Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias

53 Pages Posted: 16 Mar 2008

See all articles by Eric Jondeau

Eric Jondeau

University of Lausanne - Faculty of Business and Economics (HEC Lausanne); Swiss Finance Institute; Swiss Finance Institute

Multiple version iconThere are 2 versions of this paper

Date Written: February 2008

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

JEL Classification: C13, C21, G11

Suggested Citation

Jondeau, Eric, Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias (February 2008). Swiss Finance Institute Research Paper No. 08-06, Available at SSRN: https://ssrn.com/abstract=1105784 or http://dx.doi.org/10.2139/ssrn.1105784

Eric Jondeau (Contact Author)

University of Lausanne - Faculty of Business and Economics (HEC Lausanne) ( email )

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HOME PAGE: http://people.unil.ch/ericjondeau/

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Swiss Finance Institute

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