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Contemporaneous Aggregation of GARCH Processes

  • Paolo Zaffaroni
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    We study the impact of large cross-sections of contemporaneous aggregation of GARCH processes and of dynamic GARCH factor models. The results crucially depend on the shape of the cross-sectional distribution of the GARCH coefficients and on the cross-sectional dependence properties of the rescaled innovation. The aggregate maintains the core nonlinearity of a volatility model, uncorrelation in the levels but autocorrelation in the squares, when the rescaled innovation is common across units. The nonlinearity is, however, lost at the aggregate level, when the rescaled innovation is orthogonal across units. This is not a consequence of the usual result of a vanishing importance of purely idiosyncratic risk as, under appropriate conditions, this is simply not fully diversifiable in arbitrary large portfolios. Non-GARCH memory properties arise at the aggregate level. Strict stationarity, ergodicity and finite kurtosis might fail for the aggregate despite the micro GARCH do satisfy these properties. Under no conditions aggregation of GARCH induces long memory conditional heteroskedasticity.

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    Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2000/378.

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    Date of creation: Jan 2000
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    Handle: RePEc:cep:stiecm:/2000/378
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    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
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    4. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    5. Nijman, T.E. & Sentana, E., 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Other publications TiSEM 1faf40e0-ce91-45fd-a98d-4, Tilburg University, School of Economics and Management.
    6. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    7. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    8. Francis X. Diebold & Marc Nerlove, 1986. "The dynamics of exchange rate volatility: a multivariate latent factor ARCH model," Special Studies Papers 205, Board of Governors of the Federal Reserve System (U.S.).
    9. Enrique Sentana, 1998. "The relation between conditionally heteroskedastic factor models and factor GARCH models," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 1-9.
    10. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
    11. Andersen, Torben G & Bollerslev, Tim, 1997. " Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    12. MEDDAHI, Nour & RENAULT, Éric, 1998. "Aggregations and Marginalization of GARCH and Stochastic Volatility Models," Cahiers de recherche 9818, Universite de Montreal, Departement de sciences economiques.
    13. Peter M Robinson & Paolo Zaffaroni, 1997. "Modelling Nonlinearity and Long Memory in Time Series - (Now published in 'Nonlinear Dynamics and Time Series', C D Cutler and D T Kaplan (eds), Fields Institute Communications, 11 (1997), pp.61-170.)," STICERD - Econometrics Paper Series /1997/319, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    15. Werker, B.J.M. & Drost, F.C., 1996. "Closing the GARCH gap : Continuous time GARCH modeling," Other publications TiSEM c3d29817-403a-4ad1-9295-8, Tilburg University, School of Economics and Management.
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    17. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
    18. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
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