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Higher-order dependence in the general Power ARCH process and a special case

  • He, Changli

    ()

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

  • Teräsvirta, Timo

    ()

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

In this paper we consider a general first-order power ARCH process and, in particular, a special case in which the power parameter approaches zero. These considerations give us the autocorrelation function of the logarithms of the squared observations for first-order exponential and logarithmic GARCH processes. These autocorrelations decay exponentially with the lag and may be used for checking how well an estimated exponential or logarithmic GARCH model characterizes the corresponding autocorrelation structure of the observations. The results of the paper are also useful in illustrating differences in the autocorrelation structures of the classical first-order GARCH and the exponential or logarithmic GARCH models.

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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 315.

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Length: 16 pages
Date of creation: 21 Apr 1999
Date of revision:
Publication status: Published in Recent advances in linear models and related areas, Shalabh, X, Heumann, C. (eds.), 2008, pages 231-251, Springer.
Handle: RePEc:hhs:hastef:0315
Note: The forthcoming version of the paper is C. He, H. Malmsten and T. Teräsvirta: Higher-order dependence in the general Power ARCH process and the role of the power parameter
Contact details of provider: Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
Phone: +46-(0)8-736 90 00
Fax: +46-(0)8-31 01 57
Web page: http://www.hhs.se/
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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. 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.
  3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  4. 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.
  5. He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," SSE/EFI Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
  6. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
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