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Dependence structure of stable R-GARCH processes


  • Joanna Nowicka-Zagrajek
  • Aleksander Weron


In this paper we investigate properties of R-GARCH processes with positive strictly stable innovations. We derive the unconditional distributions and analyze the dependence structure. This analysis is carried out by means of the measure of dependence - the codifference - which extends the behavior of the covariance function to situations where the covariance function is no longer defined. In the case of R-GARCH(1,1,0) process we determine the exact asymptotic behavior.

Suggested Citation

  • Joanna Nowicka-Zagrajek & Aleksander Weron, 2001. "Dependence structure of stable R-GARCH processes," HSC Research Reports HSC/01/02, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc0102

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    File Function: Final draft, 2001
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    References listed on IDEAS

    1. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    2. de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 313-324, June.
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    More about this item


    Stable distribution; R-GARCH process; dependence; codifference;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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