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Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias

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  • Eric Jondeau

    (University of Lausanne and Swiss Finance Institute)

Abstract

It is well known that the class of strong (Generalized) AutoRegressive Conditional Heteroskedasticity (or GARCH) processes is not closed under contemporaneous aggregation. This paper provides the dynamics followed by the aggregate process when the individual persistence parameters are drawn from the same (unknown) distribution. Assuming heterogeneity across individual parameters, the dynamics of the aggregate volatility involves additional lags that reflect the moments of the distribution of the individual persistence parameters. Then the paper describes a consistent estimator of the aggregate process, based on nonlinear least squares. A simulation study reveals that this aggregation-corrected estimator performs very well under realistic sets of parameters. Last, this approach is extended to a multi-sector context. This extension is used to evaluate the importance of the aggregation bias. Using size and book-to-market portfolios, I show that the investor is willing to pay one fifth of her expected return to switch from the standard GARCH (1,1) estimator to the aggregation-corrected estimator.

Suggested Citation

  • Eric Jondeau, 2008. "Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias," Swiss Finance Institute Research Paper Series 08-06, Swiss Finance Institute.
  • Handle: RePEc:chf:rpseri:rp0806
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    File URL: http://ssrn.com/abstract=1105784
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    References listed on IDEAS

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    More about this item

    Keywords

    Contemporaneous aggregation; Heterogeneity; Volatility; GARCH model.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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