Contemporaneous aggregation of GARCH processes

Paolo Zaffaroni

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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.

Keywords: Contemporaneous aggregation; GARCH; conditionally heteroskedastic factor models; common and idiosyncratic risk; nonlinearity; memory (search for similar items in EconPapers)
JEL-codes: C32 C43 (search for similar items in EconPapers)
Pages: 46 pages
Date: 2000-01
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Citations: View citations in EconPapers (5)

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http://eprints.lse.ac.uk/6869/ Open access version. (application/pdf)

Related works:
Journal Article: Contemporaneous aggregation of GARCH processes (2007)
Working Paper: Contemporaneous aggregation of GARCH processes (2002)
Working Paper: Contemporaneous Aggregation of GARCH Processes (2000)
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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:6869

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