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Aggregation and marginalization of GARCH processes: some further results

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  • Giacomo Sbrana

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Abstract

This paper focuses on the contemporaneous aggregation of GARCH processes. It reconsiders and extends the results achieved by Nijman and Sentana (1996) by showing that the parameters of the weak aggregate GARCH process are exact functions of the underlying processes. More specifically, an algebraic solution is provided in order to derive the implied parameters of the aggregated and marginal processes. Analytical results are given for the sum of two independent GARCH and in the context of a bivariate constant conditional correlation GARCH. Copyright Sapienza Università di Roma 2012

Suggested Citation

  • Giacomo Sbrana, 2012. "Aggregation and marginalization of GARCH processes: some further results," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 165-172, August.
  • Handle: RePEc:spr:metron:v:70:y:2012:i:2:p:165-172
    DOI: 10.1007/BF03321973
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    References listed on IDEAS

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    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    2. Nijman, Theo & Sentana, Enrique, 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 71-87.
    3. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
    4. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    5. SILVESTRINI, Andrea & VEREDAS, David, 2005. "Temporal aggregation of univariate linear time series models," CORE Discussion Papers 2005059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Paolo Zaffaroni, 2007. "Contemporaneous aggregation of GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 521-544, July.
    7. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
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    Keywords

    Aggregation; GARCH;

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