the moments of a family of first-order GARCH processes. First, a general condition of the existence of any integer moment of the absolute values of the observations is given. Second, a general expression for this moment as a function of lower-order moments is derived. Third, the kurtosis and the autocorrelation function of the squared and absolute-valued observations are derived. The results apply to a host of different GARCH parameterizations. Finally, the existence, or the lack thereof, of a theoretical counterpart to the so-called Taylor effect for some members of this GARCH family is discussed. Possibilities of extending some of the results to higher-order GARCH processes are indicated and potential applications of the statistical theory proposed.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 92 (1999)
Issue (Month): 1 (September)
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Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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.:
- 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.
- Fornari, Fabio & Mele, Antonio, 1996. "Modeling the changing asymmetry of conditional variances," Economics Letters, Elsevier, vol. 50(2), pages 197-203, February.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- He, Changli & Teräsvirta, Timo, 1997. "Statistical Properties of the Asymmetric Power ARCH Process," Working Paper Series in Economics and Finance 199, Stockholm School of Economics, revised 30 Sep 1997.
- Sentana, Enrique, 1995.
"Quadratic ARCH Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 62(4), pages 639-61, October.
- Yang, Minxian & Bewley, Ronald, 1995.
"Moving average conditional heteroskedastic processes,"
Elsevier, vol. 49(4), pages 367-372, October.
- Yang, M. & Bewley, R., 1992. "Moving Average Conditional Heterscedastic Processes," Papers 92-23, New South Wales - School of Economics.
- Francis X. Diebold & Jose A. Lopez, 1995.
"Modeling volatility dynamics,"
9522, Federal Reserve Bank of New York.
- Fornari, F. & Mele, A., 1995.
"Sign- and Volatility -Switching ARCH Models: Theory and Applications to International Stock Markets,"
251, Banca Italia - Servizio di Studi.
- Fornari, Fabio & Mele, Antonio, 1997. "Sign- and Volatility-Switching ARCH Models: Theory and Applications to International Stock Markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(1), pages 49-65, Jan.-Feb..
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993.
" On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1779-1801, December.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
- G. William Schwert, 1990.
"Why Does Stock Market Volatility Change Over Time?,"
NBER Working Papers
2798, National Bureau of Economic Research, Inc.
- Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-53, December.
- 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.
- C. W. J. GRANGER & Zhuanxin DING, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annales d'Economie et de Statistique, ENSAE, issue 40, pages 67-91.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Neil Shephard, 2005.
2005-W17, Economics Group, Nuffield College, University of Oxford.
- Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
- Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
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