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Contemporaneous aggregation of GARCH processes

Zaffaroni, Paolo (2000) Contemporaneous aggregation of GARCH processes. EM, 378. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.

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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.

Item Type: Monograph (Discussion Paper)
Official URL: http://sticerd.lse.ac.uk
Additional Information: © 2000 Paolo Zaffaroni
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Journal of Economic Literature Classification System: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation
C - Mathematical and Quantitative Methods > C3 - Econometric Methods: Multiple; Simultaneous Equation Models; Multiple Variables; Endogenous Regressors > C32 - Time-Series Models
Sets: Collections > Economists Online
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: 378
Date Deposited: 09 Jul 2008 16:49
URL: http://eprints.lse.ac.uk/6869/

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