Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias

Eric Jondeau

No 08-06, Swiss Finance Institute Research Paper Series from 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.

Keywords: Contemporaneous aggregation; Heterogeneity; Volatility; GARCH model. (search for similar items in EconPapers)
JEL-codes: C13 C21 G11 (search for similar items in EconPapers)
Pages: 53 pages
Date: 2008-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp0806

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